niapy.algorithms

Module with implementations of basic and hybrid algorithms.

class niapy.algorithms.Algorithm(population_size=50, initialization_function=<function default_numpy_init>, individual_type=None, seed=None, *args, **kwargs)

Bases: object

Class for implementing algorithms.

Date:

2018

Author

Klemen Berkovič

License:

MIT

Variables

• Name (List[str]) – List of names for algorithm.

• rng (numpy.random.Generator) – Random generator.

• population_size (int) – Population size.

• initialization_function (Callable[[int, Task, numpy.random.Generator, Dict[str, Any]], Tuple[numpy.ndarray, numpy.ndarray[float]]]) – Population initialization function.

• individual_type (Optional[Type[Individual]]) – Type of individuals used in population, default value is None for Numpy arrays.

Initialize algorithm and create name for an algorithm.

Parameters

• population_size (Optional[int]) – Population size.

• initialization_function (Optional[Callable[[int, Task, numpy.random.Generator, Dict[str, Any]], Tuple[numpy.ndarray, numpy.ndarray[float]]]]) – Population initialization function.

• individual_type (Optional[Type[Individual]]) – Individual type used in population, default is Numpy array.

• seed (Optional[int]) – Starting seed for random generator.

See also

• niapy.algorithms.Algorithm.set_parameters()

Name = ['Algorithm', 'AAA']

__init__(population_size=50, initialization_function=<function default_numpy_init>, individual_type=None, seed=None, *args, **kwargs)

Initialize algorithm and create name for an algorithm.

Parameters

• population_size (Optional[int]) – Population size.

• initialization_function (Optional[Callable[[int, Task, numpy.random.Generator, Dict[str, Any]], Tuple[numpy.ndarray, numpy.ndarray[float]]]]) – Population initialization function.

• individual_type (Optional[Type[Individual]]) – Individual type used in population, default is Numpy array.

• seed (Optional[int]) – Starting seed for random generator.

See also

• niapy.algorithms.Algorithm.set_parameters()

bad_run()

Check if some exceptions where thrown when the algorithm was running.

Returns

True if some error where detected at runtime of the algorithm, otherwise False

Return type

bool

static get_best(population, population_fitness, best_x=None, best_fitness=inf)

Get the best individual for population.

Parameters

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current populations fitness/function values of aligned individuals.

• best_x (Optional[numpy.ndarray]) – Best individual.

• best_fitness (float) – Fitness value of best individual.

Returns

1. Coordinates of best solution.

2. beset fitness/function value.

Return type

Tuple[numpy.ndarray, float]

get_parameters()

Get parameters of the algorithm.

Returns

• Parameter name (str): Represents a parameter name

• Value of parameter (Any): Represents the value of the parameter

Return type

Dict[str, Any]

static info()

Get algorithm information.

Returns

Bit item.

Return type

str

init_population(task)

Initialize starting population of optimization algorithm.

Parameters

task (Task) – Optimization task.

Returns

1. New population.

2. New population fitness values.

3. Additional arguments.

Return type

Tuple[numpy.ndarray, numpy.ndarray, Dict[str, Any]]

See also

• niapy.algorithms.Algorithm.set_parameters()

integers(low, high=None, size=None, skip=None)

Get discrete uniform (integer) random distribution of D shape in range from “low” to “high”.

Parameters

• low (Union[int, Iterable[int]]) – Lower integer bound. If high = None low is 0 and this value is used as high

• high (Union[int, Iterable[int]]) – One above upper integer bound.

• size (Union[None, int, Iterable[int]]) – shape of returned discrete uniform random distribution.

• skip (Union[None, int, Iterable[int], numpy.ndarray[int]]) – numbers to skip.

Returns

Random generated integer number.

Return type

Union[int, numpy.ndarray[int]]

iteration_generator(task)

Run the algorithm for a single iteration and return the best solution.

Parameters

task (Task) – Task with bounds and objective function for optimization.

Returns

Generator getting new/old optimal global values.

Return type

Generator[Tuple[numpy.ndarray, float], None, None]

Yields

Tuple[numpy.ndarray, float] – 1. New population best individuals coordinates. 2. Fitness value of the best solution.

See also

• niapy.algorithms.Algorithm.init_population()

• niapy.algorithms.Algorithm.run_iteration()

normal(loc, scale, size=None)

Get normal random distribution of shape size with mean “loc” and standard deviation “scale”.

Parameters

• loc (float) – Mean of the normal random distribution.

• scale (float) – Standard deviation of the normal random distribution.

• size (Union[int, Iterable[int]]) – Shape of returned normal random distribution.

Returns

Array of numbers.

Return type

Union[numpy.ndarray[float], float]

random(size=None)

Get random distribution of shape size in range from 0 to 1.

Parameters

size (Union[None, int, Iterable[int]]) – Shape of returned random distribution.

Returns

Random number or numbers \(\in [0, 1]\).

Return type

Union[numpy.ndarray[float], float]

run(task)

Start the optimization.

Parameters

task (Task) – Optimization task.

Returns

1. Best individuals components found in optimization process.

2. Best fitness value found in optimization process.

Return type

Tuple[numpy.ndarray, float]

See also

• niapy.algorithms.Algorithm.run_task()

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core functionality of algorithm.

This function is called on every algorithm iteration.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population coordinates.

• population_fitness (numpy.ndarray) – Current population fitness value.

• best_x (numpy.ndarray) – Current generation best individuals coordinates.

• best_fitness (float) – current generation best individuals fitness value.

• **params (Dict[str, Any]) – Additional arguments for algorithms.

Returns

1. New populations coordinates.

2. New populations fitness values.

3. New global best position/solution

4. New global best fitness/objective value

5. Additional arguments of the algorithm.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

See also

• niapy.algorithms.Algorithm.iteration_generator()

run_task(task)

Start the optimization.

Parameters

task (Task) – Task with bounds and objective function for optimization.

Returns

1. Best individuals components found in optimization process.

2. Best fitness value found in optimization process.

Return type

Tuple[numpy.ndarray, float]

See also

• niapy.algorithms.Algorithm.iteration_generator()

set_parameters(population_size=50, initialization_function=<function default_numpy_init>, individual_type=None, *args, **kwargs)

Set the parameters/arguments of the algorithm.

Parameters

• population_size (Optional[int]) – Population size.

• initialization_function (Optional[Callable[[int, Task, numpy.random.Generator, Dict[str, Any]], Tuple[numpy.ndarray, numpy.ndarray[float]]]]) – Population initialization function.

• individual_type (Optional[Type[Individual]]) – Individual type used in population, default is Numpy array.

See also

• niapy.algorithms.default_numpy_init()

• niapy.algorithms.default_individual_init()

standard_normal(size=None)

Get standard normal distribution of shape size.

Parameters

size (Union[int, Iterable[int]]) – Shape of returned standard normal distribution.

Returns

Random generated numbers or one random generated number \(\in [0, 1]\).

Return type

Union[numpy.ndarray[float], float]

uniform(low, high, size=None)

Get uniform random distribution of shape size in range from “low” to “high”.

Parameters

• low (Union[float, Iterable[float]]) – Lower bound.

• high (Union[float, Iterable[float]]) – Upper bound.

• size (Union[None, int, Iterable[int]]) – Shape of returned uniform random distribution.

Returns

Array of numbers \(\in [\mathit{Lower}, \mathit{Upper}]\).

Return type

Union[numpy.ndarray[float], float]

class niapy.algorithms.Individual(x=None, task=None, e=True, rng=None, **kwargs)

Bases: object

Class that represents one solution in population of solutions.

Date:

2018

Author:

Klemen Berkovič

License:

MIT

Variables

• x (numpy.ndarray) – Coordinates of individual.

• f (float) – Function/fitness value of individual.

Initialize new individual.

Parameters

• task (Optional[Task]) – Optimization task.

• rand (Optional[numpy.random.Generator]) – Random generator.

• x (Optional[numpy.ndarray]) – Individuals components.

• e (Optional[bool]) – True to evaluate the individual on initialization. Default value is True.

__eq__(other)

Compare the individuals for equalities.

Parameters

other (Union[Any, numpy.ndarray]) – Object that we want to compare this object to.

Returns

True if equal or False if no equal.

Return type

bool

__getitem__(i)

Get the value of i-th component of the solution.

Parameters

i (int) – Position of the solution component.

Returns

Value of ith component.

Return type

Any

__init__(x=None, task=None, e=True, rng=None, **kwargs)

Initialize new individual.

Parameters

• task (Optional[Task]) – Optimization task.

• rand (Optional[numpy.random.Generator]) – Random generator.

• x (Optional[numpy.ndarray]) – Individuals components.

• e (Optional[bool]) – True to evaluate the individual on initialization. Default value is True.

__len__()

Get the length of the solution or the number of components.

Returns

Number of components.

Return type

int

__setitem__(i, v)

Set the value of i-th component of the solution to v value.

Parameters

• i (int) – Position of the solution component.

• v (Any) – Value to set to i-th component.

__str__()

Print the individual with the solution and objective value.

Returns

String representation of self.

Return type

str

copy()

Return a copy of self.

Method returns copy of this object so it is safe for editing.

Returns

Copy of self.

Return type

Individual

evaluate(task, rng=None)

Evaluate the solution.

Evaluate solution this.x with the help of task. Task is used for repairing the solution and then evaluating it.

Parameters

• task (Task) – Objective function object.

• rng (Optional[numpy.random.Generator]) – Random generator.

See also

• niapy.task.Task.repair()

generate_solution(task, rng)

Generate new solution.

Generate new solution for this individual and set it to self.x. This method uses rng for getting random numbers. For generating random components rng and task is used.

Parameters

• task (Task) – Optimization task.

• rng (numpy.random.Generator) – Random numbers generator object.

niapy.algorithms.default_individual_init(task, population_size, rng, individual_type=None, **_kwargs)

Initialize population_size individuals of type individual_type.

Parameters

• task (Task) – Optimization task.

• population_size (int) – Number of individuals in population.

• rng (numpy.random.Generator) – Random number generator.

• individual_type (Optional[Individual]) – Class of individual in population.

Returns

1. Initialized individuals.

2. Initialized individuals function/fitness values.

Return type

Tuple[numpy.ndarray[Individual], numpy.ndarray[float]

niapy.algorithms.default_numpy_init(task, population_size, rng, **_kwargs)

Initialize starting population that is represented with numpy.ndarray with shape (population_size, task.dimension).

Parameters

• task (Task) – Optimization task.

• population_size (int) – Number of individuals in population.

• rng (numpy.random.Generator) – Random number generator.

Returns

1. New population with shape (population_size, task.D).

2. New population function/fitness values.

Return type

Tuple[numpy.ndarray, numpy.ndarray[float]]

niapy.algorithms.basic

Implementation of basic nature-inspired algorithms.

class niapy.algorithms.basic.AgingNpDifferentialEvolution(min_lifetime=0, max_lifetime=12, delta_np=0.3, omega=0.3, age=<function proportional>, *args, **kwargs)

Bases: DifferentialEvolution

Implementation of Differential evolution algorithm with aging individuals.

Algorithm:

Differential evolution algorithm with dynamic population size that is defined by the quality of population

Date:

2018

Author:

Klemen Berkovič

License:

MIT

Variables

• Name (List[str]) – list of strings representing algorithm names.

• Lt_min (int) – Minimal age of individual.

• Lt_max (int) – Maximal age of individual.

• delta_np (float) – Proportion of how many individuals shall die.

• omega (float) – Acceptance rate for individuals to die.

• mu (int) – Mean of individual max and min age.

• age (Callable[[int, int, float, float, float, float, float], int]) – Function for calculation of age for individual.

See also

• niapy.algorithms.basic.DifferentialEvolution

Initialize AgingNpDifferentialEvolution.

Parameters

• min_lifetime (Optional[int]) – Minimum life time.

• max_lifetime (Optional[int]) – Maximum life time.

• delta_np (Optional[float]) – Proportion of how many individuals shall die.

• omega (Optional[float]) – Acceptance rate for individuals to die.

• age (Optional[Callable[[int, int, float, float, float, float, float], int]]) – Function for calculation of age for individual.

See also

• niapy.algorithms.basic.DifferentialEvolution.__init__()

Name = ['AgingNpDifferentialEvolution', 'ANpDE']

__init__(min_lifetime=0, max_lifetime=12, delta_np=0.3, omega=0.3, age=<function proportional>, *args, **kwargs)

Initialize AgingNpDifferentialEvolution.

Parameters

• min_lifetime (Optional[int]) – Minimum life time.

• max_lifetime (Optional[int]) – Maximum life time.

• delta_np (Optional[float]) – Proportion of how many individuals shall die.

• omega (Optional[float]) – Acceptance rate for individuals to die.

• age (Optional[Callable[[int, int, float, float, float, float, float], int]]) – Function for calculation of age for individual.

See also

• niapy.algorithms.basic.DifferentialEvolution.__init__()

aging(task, pop)

Apply aging to individuals.

Parameters

• task (Task) – Optimization task.

• pop (numpy.ndarray[Individual]) – Current population.

Returns

New population.

Return type

numpy.ndarray[Individual]

decrement_population(pop, task)

Decrement population.

Parameters

• pop (numpy.ndarray) – Current population.

• task (Task) – Optimization task.

Returns

Decreased population.

Return type

numpy.ndarray[Individual]

delta_pop_created(t)

Calculate how many individuals are going to be created.

Parameters

t (int) – Number of generations made by the algorithm.

Returns

Number of individuals to be born.

Return type

int

delta_pop_eliminated(t)

Calculate how many individuals are going to die.

Parameters

t (int) – Number of generations made by the algorithm.

Returns

Number of individuals to dye.

Return type

int

get_parameters()

Get parameters values of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

See also

• niapy.algorithms.Algorithm.get_parameters()

increment_population(task)

Increment population.

Parameters

task (Task) – Optimization task.

Returns

Increased population.

Return type

numpy.ndarray[Individual]

static info()

Get basic information of algorithm.

Returns

Basic information of algorithm.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

post_selection(pop, task, xb, fxb, **kwargs)

Post selection operator.

Parameters

• pop (numpy.ndarray) – Current population.

• task (Task) – Optimization task.

• xb (Individual) – Global best individual.

• fxb (float) – Global best fitness.

Returns

1. New population.

2. New global best solution

3. New global best solutions fitness/objective value

Return type

Tuple[numpy.ndarray, numpy.ndarray, float]

selection(population, new_population, best_x, best_fitness, task, **kwargs)

Select operator for individuals with aging.

Parameters

• population (numpy.ndarray) – Current population.

• new_population (numpy.ndarray) – New population.

• best_x (numpy.ndarray) – Current global best solution.

• best_fitness (float) – Current global best solutions fitness/objective value.

• task (Task) – Optimization task.

Returns

1. New population of individuals.

2. New global best solution.

3. New global best solutions fitness/objective value.

Return type

Tuple[numpy.ndarray, numpy.ndarray, float]

set_parameters(min_lifetime=0, max_lifetime=12, delta_np=0.3, omega=0.3, age=<function proportional>, **kwargs)

Set the algorithm parameters.

Parameters

• min_lifetime (Optional[int]) – Minimum life time.

• max_lifetime (Optional[int]) – Maximum life time.

• delta_np (Optional[float]) – Proportion of how many individuals shall die.

• omega (Optional[float]) – Acceptance rate for individuals to die.

• age (Optional[Callable[[int, int, float, float, float, float, float], int]]) – Function for calculation of age for individual.

See also

• niapy.algorithms.basic.DifferentialEvolution.set_parameters()

class niapy.algorithms.basic.ArtificialBeeColonyAlgorithm(population_size=10, limit=100, *args, **kwargs)

Bases: Algorithm

Implementation of Artificial Bee Colony algorithm.

Algorithm:

Artificial Bee Colony algorithm

Date:

2018

Author:

Uros Mlakar and Klemen Berkovič

License:

MIT

Reference paper:

Karaboga, D., and Bahriye B. “A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm.” Journal of global optimization 39.3 (2007): 459-471.

Arguments

Name (List[str]): List containing strings that represent algorithm names limit (Union[float, numpy.ndarray[float]]): Maximum number of cycles without improvement.

See also

• niapy.algorithms.Algorithm

Initialize ArtificialBeeColonyAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• limit (Optional[int]) – Maximum number of cycles without improvement.

See also

niapy.algorithms.Algorithm.__init__()

Name = ['ArtificialBeeColonyAlgorithm', 'ABC']

__init__(population_size=10, limit=100, *args, **kwargs)

Initialize ArtificialBeeColonyAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• limit (Optional[int]) – Maximum number of cycles without improvement.

See also

niapy.algorithms.Algorithm.__init__()

calculate_probabilities(foods)

Calculate the probes.

Parameters

foods (numpy.ndarray) – Current population.

Returns

Probabilities.

Return type

numpy.ndarray

get_parameters()

Get parameters.

static info()

Get algorithms information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize the starting population.

Parameters

task (Task) – Optimization task

Returns

1. New population

2. New population fitness/function values

3. Additional arguments:

   • trials (numpy.ndarray): Number of cycles without improvement.

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], Dict[str, Any]]

See also

• niapy.algorithms.Algorithm.init_population()

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of the algorithm.

Parameters

• task (Task) – Optimization task

• population (numpy.ndarray) – Current population

• population_fitness (numpy.ndarray[float]) – Function/fitness values of current population

• best_x (numpy.ndarray) – Current best individual

• best_fitness (float) – Current best individual fitness/function value

• params (Dict[str, Any]) – Additional parameters

Returns

1. New population

2. New population fitness/function values

3. New global best solution

4. New global best fitness/objective value

5. Additional arguments:

   • trials (numpy.ndarray): Number of cycles without improvement.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(population_size=10, limit=100, **kwargs)

Set the parameters of Artificial Bee Colony Algorithm.

Parameters

• population_size (Optional[int]) – Population size.

• limit (Optional[int]) – Maximum number of cycles without improvement.

See also

• niapy.algorithms.Algorithm.set_parameters()

class niapy.algorithms.basic.BacterialForagingOptimization(population_size=50, n_chemotactic=100, n_swim=4, n_reproduction=4, n_elimination=2, prob_elimination=0.25, step_size=0.1, swarming=True, d_attract=0.1, w_attract=0.2, h_repel=0.1, w_repel=10.0, *args, **kwargs)

Bases: Algorithm

Implementation of the Bacterial foraging optimization algorithm.

Algorithm:

Bacterial Foraging Optimization

Date:

2021

Author:

Žiga Stupan

License:

MIT

Reference paper:

11. 13. Passino, “Biomimicry of bacterial foraging for distributed optimization and control,” in IEEE Control Systems Magazine, vol. 22, no. 3, pp. 52-67, June 2002, doi: 10.1109/MCS.2002.1004010.

Variables

• Name (List[str]) – list of strings representing algorithm names.

• population_size (Optional[int]) – Number of individuals in population \(\in [1, \infty]\).

• n_chemotactic (Optional[int]) – Number of chemotactic steps.

• n_swim (Optional[int]) – Number of swim steps.

• n_reproduction (Optional[int]) – Number of reproduction steps.

• n_elimination (Optional[int]) – Number of elimination and dispersal steps.

• prob_elimination (Optional[float]) – Probability of a bacterium being eliminated and a new one being created at a random location in the search space.

• step_size (Optional[float]) – Size of a chemotactic step.

• d_attract (Optional[float]) – Depth of the attractant released by the cell (a quantification of how much attractant is released).

• w_attract (Optional[float]) – Width of the attractant signal (a quantification of the diffusion rate of the chemical).

• h_repel (Optional[float]) – Height of the repellent effect (magnitude of its effect).

• w_repel (Optional[float]) – Width of the repellent.

See also

• niapy.algorithms.Algorithm

Initialize algorithm.

Parameters

• population_size (Optional[int]) – Number of individuals in population \(\in [1, \infty]\).

• n_chemotactic (Optional[int]) – Number of chemotactic steps.

• n_swim (Optional[int]) – Number of swim steps.

• n_reproduction (Optional[int]) – Number of reproduction steps.

• n_elimination (Optional[int]) – Number of elimination and dispersal steps.

• prob_elimination (Optional[float]) – Probability of a bacterium being eliminated and a new one being created at a random location in the search space.

• step_size (Optional[float]) – Size of a chemotactic step.

• swarming (Optional[bool]) – If True use swarming.

• d_attract (Optional[float]) – Depth of the attractant released by the cell (a quantification of how much attractant is released).

• w_attract (Optional[float]) – Width of the attractant signal (a quantification of the diffusion rate of the chemical).

• h_repel (Optional[float]) – Height of the repellent effect (magnitude of its effect).

• w_repel (Optional[float]) – Width of the repellent.

See also

• niapy.algorithms.Algorithm.__init__()

Name = ['BacterialForagingOptimization', 'BFO', 'BFOA']

__init__(population_size=50, n_chemotactic=100, n_swim=4, n_reproduction=4, n_elimination=2, prob_elimination=0.25, step_size=0.1, swarming=True, d_attract=0.1, w_attract=0.2, h_repel=0.1, w_repel=10.0, *args, **kwargs)

Initialize algorithm.

Parameters

• population_size (Optional[int]) – Number of individuals in population \(\in [1, \infty]\).

• n_chemotactic (Optional[int]) – Number of chemotactic steps.

• n_swim (Optional[int]) – Number of swim steps.

• n_reproduction (Optional[int]) – Number of reproduction steps.

• n_elimination (Optional[int]) – Number of elimination and dispersal steps.

• prob_elimination (Optional[float]) – Probability of a bacterium being eliminated and a new one being created at a random location in the search space.

• step_size (Optional[float]) – Size of a chemotactic step.

• swarming (Optional[bool]) – If True use swarming.

• d_attract (Optional[float]) – Depth of the attractant released by the cell (a quantification of how much attractant is released).

• w_attract (Optional[float]) – Width of the attractant signal (a quantification of the diffusion rate of the chemical).

• h_repel (Optional[float]) – Height of the repellent effect (magnitude of its effect).

• w_repel (Optional[float]) – Width of the repellent.

See also

• niapy.algorithms.Algorithm.__init__()

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get algorithm information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize the starting population.

Parameters

task (Task) – Optimization task

Returns

1. New population.

2. New population fitness/function values.

3. Additional arguments:

   • cost (numpy.ndarray): Costs of cells i.e. Fitness + cell interaction

   • health (numpy.ndarray): Cell health i.e. The accumulation of costs over all chemotactic steps.

Return type

Tuple[numpy.ndarray, numpy.ndarray, Dict[str, Any]]

See also

• niapy.algorithms.Algorithm.init_population()

interaction(cell, population)

Compute cell to cell interaction J_cc.

Parameters

• cell (numpy.ndarray) – Cell to compute interaction for.

• population (numpy.ndarray) – Population

Returns

Cell to cell interaction J_cc

Return type

float

random_direction(dimension)

Generate a random direction vector.

Parameters

dimension (int) – Problem dimension

Returns

Normalised random direction vector

Return type

numpy.ndarray

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Bacterial Foraging Optimization algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current population’s fitness/function values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best individuals function/fitness value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New population.

2. New populations function/fitness values.

3. New global best solution,

4. New global best solution’s fitness/objective value.

5. Additional arguments:

   • cost (numpy.ndarray): Costs of cells i.e. Fitness + cell interaction

   • health (numpy.ndarray): Cell health i.e. The accumulation of costs over all chemotactic steps.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(population_size=50, n_chemotactic=100, n_swim=4, n_reproduction=4, n_elimination=2, prob_elimination=0.25, step_size=0.1, swarming=True, d_attract=0.1, w_attract=0.2, h_repel=0.1, w_repel=10.0, **kwargs)

Set the parameters/arguments of the algorithm.

Parameters

• population_size (Optional[int]) – Number of individuals in population \(\in [1, \infty]\).

• n_chemotactic (Optional[int]) – Number of chemotactic steps.

• n_swim (Optional[int]) – Number of swim steps.

• n_reproduction (Optional[int]) – Number of reproduction steps.

• n_elimination (Optional[int]) – Number of elimination and dispersal steps.

• prob_elimination (Optional[float]) – Probability of a bacterium being eliminated and a new one being created at a random location in the search space.

• step_size (Optional[float]) – Size of a chemotactic step.

• swarming (Optional[bool]) – If True use swarming.

• d_attract (Optional[float]) – Depth of the attractant released by the cell (a quantification of how much attractant is released).

• w_attract (Optional[float]) – Width of the attractant signal (a quantification of the diffusion rate of the chemical).

• h_repel (Optional[float]) – Height of the repellent effect (magnitude of its effect).

• w_repel (Optional[float]) – Width of the repellent.

class niapy.algorithms.basic.BareBonesFireworksAlgorithm(num_sparks=10, amplification_coefficient=1.5, reduction_coefficient=0.5, *args, **kwargs)

Bases: Algorithm

Implementation of Bare Bones Fireworks Algorithm.

Algorithm:

Bare Bones Fireworks Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

https://www.sciencedirect.com/science/article/pii/S1568494617306609

Reference paper:

Junzhi Li, Ying Tan, The bare bones fireworks algorithm: A minimalist global optimizer, Applied Soft Computing, Volume 62, 2018, Pages 454-462, ISSN 1568-4946, https://doi.org/10.1016/j.asoc.2017.10.046.

Variables

• Name (List[str]) – List of strings representing algorithm names

• num_sparks (int) – Number of sparks

• amplification_coefficient (float) – amplification coefficient

• reduction_coefficient (float) – reduction coefficient

Initialize BareBonesFireworksAlgorithm.

Parameters

• num_sparks (int) – Number of sparks \(\in[1, \infty)\).

• amplification_coefficient (float) – Amplification coefficient \(\in [1, \infty)\).

• reduction_coefficient (float) – Reduction coefficient \(\in (0, 1)\).

Name = ['BareBonesFireworksAlgorithm', 'BBFWA']

__init__(num_sparks=10, amplification_coefficient=1.5, reduction_coefficient=0.5, *args, **kwargs)

Initialize BareBonesFireworksAlgorithm.

Parameters

• num_sparks (int) – Number of sparks \(\in[1, \infty)\).

• amplification_coefficient (float) – Amplification coefficient \(\in [1, \infty)\).

• reduction_coefficient (float) – Reduction coefficient \(\in (0, 1)\).

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get default information of algorithm.

Returns

Basic information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize starting population.

Parameters

task (Task) – Optimization task.

Returns

1. Initial solution.

2. Initial solution function/fitness value.

3. Additional arguments:

   • A (numpy.ndarray): Starting amplitude or search range.

Return type

Tuple[numpy.ndarray, float, Dict[str, Any]]

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Bare Bones Fireworks Algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current solution.

• population_fitness (float) – Current solution fitness/function value.

• best_x (numpy.ndarray) – Current best solution.

• best_fitness (float) – Current best solution fitness/function value.

• params (Dict[str, Any]) – Additional parameters.

Returns

1. New solution.

2. New solution fitness/function value.

3. New global best solution.

4. New global best solutions fitness/objective value.

5. Additional arguments:

   • amplitude (numpy.ndarray): Search range.

Return type

Tuple[numpy.ndarray, float, numpy.ndarray, float, Dict[str, Any]]

set_parameters(num_sparks=10, amplification_coefficient=1.5, reduction_coefficient=0.5, **kwargs)

Set the arguments of an algorithm.

Parameters

• num_sparks (int) – Number of sparks \(\in [1, \infty)\).

• amplification_coefficient (float) – Amplification coefficient \(\in [1, \infty)\).

• reduction_coefficient (float) – Reduction coefficient \(\in (0, 1)\).

class niapy.algorithms.basic.BatAlgorithm(population_size=40, loudness=1.0, pulse_rate=1.0, alpha=0.97, gamma=0.1, min_frequency=0.0, max_frequency=2.0, *args, **kwargs)

Bases: Algorithm

Implementation of Bat algorithm.

Algorithm:

Bat algorithm

Date:

2015

Authors:

Iztok Fister Jr., Marko Burjek and Klemen Berkovič

License:

MIT

Reference paper:

Yang, Xin-She. “A new metaheuristic bat-inspired algorithm.” Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, Heidelberg, 2010. 65-74.

Variables

• Name (List[str]) – List of strings representing algorithm name.

• loudness (float) – Initial loudness.

• pulse_rate (float) – Initial pulse rate.

• alpha (float) – Parameter for controlling loudness decrease.

• gamma (float) – Parameter for controlling pulse rate increase.

• min_frequency (float) – Minimum frequency.

• max_frequency (float) – Maximum frequency.

See also

• niapy.algorithms.Algorithm

Initialize BatAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• loudness (Optional[float]) – Initial loudness.

• pulse_rate (Optional[float]) – Initial pulse rate.

• alpha (Optional[float]) – Parameter for controlling loudness decrease.

• gamma (Optional[float]) – Parameter for controlling pulse rate increase.

• min_frequency (Optional[float]) – Minimum frequency.

• max_frequency (Optional[float]) – Maximum frequency.

See also

niapy.algorithms.Algorithm.__init__()

Name = ['BatAlgorithm', 'BA']

__init__(population_size=40, loudness=1.0, pulse_rate=1.0, alpha=0.97, gamma=0.1, min_frequency=0.0, max_frequency=2.0, *args, **kwargs)

Initialize BatAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• loudness (Optional[float]) – Initial loudness.

• pulse_rate (Optional[float]) – Initial pulse rate.

• alpha (Optional[float]) – Parameter for controlling loudness decrease.

• gamma (Optional[float]) – Parameter for controlling pulse rate increase.

• min_frequency (Optional[float]) – Minimum frequency.

• max_frequency (Optional[float]) – Maximum frequency.

See also

niapy.algorithms.Algorithm.__init__()

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get algorithms information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize the starting population.

Parameters

task (Task) – Optimization task

Returns

1. New population.

2. New population fitness/function values.

3. Additional arguments:

   • velocities (numpy.ndarray[float]): Velocities.

   • alpha (float): Previous iterations loudness.

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], Dict[str, Any]]

See also

• niapy.algorithms.Algorithm.init_population()

local_search(best, loudness, task, **kwargs)

Improve the best solution according to the Yang (2010).

Parameters

• best (numpy.ndarray) – Global best individual.

• loudness (float) – Current loudness.

• task (Task) – Optimization task.

Returns

New solution based on global best individual.

Return type

numpy.ndarray

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Bat Algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population

• population_fitness (numpy.ndarray[float]) – Current population fitness/function values

• best_x (numpy.ndarray) – Current best individual

• best_fitness (float) – Current best individual function/fitness value

• params (Dict[str, Any]) – Additional algorithm arguments

Returns

1. New population

2. New population fitness/function values

3. New global best solution

4. New global best fitness/objective value

5. Additional arguments:

   • velocities (numpy.ndarray): Velocities.

   • alpha (float): Previous iterations loudness.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(population_size=20, loudness=1.0, pulse_rate=1.0, alpha=0.97, gamma=0.1, min_frequency=0.0, max_frequency=2.0, **kwargs)

Set the parameters of the algorithm.

Parameters

• population_size (Optional[int]) – Population size.

• loudness (Optional[float]) – Initial loudness.

• pulse_rate (Optional[float]) – Initial pulse rate.

• alpha (Optional[float]) – Parameter for controlling loudness decrease.

• gamma (Optional[float]) – Parameter for controlling pulse rate increase.

• min_frequency (Optional[float]) – Minimum frequency.

• max_frequency (Optional[float]) – Maximum frequency.

See also

• niapy.algorithms.Algorithm.set_parameters()

class niapy.algorithms.basic.BeesAlgorithm(population_size=40, m=5, e=4, ngh=1, nep=4, nsp=2, *args, **kwargs)

Bases: Algorithm

Implementation of Bees algorithm.

Algorithm:

The Bees algorithm

Date:

2019

Authors:

Rok Potočnik

License:

MIT

Reference paper:

DT Pham, A Ghanbarzadeh, E Koc, S Otri, S Rahim, and M Zaidi. The bees algorithm-a novel tool for complex optimisation problems. In Proceedings of the 2nd Virtual International Conference on Intelligent Production Machines and Systems (IPROMS 2006), pages 454–459, 2006

Variables

• population_size (Optional[int]) – Number of scout bees parameter.

• m (Optional[int]) – Number of sites selected out of n visited sites parameter.

• e (Optional[int]) – Number of best sites out of m selected sites parameter.

• nep (Optional[int]) – Number of bees recruited for best e sites parameter.

• nsp (Optional[int]) – Number of bees recruited for the other selected sites parameter.

• ngh (Optional[float]) – Initial size of patches parameter.

See also

• niapy.algorithms.Algorithm.set_parameters()

Initialize BeesAlgorithm.

Parameters

• population_size (Optional[int]) – Number of scout bees parameter.

• m (Optional[int]) – Number of sites selected out of n visited sites parameter.

• e (Optional[int]) – Number of best sites out of m selected sites parameter.

• nep (Optional[int]) – Number of bees recruited for best e sites parameter.

• nsp (Optional[int]) – Number of bees recruited for the other selected sites parameter.

• ngh (Optional[float]) – Initial size of patches parameter.

See also

• niapy.algorithms.Algorithm.__init__()

Name = ['BeesAlgorithm', 'BEA']

__init__(population_size=40, m=5, e=4, ngh=1, nep=4, nsp=2, *args, **kwargs)

Initialize BeesAlgorithm.

Parameters

• population_size (Optional[int]) – Number of scout bees parameter.

• m (Optional[int]) – Number of sites selected out of n visited sites parameter.

• e (Optional[int]) – Number of best sites out of m selected sites parameter.

• nep (Optional[int]) – Number of bees recruited for best e sites parameter.

• nsp (Optional[int]) – Number of bees recruited for the other selected sites parameter.

• ngh (Optional[float]) – Initial size of patches parameter.

See also

• niapy.algorithms.Algorithm.__init__()

bee_dance(x, task, ngh)

Bees Dance. Search for new positions.

Parameters

• x (numpy.ndarray) – One individual from the population.

• task (Task) – Optimization task.

• ngh (float) – A small value for patch search.

Returns

1. New individual.

2. New individual fitness/function values.

Return type

Tuple[numpy.ndarray, float]

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm Parameters.

Return type

Dict[str, Any]

static info()

Get information about algorithm.

Returns

Algorithm information

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize the starting population.

Parameters

task (Task) – Optimization task

Returns

1. New population.

2. New population fitness/function values.

Return type

Tuple[numpy.ndarray, numpy.ndarray, Dict[str, Any]]

See also

• niapy.algorithms.Algorithm.init_population()

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Forest Optimization Algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray[float]) – Current population.

• population_fitness (numpy.ndarray[float]) – Current population function/fitness values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best individual fitness/function value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New population.

2. New population fitness/function values.

3. New global best solution.

4. New global best fitness/objective value.

5. Additional arguments:

   • ngh (float): A small value used for patches.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(population_size=40, m=5, e=4, ngh=1, nep=4, nsp=2, **kwargs)

Set the parameters of the algorithm.

Parameters

• population_size (Optional[int]) – Number of scout bees parameter.

• m (Optional[int]) – Number of sites selected out of n visited sites parameter.

• e (Optional[int]) – Number of best sites out of m selected sites parameter.

• nep (Optional[int]) – Number of bees recruited for best e sites parameter.

• nsp (Optional[int]) – Number of bees recruited for the other selected sites parameter.

• ngh (Optional[float]) – Initial size of patches parameter.

See also

• niapy.algorithms.Algorithm.set_parameters()

class niapy.algorithms.basic.CamelAlgorithm(population_size=50, burden_factor=0.25, death_rate=0.5, visibility=0.5, supply_init=10, endurance_init=10, min_temperature=-10, max_temperature=10, *args, **kwargs)

Bases: Algorithm

Implementation of Camel traveling behavior.

Algorithm:

Camel algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

https://www.iasj.net/iasj?func=fulltext&aId=118375

Reference paper:

Ali, Ramzy. (2016). Novel Optimization Algorithm Inspired by Camel Traveling Behavior. Iraq J. Electrical and Electronic Engineering. 12. 167-177.

Variables

• Name (List[str]) – List of strings representing name of the algorithm.

• population_size (Optional[int]) – Population size \(\in [1, \infty)\).

• burden_factor (Optional[float]) – Burden factor \(\in [0, 1]\).

• death_rate (Optional[float]) – Dying rate \(\in [0, 1]\).

• visibility (Optional[float]) – View range of camel.

• supply_init (Optional[float]) – Initial supply \(\in (0, \infty)\).

• endurance_init (Optional[float]) – Initial endurance \(\in (0, \infty)\).

• min_temperature (Optional[float]) – Minimum temperature, must be true \($T_{min} < T_{max}\).

• max_temperature (Optional[float]) – Maximum temperature, must be true \(T_{min} < T_{max}\).

See also

• niapy.algorithms.Algorithm

Initialize CamelAlgorithm.

Parameters

• population_size (Optional[int]) – Population size \(\in [1, \infty)\).

• burden_factor (Optional[float]) – Burden factor \(\in [0, 1]\).

• death_rate (Optional[float]) – Dying rate \(\in [0, 1]\).

• visibility (Optional[float]) – View range of camel.

• supply_init (Optional[float]) – Initial supply \(\in (0, \infty)\).

• endurance_init (Optional[float]) – Initial endurance \(\in (0, \infty)\).

• min_temperature (Optional[float]) – Minimum temperature, must be true \($T_{min} < T_{max}\).

• max_temperature (Optional[float]) – Maximum temperature, must be true \(T_{min} < T_{max}\).

See also

• niapy.algorithms.Algorithm.__init__()

Name = ['CamelAlgorithm', 'CA']

__init__(population_size=50, burden_factor=0.25, death_rate=0.5, visibility=0.5, supply_init=10, endurance_init=10, min_temperature=-10, max_temperature=10, *args, **kwargs)

Initialize CamelAlgorithm.

Parameters

• population_size (Optional[int]) – Population size \(\in [1, \infty)\).

• burden_factor (Optional[float]) – Burden factor \(\in [0, 1]\).

• death_rate (Optional[float]) – Dying rate \(\in [0, 1]\).

• visibility (Optional[float]) – View range of camel.

• supply_init (Optional[float]) – Initial supply \(\in (0, \infty)\).

• endurance_init (Optional[float]) – Initial endurance \(\in (0, \infty)\).

• min_temperature (Optional[float]) – Minimum temperature, must be true \($T_{min} < T_{max}\).

• max_temperature (Optional[float]) – Maximum temperature, must be true \(T_{min} < T_{max}\).

See also

• niapy.algorithms.Algorithm.__init__()

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm Parameters.

Return type

Dict[str, Any]

static info()

Get information about algorithm.

Returns

Algorithm information

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_pop(task, population_size, rng, individual_type, **_kwargs)

Initialize starting population.

Parameters

• task (Task) – Optimization task.

• population_size (int) – Number of camels in population.

• rng (numpy.random.Generator) – Random number generator.

• individual_type (Type[Individual]) – Individual type.

Returns

1. Initialize population of camels.

2. Initialized populations function/fitness values.

Return type

Tuple[numpy.ndarray[Camel], numpy.ndarray[float]]

life_cycle(camel, task)

Apply life cycle to Camel.

Parameters

• camel (Camel) – Camel to apply life cycle.

• task (Task) – Optimization task.

Returns

Camel with life cycle applied to it.

Return type

Camel

oasis(c)

Apply oasis function to camel.

Parameters

c (Camel) – Camel to apply oasis on.

Returns

Camel with applied oasis on.

Return type

Camel

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Camel Algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray[Camel]) – Current population of Camels.

• population_fitness (numpy.ndarray[float]) – Current population fitness/function values.

• best_x (numpy.ndarray) – Current best Camel.

• best_fitness (float) – Current best Camel fitness/function value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New population

2. New population function/fitness value

3. New global best solution

4. New global best fitness/objective value

5. Additional arguments

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, dict]

set_parameters(population_size=50, burden_factor=0.25, death_rate=0.5, visibility=0.5, supply_init=10, endurance_init=10, min_temperature=-10, max_temperature=10, **kwargs)

Set the arguments of an algorithm.

Parameters

• population_size (Optional[int]) – Population size \(\in [1, \infty)\).

• burden_factor (Optional[float]) – Burden factor \(\in [0, 1]\).

• death_rate (Optional[float]) – Dying rate \(\in [0, 1]\).

• visibility (Optional[float]) – View range of camel.

• supply_init (Optional[float]) – Initial supply \(\in (0, \infty)\).

• endurance_init (Optional[float]) – Initial endurance \(\in (0, \infty)\).

• min_temperature (Optional[float]) – Minimum temperature, must be true \($T_{min} < T_{max}\).

• max_temperature (Optional[float]) – Maximum temperature, must be true \(T_{min} < T_{max}\).

See also

• niapy.algorithms.Algorithm.set_parameters()

walk(camel, best_x, task)

Move the camel in search space.

Parameters

• camel (Camel) – Camel that we want to move.

• best_x (numpy.ndarray) – Global best coordinates.

• task (Task) – Optimization task.

Returns

Camel that moved in the search space.

Return type

Camel

class niapy.algorithms.basic.CatSwarmOptimization(population_size=30, mixture_ratio=0.1, c1=2.05, smp=3, spc=True, cdc=0.85, srd=0.2, max_velocity=1.9, *args, **kwargs)

Bases: Algorithm

Implementation of Cat swarm optimization algorithm.

Algorithm: Cat swarm optimization

Date: 2019

Author: Mihael Baketarić

License: MIT

Reference paper: Chu, S. C., Tsai, P. W., & Pan, J. S. (2006). Cat swarm optimization. In Pacific Rim international conference on artificial intelligence (pp. 854-858). Springer, Berlin, Heidelberg.

Initialize CatSwarmOptimization.

Parameters

• population_size (int) – Number of individuals in population.

• mixture_ratio (float) – Mixture ratio.

• c1 (float) – Constant in tracing mode.

• smp (int) – Seeking memory pool.

• spc (bool) – Self-position considering.

• cdc (float) – Decides how many dimensions will be varied.

• srd (float) – Seeking range of the selected dimension.

• max_velocity (float) – Maximal velocity.

• Also (See) –

  • niapy.algorithms.Algorithm.__init__()

Name = ['CatSwarmOptimization', 'CSO']

__init__(population_size=30, mixture_ratio=0.1, c1=2.05, smp=3, spc=True, cdc=0.85, srd=0.2, max_velocity=1.9, *args, **kwargs)

Initialize CatSwarmOptimization.

Parameters

• population_size (int) – Number of individuals in population.

• mixture_ratio (float) – Mixture ratio.

• c1 (float) – Constant in tracing mode.

• smp (int) – Seeking memory pool.

• spc (bool) – Self-position considering.

• cdc (float) – Decides how many dimensions will be varied.

• srd (float) – Seeking range of the selected dimension.

• max_velocity (float) – Maximal velocity.

• Also (See) –

  • niapy.algorithms.Algorithm.__init__()

get_parameters()

Get parameters values of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get algorithm information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize population.

Parameters

task (Task) – Optimization task.

Returns

1. Initialized population.

2. Initialized populations fitness/function values.

3. Additional arguments:

   • Dictionary of modes (seek or trace) and velocities for each cat

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], Dict[str, Any]]

See also

• niapy.algorithms.Algorithm.init_population()

random_seek_trace()

Set cats into seeking/tracing mode randomly.

Returns

One or zero. One means tracing mode. Zero means seeking mode. Length of list is equal to population_size.

Return type

numpy.ndarray

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Cat Swarm Optimization algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current population fitness/function values.

• best_x (numpy.ndarray) – Current best individual.

• best_fitness (float) – Current best cat fitness/function value.

• **params (Dict[str, Any]) – Additional function arguments.

Returns

1. New population.

2. New population fitness/function values.

3. New global best solution.

4. New global best solutions fitness/objective value.

5. Additional arguments:

   • velocities (numpy.ndarray): velocities of cats.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

seeking_mode(task, cat, cat_fitness, pop, fpop, fxb)

Seeking mode.

Parameters

• task (Task) – Optimization task.

• cat (numpy.ndarray) – Individual from population.

• cat_fitness (float) – Current individual’s fitness/function value.

• pop (numpy.ndarray) – Current population.

• fpop (numpy.ndarray) – Current population fitness/function values.

• fxb (float) – Current best cat fitness/function value.

Returns

1. Updated individual’s position

2. Updated individual’s fitness/function value

3. Updated global best position

4. Updated global best fitness/function value

Return type

Tuple[numpy.ndarray, float, numpy.ndarray, float]

set_parameters(population_size=30, mixture_ratio=0.1, c1=2.05, smp=3, spc=True, cdc=0.85, srd=0.2, max_velocity=1.9, **kwargs)

Set the algorithm parameters.

Parameters

• population_size (int) – Number of individuals in population.

• mixture_ratio (float) – Mixture ratio.

• c1 (float) – Constant in tracing mode.

• smp (int) – Seeking memory pool.

• spc (bool) – Self-position considering.

• cdc (float) – Decides how many dimensions will be varied.

• srd (float) – Seeking range of the selected dimension.

• max_velocity (float) – Maximal velocity.

• Also (See) –

  • niapy.algorithms.Algorithm.set_parameters()

tracing_mode(task, cat, velocity, xb)

Tracing mode.

Parameters

• task (Task) – Optimization task.

• cat (numpy.ndarray) – Individual from population.

• velocity (numpy.ndarray) – Velocity of individual.

• xb (numpy.ndarray) – Current best individual.

Returns

1. Updated individual’s position

2. Updated individual’s fitness/function value

3. Updated individual’s velocity vector

Return type

Tuple[numpy.ndarray, float, numpy.ndarray]

weighted_selection(weights)

Random selection considering the weights.

Parameters

weights (numpy.ndarray) – weight for each potential position.

Returns

index of selected next position.

Return type

int

class niapy.algorithms.basic.CenterParticleSwarmOptimization(*args, **kwargs)

Bases: ParticleSwarmAlgorithm

Implementation of Center Particle Swarm Optimization.

Algorithm:

Center Particle Swarm Optimization

Date:

2019

Authors:

Klemen Berkovič

License:

MIT

Reference paper:

H.-C. Tsai, Predicting strengths of concrete-type specimens using hybrid multilayer perceptrons with center-Unified particle swarm optimization, Adv. Eng. Softw. 37 (2010) 1104–1112.

See also

• niapy.algorithms.basic.WeightedVelocityClampingParticleSwarmAlgorithm

Initialize CPSO.

Name = ['CenterParticleSwarmOptimization', 'CPSO']

__init__(*args, **kwargs)

Initialize CPSO.

get_parameters()

Get value of parameters for this instance of algorithm.

Returns

Dictionary which has parameters mapped to values.

Return type

Dict[str, Union[int, float, numpy.ndarray]]

See also

• niapy.algorithms.basic.ParticleSwarmAlgorithm.get_parameters()

static info()

Get basic information of algorithm.

Returns

Basic information of algorithm.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

run_iteration(task, pop, fpop, xb, fxb, **params)

Core function of algorithm.

Parameters

• task (Task) – Optimization task.

• pop (numpy.ndarray) – Current population of particles.

• fpop (numpy.ndarray) – Current particles function/fitness values.

• xb (numpy.ndarray) – Current global best particle.

• fxb (numpy.float) – Current global best particles function/fitness value.

Returns

1. New population of particles.

2. New populations function/fitness values.

3. New global best particle.

4. New global best particle function/fitness value.

5. Additional arguments.

6. Additional keyword arguments.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, dict]

See also

• niapy.algorithm.basic.WeightedVelocityClampingParticleSwarmAlgorithm.run_iteration()

set_parameters(**kwargs)

Set core algorithm parameters.

Parameters

**kwargs – Additional arguments.

See also

niapy.algorithm.basic.WeightedVelocityClampingParticleSwarmAlgorithm.set_parameters()

class niapy.algorithms.basic.ClonalSelectionAlgorithm(population_size=10, clone_factor=0.1, mutation_factor=10.0, num_rand=1, bits_per_param=16, *args, **kwargs)

Bases: Algorithm

Implementation of Clonal Selection Algorithm.

Algorithm:

Clonal selection algorithm

Date:

2021

Authors:

Andraž Peršon

License:

MIT

Reference papers:

• L. N. de Castro and F. J. Von Zuben. Learning and optimization using the clonal selection principle. IEEE Transactions on Evolutionary Computation, 6:239–251, 2002.

• Brownlee, J. “Clever Algorithms: Nature-Inspired Programming Recipes” Revision 2. 2012. 280-286.

Variables

• population_size (int) – Population size.

• clone_factor (float) – Clone factor.

• mutation_factor (float) – Mutation factor.

• num_rand (int) – Number of random antibodies to be added to the population each generation.

• bits_per_param (int) – Number of bits per parameter of solution vector.

See also

• niapy.algorithms.Algorithm

Initialize ClonalSelectionAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• clone_factor (Optional[float]) – Clone factor.

• mutation_factor (Optional[float]) – Mutation factor.

• num_rand (Optional[int]) – Number of random antibodies to be added to the population each generation.

• bits_per_param (Optional[int]) – Number of bits per parameter of solution vector.

See also

niapy.algorithms.Algorithm.__init__()

Name = ['ClonalSelectionAlgorithm', 'CLONALG']

__init__(population_size=10, clone_factor=0.1, mutation_factor=10.0, num_rand=1, bits_per_param=16, *args, **kwargs)

Initialize ClonalSelectionAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• clone_factor (Optional[float]) – Clone factor.

• mutation_factor (Optional[float]) – Mutation factor.

• num_rand (Optional[int]) – Number of random antibodies to be added to the population each generation.

• bits_per_param (Optional[int]) – Number of bits per parameter of solution vector.

See also

niapy.algorithms.Algorithm.__init__()

clone_and_hypermutate(bitstrings, population, population_fitness, task)

decode(bitstrings, task)

evaluate(bitstrings, task)

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get algorithms information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize the starting population.

Parameters

task (Task) – Optimization task

Returns

1. New population.

2. New population fitness/function values.

3. Additional arguments:

   • bitstring (numpy.ndarray): Binary representation of the population.

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], Dict[str, Any]]

See also

• niapy.algorithms.Algorithm.init_population()

mutate(bitstring, mutation_rate)

random_insertion(bitstrings, population, population_fitness, task)

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Clonal Selection Algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population

• population_fitness (numpy.ndarray[float]) – Current population fitness/function values

• best_x (numpy.ndarray) – Current best individual

• best_fitness (float) – Current best individual function/fitness value

• params (Dict[str, Any]) – Additional algorithm arguments

Returns

1. New population

2. New population fitness/function values

3. New global best solution

4. New global best fitness/objective value

5. Additional arguments:

   • bitstring (numpy.ndarray): Binary representation of the population.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(population_size=10, clone_factor=0.1, mutation_factor=10.0, num_rand=1, bits_per_param=16, **kwargs)

Set the parameters of the algorithm.

Parameters

• population_size (Optional[int]) – Population size.

• clone_factor (Optional[float]) – Clone factor.

• mutation_factor (Optional[float]) – Mutation factor.

• num_rand (Optional[int]) – Random number.

• bits_per_param (Optional[int]) – Number of bits per parameter of solution vector.

See also

• niapy.algorithms.Algorithm.set_parameters()

class niapy.algorithms.basic.ComprehensiveLearningParticleSwarmOptimizer(m=10, w0=0.9, w1=0.4, c=1.49445, *args, **kwargs)

Bases: ParticleSwarmAlgorithm

Implementation of Mutated Particle Swarm Optimization.

Algorithm:

Comprehensive Learning Particle Swarm Optimizer

Date:

2019

Authors:

Klemen Berkovič

License:

MIT

Reference paper:

10. 10. Liang, a. K. Qin, P. N. Suganthan and S. Baskar, “Comprehensive learning particle swarm optimizer for global optimization of multimodal functions,” in IEEE Transactions on Evolutionary Computation, vol. 10, no. 3, pp. 281-295, June 2006. doi: 10.1109/TEVC.2005.857610

Reference URL:

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1637688&isnumber=34326

Variables

• w0 (float) – Inertia weight.

• w1 (float) – Inertia weight.

• c (float) – Velocity constant.

• m (int) – Refresh rate.

See also

• niapy.algorithms.basic.ParticleSwarmAlgorithm

Initialize CLPSO.

Name = ['ComprehensiveLearningParticleSwarmOptimizer', 'CLPSO']

__init__(m=10, w0=0.9, w1=0.4, c=1.49445, *args, **kwargs)

Initialize CLPSO.

generate_personal_best_cl(i, pc, personal_best, personal_best_fitness)

Generate new personal best position for learning.

Parameters

• i (int) – Current particle.

• pc (float) – Learning probability.

• personal_best (numpy.ndarray) – Personal best positions for population.

• personal_best_fitness (numpy.ndarray) – Personal best positions function/fitness values for personal best position.

Returns

Personal best for learning.

Return type

numpy.ndarray

get_parameters()

Get value of parameters for this instance of algorithm.

Returns

Dictionary which has parameters mapped to values.

Return type

Dict[str, Union[int, float, numpy.ndarray]]

See also

• niapy.algorithms.basic.ParticleSwarmAlgorithm.get_parameters()

static info()

Get basic information of algorithm.

Returns

Basic information of algorithm.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init(task)

Initialize dynamic arguments of Particle Swarm Optimization algorithm.

Parameters

task (Task) – Optimization task.

Returns

• vMin: Minimal velocity.

• vMax: Maximal velocity.

• V: Initial velocity of particle.

• flag: Refresh gap counter.

Return type

Dict[str, numpy.ndarray]

run_iteration(task, pop, fpop, xb, fxb, **params)

Core function of algorithm.

Parameters

• task (Task) – Optimization task.

• pop (numpy.ndarray) – Current populations.

• fpop (numpy.ndarray) – Current population fitness/function values.

• xb (numpy.ndarray) – Current best particle.

• fxb (float) – Current best particle fitness/function value.

• params (dict) – Additional function keyword arguments.

Returns

1. New population.

2. New population fitness/function values.

3. New global best position.

4. New global best positions function/fitness value.

5. Additional arguments.

6. Additional keyword arguments:

   • personal_best: Particles best population.

   • personal_best_fitness: Particles best positions function/fitness value.

   • min_velocity: Minimal velocity.

   • max_velocity: Maximal velocity.

   • V: Initial velocity of particle.

   • flag: Refresh gap counter.

   • pc: Learning rate.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, list, dict]

See also

• niapy.algorithms.basic.ParticleSwarmAlgorithm.run_iteration

set_parameters(m=10, w0=0.9, w1=0.4, c=1.49445, **kwargs)

Set Particle Swarm Algorithm main parameters.

Parameters

• w0 (int) – Inertia weight.

• w1 (float) – Inertia weight.

• c (float) – Velocity constant.

• m (float) – Refresh rate.

• kwargs (dict) – Additional arguments

See also

• niapy.algorithms.basic.ParticleSwarmAlgorithm.set_parameters()

update_velocity_cl(v, p, pb, w, min_velocity, max_velocity, task, **_kwargs)

Update particle velocity.

Parameters

• v (numpy.ndarray) – Current velocity of particle.

• p (numpy.ndarray) – Current position of particle.

• pb (numpy.ndarray) – Personal best position of particle.

• w (numpy.ndarray) – Weights for velocity adjustment.

• min_velocity (numpy.ndarray) – Minimal velocity allowed.

• max_velocity (numpy.ndarray) – Maximal velocity allowed.

• task (Task) – Optimization task.

Returns

Updated velocity of particle.

Return type

numpy.ndarray

class niapy.algorithms.basic.CoralReefsOptimization(population_size=25, phi=0.4, asexual_reproduction_prob=0.5, broadcast_prob=0.5, depredation_prob=0.3, k=25, crossover_rate=0.5, mutation_rate=0.36, sexual_crossover=<function default_sexual_crossover>, brooding=<function default_brooding>, *args, **kwargs)

Bases: Algorithm

Implementation of Coral Reefs Optimization Algorithm.

Algorithm:

Coral Reefs Optimization Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference Paper:

S. Salcedo-Sanz, J. Del Ser, I. Landa-Torres, S. Gil-López, and J. A. Portilla-Figueras, “The Coral Reefs Optimization Algorithm: A Novel Metaheuristic for Efficiently Solving Optimization Problems,” The Scientific World Journal, vol. 2014, Article ID 739768, 15 pages, 2014.

Reference URL:

https://doi.org/10.1155/2014/739768

Variables

• Name (List[str]) – List of strings representing algorithm name.

• phi (float) – Range of neighborhood.

• num_asexual_reproduction (int) – Number of corals used in asexual reproduction.

• num_broadcast (int) – Number of corals used in brooding.

• num_depredation (int) – Number of corals used in depredation.

• k (int) – Number of tries for larva setting.

• mutation_rate (float) – Mutation variable \(\in [0, \infty]\).

• crossover_rate (float) – Crossover rate in [0, 1].

• sexual_crossover (Callable[[numpy.ndarray, float, Task, numpy.random.Generator, Dict[str, Any]], Tuple[numpy.ndarray, numpy.ndarray[float]]]) – Crossover function.

• brooding (Callable[[numpy.ndarray, float, Task, numpy.random.Generator, Dict[str, Any]], Tuple[numpy.ndarray, numpy.ndarray]]) – Brooding function.

See also

• niapy.algorithms.Algorithm

Initialize CoralReefsOptimization.

Parameters

• population_size (int) – population size for population initialization.

• phi (int) – distance.

• asexual_reproduction_prob (float) – Value $in [0, 1]$ for Asexual reproduction size.

• broadcast_prob (float) – Value $in [0, 1]$ for brooding size.

• depredation_prob (float) – Value $in [0, 1]$ for Depredation size.

• k (int) – Tries for larvae setting.

• sexual_crossover (Callable[[numpy.ndarray, float, Task, numpy.random.Generator, Dict[str, Any]], Tuple[numpy.ndarray, numpy.ndarray]]) – Crossover function.

• crossover_rate (float) – Crossover rate $in [0, 1]$.

• brooding (Callable[[numpy.ndarray, float, Task, numpy.random.Generator, Dict[str, Any]], Tuple[numpy.ndarray, numpy.ndarray]]) – brooding function.

• mutation_rate (float) – Crossover rate $in [0, 1]$.

See also

• niapy.algorithms.Algorithm.__init__()

Name = ['CoralReefsOptimization', 'CRO']

__init__(population_size=25, phi=0.4, asexual_reproduction_prob=0.5, broadcast_prob=0.5, depredation_prob=0.3, k=25, crossover_rate=0.5, mutation_rate=0.36, sexual_crossover=<function default_sexual_crossover>, brooding=<function default_brooding>, *args, **kwargs)

Initialize CoralReefsOptimization.

Parameters

• population_size (int) – population size for population initialization.

• phi (int) – distance.

• asexual_reproduction_prob (float) – Value $in [0, 1]$ for Asexual reproduction size.

• broadcast_prob (float) – Value $in [0, 1]$ for brooding size.

• depredation_prob (float) – Value $in [0, 1]$ for Depredation size.

• k (int) – Tries for larvae setting.

• sexual_crossover (Callable[[numpy.ndarray, float, Task, numpy.random.Generator, Dict[str, Any]], Tuple[numpy.ndarray, numpy.ndarray]]) – Crossover function.

• crossover_rate (float) – Crossover rate $in [0, 1]$.

• brooding (Callable[[numpy.ndarray, float, Task, numpy.random.Generator, Dict[str, Any]], Tuple[numpy.ndarray, numpy.ndarray]]) – brooding function.

• mutation_rate (float) – Crossover rate $in [0, 1]$.

See also

• niapy.algorithms.Algorithm.__init__()

asexual_reproduction(reef, reef_fitness, best_x, best_fitness, task)

Asexual reproduction of corals.

Parameters

• reef (numpy.ndarray) – Current population of reefs.

• reef_fitness (numpy.ndarray) – Current populations function/fitness values.

• best_x (numpy.ndarray) – Global best coordinates.

• best_fitness (float) – Global best fitness.

• task (Task) – Optimization task.

Returns

1. New population.

2. New population fitness/function values.

Return type

Tuple[numpy.ndarray, numpy.ndarray]

See also

• niapy.algorithms.basic.CoralReefsOptimization.setting()

• niapy.algorithms.basic.default_brooding()

depredation(reef, reef_fitness)

Depredation operator for reefs.

Parameters

• reef (numpy.ndarray) – Current reefs.

• reef_fitness (numpy.ndarray) – Current reefs function/fitness values.

Returns

1. Best individual

2. Best individual fitness/function value

Return type

Tuple[numpy.ndarray, numpy.ndarray]

get_parameters()

Get parameters values of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get algorithms information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Coral Reefs Optimization algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current population fitness/function value.

• best_x (numpy.ndarray) – Global best solution.

• best_fitness (float) – Global best solution fitness/function value.

• **params – Additional arguments

Returns

1. New population.

2. New population fitness/function values.

3. New global best solution

4. New global best solutions fitness/objective value

5. Additional arguments:

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

See also

• niapy.algorithms.basic.CoralReefsOptimization.sexual_crossover()

• niapy.algorithms.basic.CoralReefsOptimization.brooding()

set_parameters(population_size=25, phi=0.4, asexual_reproduction_prob=0.5, broadcast_prob=0.5, depredation_prob=0.3, k=25, crossover_rate=0.5, mutation_rate=0.36, sexual_crossover=<function default_sexual_crossover>, brooding=<function default_brooding>, **kwargs)

Set the parameters of the algorithm.

Parameters

• population_size (int) – population size for population initialization.

• phi (int) – distance.

• asexual_reproduction_prob (float) – Value $in [0, 1]$ for Asexual reproduction size.

• broadcast_prob (float) – Value $in [0, 1]$ for brooding size.

• depredation_prob (float) – Value $in [0, 1]$ for Depredation size.

• k (int) – Tries for larvae setting.

• sexual_crossover (Callable[[numpy.ndarray, float, Task, numpy.random.Generator, Dict[str, Any]], Tuple[numpy.ndarray, numpy.ndarray]]) – Crossover function.

• crossover_rate (float) – Crossover rate $in [0, 1]$.

• brooding (Callable[[numpy.ndarray, float, Task, numpy.random.Generator, Dict[str, Any]], Tuple[numpy.ndarray, numpy.ndarray]]) – brooding function.

• mutation_rate (float) – Crossover rate $in [0, 1]$.

See also

• niapy.algorithms.Algorithm.set_parameters()

settling(reef, reef_fitness, new_reef, new_reef_fitness, best_x, best_fitness, task)

Operator for setting reefs.

New reefs try to settle to selected position in search space. New reefs are successful if their fitness values is better or if they have no reef occupying same search space.

Parameters

• reef (numpy.ndarray) – Current population of reefs.

• reef_fitness (numpy.ndarray) – Current populations function/fitness values.

• new_reef (numpy.ndarray) – New population of reefs.

• new_reef_fitness (numpy.ndarray) – New populations function/fitness values.

• best_x (numpy.ndarray) – Global best solution.

• best_fitness (float) – Global best solutions fitness/objective value.

• task (Task) – Optimization task.

Returns

1. New settled population.

2. New settled population fitness/function values.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float]

class niapy.algorithms.basic.CuckooSearch(population_size=25, pa=0.25, *args, **kwargs)

Bases: Algorithm

Implementation of Cuckoo behaviour and levy flights.

Algorithm:

Cuckoo Search

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference:

Yang, Xin-She, and Suash Deb. “Cuckoo search via Lévy flights.” Nature & Biologically Inspired Computing, 2009. NaBIC 2009. World Congress on. IEEE, 2009.

Variables

• Name (List[str]) – list of strings representing algorithm names.

• pa (float) – Probability of a nest being abandoned.

See also

• niapy.algorithms.Algorithm

Initialize CuckooSearch.

Parameters

• population_size (int) – Population size.

• pa (float) – Probability of a nest being abandoned.

See also

• niapy.algorithms.Algorithm.__init__()

Name = ['CuckooSearch', 'CS']

__init__(population_size=25, pa=0.25, *args, **kwargs)

Initialize CuckooSearch.

Parameters

• population_size (int) – Population size.

• pa (float) – Probability of a nest being abandoned.

See also

• niapy.algorithms.Algorithm.__init__()

empty_nests(population, task)

get_cuckoos(population, best_x, task)

get_parameters()

Get parameters of the algorithm.

static info()

Get algorithms information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of CuckooSearch algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current populations fitness/function values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best individual function/fitness values.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. Initialized population.

2. Initialized populations fitness/function values.

3. New global best solution.

4. New global best solutions fitness/objective value.

5. Additional arguments.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(population_size=50, pa=0.2, **kwargs)

Set the arguments of an algorithm.

Parameters

• population_size (int) – Population size.

• pa (float) – Probability of a nest being abandoned.

See also

• niapy.algorithms.Algorithm.set_parameters()

class niapy.algorithms.basic.DifferentialEvolution(population_size=50, differential_weight=1, crossover_probability=0.8, strategy=<function cross_rand1>, *args, **kwargs)

Bases: Algorithm

Implementation of Differential evolution algorithm.

Algorithm:

Differential evolution algorithm

Date:

2018

Author:

Uros Mlakar and Klemen Berkovič

License:

MIT

Reference paper:

Storn, Rainer, and Kenneth Price. “Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces.” Journal of global optimization 11.4 (1997): 341-359.

Variables

• Name (List[str]) – List of string of names for algorithm.

• differential_weight (float) – Scale factor.

• crossover_probability (float) – Crossover probability.

• strategy (Callable[numpy.ndarray, int, numpy.ndarray, float, float, numpy.random.Generator, Dict[str, Any]]) – crossover and mutation strategy.

See also

• niapy.algorithms.Algorithm

Initialize DifferentialEvolution.

Parameters

• population_size (Optional[int]) – Population size.

• differential_weight (Optional[float]) – Differential weight (differential_weight).

• crossover_probability (Optional[float]) – Crossover rate.

• strategy (Optional[Callable[[numpy.ndarray, int, numpy.ndarray, float, float, numpy.random.Generator, list], numpy.ndarray]]) – Crossover and mutation strategy.

See also

• niapy.algorithms.Algorithm.__init__()

Name = ['DifferentialEvolution', 'DE']

__init__(population_size=50, differential_weight=1, crossover_probability=0.8, strategy=<function cross_rand1>, *args, **kwargs)

Initialize DifferentialEvolution.

Parameters

• population_size (Optional[int]) – Population size.

• differential_weight (Optional[float]) – Differential weight (differential_weight).

• crossover_probability (Optional[float]) – Crossover rate.

• strategy (Optional[Callable[[numpy.ndarray, int, numpy.ndarray, float, float, numpy.random.Generator, list], numpy.ndarray]]) – Crossover and mutation strategy.

See also

• niapy.algorithms.Algorithm.__init__()

evolve(pop, xb, task, **kwargs)

Evolve population.

Parameters

• pop (numpy.ndarray) – Current population.

• xb (numpy.ndarray) – Current best individual.

• task (Task) – Optimization task.

Returns

New evolved populations.

Return type

numpy.ndarray

get_parameters()

Get parameters values of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

See also

• niapy.algorithms.Algorithm.get_parameters()

static info()

Get basic information of algorithm.

Returns

Basic information of algorithm.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

post_selection(pop, task, xb, fxb, **kwargs)

Apply additional operation after selection.

Parameters

• pop (numpy.ndarray) – Current population.

• task (Task) – Optimization task.

• xb (numpy.ndarray) – Global best solution.

• fxb (float) – Global best fitness.

Returns

1. New population.

2. New global best solution.

3. New global best solutions fitness/objective value.

Return type

Tuple[numpy.ndarray, numpy.ndarray, float]

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Differential Evolution algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current populations fitness/function values.

• best_x (numpy.ndarray) – Current best individual.

• best_fitness (float) – Current best individual function/fitness value.

• **params (dict) – Additional arguments.

Returns

1. New population.

2. New population fitness/function values.

3. New global best solution.

4. New global best solutions fitness/objective value.

5. Additional arguments.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

See also

• niapy.algorithms.basic.DifferentialEvolution.evolve()

• niapy.algorithms.basic.DifferentialEvolution.selection()

• niapy.algorithms.basic.DifferentialEvolution.post_selection()

selection(population, new_population, best_x, best_fitness, task, **kwargs)

Operator for selection.

Parameters

• population (numpy.ndarray) – Current population.

• new_population (numpy.ndarray) – New Population.

• best_x (numpy.ndarray) – Current global best solution.

• best_fitness (float) – Current global best solutions fitness/objective value.

• task (Task) – Optimization task.

Returns

1. New selected individuals.

2. New global best solution.

3. New global best solutions fitness/objective value.

Return type

Tuple[numpy.ndarray, numpy.ndarray, float]

set_parameters(population_size=50, differential_weight=1, crossover_probability=0.8, strategy=<function cross_rand1>, **kwargs)

Set the algorithm parameters.

Parameters

• population_size (Optional[int]) – Population size.

• differential_weight (Optional[float]) – Differential weight (differential_weight).

• crossover_probability (Optional[float]) – Crossover rate.

• strategy (Optional[Callable[[numpy.ndarray, int, numpy.ndarray, float, float, numpy.random.Generator, list], numpy.ndarray]]) – Crossover and mutation strategy.

See also

• niapy.algorithms.Algorithm.set_parameters()

class niapy.algorithms.basic.DynNpDifferentialEvolution(population_size=10, p_max=50, rp=3, *args, **kwargs)

Bases: DifferentialEvolution

Implementation of Dynamic population size Differential evolution algorithm.

Algorithm:

Dynamic population size Differential evolution algorithm

Date:

2018

Author:

Klemen Berkovič

License:

MIT

Variables

• Name (List[str]) – List of strings representing algorithm names.

• p_max (int) – Number of population reductions.

• rp (int) – Small non-negative number which is added to value of generations.

See also

• niapy.algorithms.basic.DifferentialEvolution

Initialize DynNpDifferentialEvolution.

Parameters

• p_max (Optional[int]) – Number of population reductions.

• rp (Optional[int]) – Small non-negative number which is added to value of generations.

See also

• niapy.algorithms.basic.DifferentialEvolution.__init__()

Name = ['DynNpDifferentialEvolution', 'dynNpDE']

__init__(population_size=10, p_max=50, rp=3, *args, **kwargs)

Initialize DynNpDifferentialEvolution.

Parameters

• p_max (Optional[int]) – Number of population reductions.

• rp (Optional[int]) – Small non-negative number which is added to value of generations.

See also

• niapy.algorithms.basic.DifferentialEvolution.__init__()

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get basic information of algorithm.

Returns

Basic information of algorithm.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

post_selection(pop, task, xb, fxb, **kwargs)

Post selection operator.

In this algorithm the post selection operator decrements the population at specific iterations/generations.

Parameters

• pop (numpy.ndarray) – Current population.

• task (Task) – Optimization task.

• xb (numpy.ndarray) – Global best individual coordinates.

• fxb (float) – Global best fitness.

• kwargs (Dict[str, Any]) – Additional arguments.

Returns

1. Changed current population.

2. New global best solution.

3. New global best solutions fitness/objective value.

Return type

Tuple[numpy.ndarray, numpy.ndarray, float]

set_parameters(p_max=50, rp=3, **kwargs)

Set the algorithm parameters.

Parameters

• p_max (Optional[int]) – Number of population reductions.

• rp (Optional[int]) – Small non-negative number which is added to value of generations.

See also

• niapy.algorithms.basic.DifferentialEvolution.set_parameters()

class niapy.algorithms.basic.DynNpMultiStrategyDifferentialEvolution(population_size=40, strategies=(<function cross_rand1>, <function cross_best1>, <function cross_curr2best1>, <function cross_rand2>), *args, **kwargs)

Bases: MultiStrategyDifferentialEvolution, DynNpDifferentialEvolution

Implementation of Dynamic population size Differential evolution algorithm with dynamic population size that is defined by the quality of population.

Algorithm:

Dynamic population size Differential evolution algorithm with dynamic population size that is defined by the quality of population

Date:

2018

Author:

Klemen Berkovič

License:

MIT

Variables

Name (List[str]) – List of strings representing algorithm name.

See also

• niapy.algorithms.basic.MultiStrategyDifferentialEvolution

• niapy.algorithms.basic.DynNpDifferentialEvolution

Initialize MultiStrategyDifferentialEvolution.

Parameters

strategies (Optional[Iterable[Callable[[numpy.ndarray[Individual], int, Individual, float, float, numpy.random.Generator], numpy.ndarray[Individual]]]]) – List of mutation strategies.

See also

• niapy.algorithms.basic.DifferentialEvolution.__init__()

Name = ['DynNpMultiStrategyDifferentialEvolution', 'dynNpMsDE']

evolve(pop, xb, task, **kwargs)

Evolve the current population.

Parameters

• pop (numpy.ndarray) – Current population.

• xb (numpy.ndarray) – Global best solution.

• task (Task) – Optimization task.

Returns

Evolved new population.

Return type

numpy.ndarray

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get basic information of algorithm.

Returns

Basic information of algorithm.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

post_selection(pop, task, xb, fxb, **kwargs)

Post selection operator.

Parameters

• pop (numpy.ndarray) – Current population.

• task (Task) – Optimization task.

• xb (numpy.ndarray) – Global best individual

• fxb (float) – Global best fitness.

Returns

1. New population.

2. New global best solution.

3. New global best solutions fitness/objective value.

Return type

Tuple[numpy.ndarray, numpy.ndarray, float]

See also

• niapy.algorithms.basic.DynNpDifferentialEvolution.post_selection()

set_parameters(**kwargs)

Set the arguments of the algorithm.

See also

• niapy.algorithms.basic.MultiStrategyDifferentialEvolution.set_parameters()

• niapy.algorithms.basic.DynNpDifferentialEvolution.set_parameters()

class niapy.algorithms.basic.DynamicFireworksAlgorithm(amplification_coeff=1.2, reduction_coeff=0.9, *args, **kwargs)

Bases: DynamicFireworksAlgorithmGauss

Implementation of dynamic fireworks algorithm.

Algorithm:

Dynamic Fireworks Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6900485&isnumber=6900223

Reference paper:

19. Zheng, A. Janecek, J. Li and Y. Tan, “Dynamic search in fireworks algorithm,” 2014 IEEE Congress on Evolutionary Computation (CEC), Beijing, 2014, pp. 3222-3229. doi: 10.1109/CEC.2014.6900485

Variables

Name (List[str]) – List of strings representing algorithm name.

See also

• niapy.algorithms.basic.DynamicFireworksAlgorithmGauss

Initialize dynFWAG.

Parameters

• amplification_coeff (Union[int, float]) – Amplification coefficient.

• reduction_coeff (Union[int, float]) – Reduction coefficient.

See also

• FireworksAlgorithm.__init__()

Name = ['DynamicFireworksAlgorithm', 'dynFWA']

static info()

Get default information of algorithm.

Returns

Basic information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Co50re function of Dynamic Fireworks Algorithm.

Parameters

• task (Task) – Optimization task

• population (numpy.ndarray) – Current population

• population_fitness (numpy.ndarray[float]) – Current population fitness/function values

• best_x (numpy.ndarray) – Current best solution

• best_fitness (float) – Current best solution’s fitness/function value

• **params –

Returns

1. New population.

2. New population function/fitness values.

3. New global best solution.

4. New global best fitness.

5. Additional arguments.

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], Dict[str, Any]]

class niapy.algorithms.basic.DynamicFireworksAlgorithmGauss(amplification_coeff=1.2, reduction_coeff=0.9, *args, **kwargs)

Bases: EnhancedFireworksAlgorithm

Implementation of dynamic fireworks algorithm.

Algorithm:

Dynamic Fireworks Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6900485&isnumber=6900223

Reference paper:

19. Zheng, A. Janecek, J. Li and Y. Tan, “Dynamic search in fireworks algorithm,” 2014 IEEE Congress on Evolutionary Computation (CEC), Beijing, 2014, pp. 3222-3229. doi: 10.1109/CEC.2014.6900485

Variables

• Name (List[str]) – List of strings representing algorithm names.

• amplitude_cf (Union[float, int]) – Amplitude of the core firework.

• amplification_coeff (Union[float, int]) – Amplification coefficient.

• reduction_coeff (Union[float, int]) – Reduction coefficient.

Initialize dynFWAG.

Parameters

• amplification_coeff (Union[int, float]) – Amplification coefficient.

• reduction_coeff (Union[int, float]) – Reduction coefficient.

See also

• FireworksAlgorithm.__init__()

Name = ['DynamicFireworksAlgorithmGauss', 'dynFWAG']

__init__(amplification_coeff=1.2, reduction_coeff=0.9, *args, **kwargs)

Initialize dynFWAG.

Parameters

• amplification_coeff (Union[int, float]) – Amplification coefficient.

• reduction_coeff (Union[int, float]) – Reduction coefficient.

See also

• FireworksAlgorithm.__init__()

explosion_amplitudes(population_fitness, task=None)

Calculate explosion amplitude for other fireworks.

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get default information of algorithm.

Returns

Basic information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize population.

Parameters

task (Task) – Optimization task.

Returns

1. Initialized population.

2. Initialized population function/fitness values.

3. Additional arguments:

   • amplitude_cf (numpy.ndarray): Initial amplitude of the core firework.

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], Dict[str, Any]]

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of DynamicFireworksAlgorithmGauss algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current populations function/fitness values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best fitness/function value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New population.

2. New populations fitness/function values.

3. New global best solution.

4. New global best solutions fitness/objective value.

5. Additional arguments:

   • amplitude_cf (numpy.ndarray): Amplitude of the core firework.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

selection(population, population_fitness, sparks, task)

Select fireworks for the next generation.

set_parameters(amplification_coeff=1.2, reduction_coeff=0.9, **kwargs)

Set core arguments of DynamicFireworksAlgorithmGauss.

Parameters

• amplification_coeff (Union[int, float]) – Amplification coefficient.

• reduction_coeff (Union[int, float]) – Reduction coefficient.

See also

• FireworksAlgorithm.set_parameters()

update_cf(xnb, xcb, xcb_f, xb, xb_f, amplitude_cf, task)

Update the core firework.

Parameters

• xnb – Sparks generated by core fireworks.

• xcb – Current generations best spark.

• xcb_f – Current generations best fitness.

• xb – Global best individual.

• xb_f – Global best fitness.

• amplitude_cf – Amplitude of the core firework.

• task (Task) – Optimization task.

Returns

1. New core firework.

2. New core firework’s fitness.

3. New core firework amplitude.

Return type

Tuple[numpy.ndarray, float, numpy.ndarray]

class niapy.algorithms.basic.EnhancedFireworksAlgorithm(amplitude_init=0.2, amplitude_final=0.01, *args, **kwargs)

Bases: FireworksAlgorithm

Implementation of enhanced fireworks algorithm.

Algorithm:

Enhanced Fireworks Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

https://ieeexplore.ieee.org/document/6557813/

Reference paper:

19. Zheng, A. Janecek and Y. Tan, “Enhanced Fireworks Algorithm,” 2013 IEEE Congress on Evolutionary Computation, Cancun, 2013, pp. 2069-2077. doi: 10.1109/CEC.2013.6557813

Variables

• Name (List[str]) – List of strings representing algorithm names.

• amplitude_init (float) – Initial amplitude of sparks.

• amplitude_final (float) – Maximal amplitude of sparks.

Initialize EFWA.

Parameters

• amplitude_init (float) – Initial amplitude.

• amplitude_final (float) – Final amplitude.

See also

• FireworksAlgorithm.__init__()

Name = ['EnhancedFireworksAlgorithm', 'EFWA']

__init__(amplitude_init=0.2, amplitude_final=0.01, *args, **kwargs)

Initialize EFWA.

Parameters

• amplitude_init (float) – Initial amplitude.

• amplitude_final (float) – Final amplitude.

See also

• FireworksAlgorithm.__init__()

explosion_amplitudes(population_fitness, task=None)

Calculate explosion amplitude.

Parameters

• population_fitness (numpy.ndarray) –

• task (Task) – Optimization task.

Returns

New amplitude.

Return type

numpy.ndarray

explosion_spark(x, amplitude, task)

Explode a spark.

Parameters

• x (numpy.ndarray) – Individuals creating spark.

• amplitude (float) – Amplitude of spark.

• task (Task) – Optimization task.

Returns

Sparks exploded in with specified amplitude.

Return type

numpy.ndarray

gaussian_spark(x, task, best_x=None)

Create new individual.

Parameters

• x (numpy.ndarray) –

• task (Task) – Optimization task.

• best_x (numpy.ndarray) – Current global best individual.

Returns

New individual generated by gaussian noise.

Return type

numpy.ndarray

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get default information of algorithm.

Returns

Basic information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

mapping(x, task)

Fix value to bounds.

Parameters

• x (numpy.ndarray) – Individual to fix.

• task (Task) – Optimization task.

Returns

Individual in search range.

Return type

numpy.ndarray

selection(population, population_fitness, sparks, task)

Generate new population.

Parameters

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray[float]) – Current populations fitness/function values.

• sparks (numpy.ndarray) – New population.

• task (Task) – Optimization task.

Returns

1. New population.

2. New populations fitness/function values.

3. New global best individual.

4. New global best fitness.

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], numpy.ndarray, float]

set_parameters(amplitude_init=0.2, amplitude_final=0.01, **kwargs)

Set EnhancedFireworksAlgorithm algorithms core parameters.

Parameters

• amplitude_init (float) – Initial amplitude.

• amplitude_final (float) – Final amplitude.

See also

• FireworksAlgorithm.set_parameters()

class niapy.algorithms.basic.EvolutionStrategy1p1(mu=1, k=10, c_a=1.1, c_r=0.5, epsilon=1e-20, *args, **kwargs)

Bases: Algorithm

Implementation of (1 + 1) evolution strategy algorithm. Uses just one individual.

Algorithm:

(1 + 1) Evolution Strategy Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

Reference paper:

KALYANMOY, Deb. “Multi-Objective optimization using evolutionary algorithms”. John Wiley & Sons, Ltd. Kanpur, India. 2001.

Variables

• Name (List[str]) – List of strings representing algorithm names.

• mu (int) – Number of parents.

• k (int) – Number of iterations before checking and fixing rho.

• c_a (float) – Search range amplification factor.

• c_r (float) – Search range reduction factor.

See also

• niapy.algorithms.Algorithm

Initialize EvolutionStrategy1p1.

Parameters

• mu (Optional[int]) – Number of parents

• k (Optional[int]) – Number of iterations before checking and fixing rho

• c_a (Optional[float]) – Search range amplification factor

• c_r (Optional[float]) – Search range reduction factor

• epsilon (Optional[float]) – Small number.

See also

• niapy.algorithms.Algorithm.__init__()

Name = ['EvolutionStrategy1p1', 'EvolutionStrategy(1+1)', 'ES(1+1)']

__init__(mu=1, k=10, c_a=1.1, c_r=0.5, epsilon=1e-20, *args, **kwargs)

Initialize EvolutionStrategy1p1.

Parameters

• mu (Optional[int]) – Number of parents

• k (Optional[int]) – Number of iterations before checking and fixing rho

• c_a (Optional[float]) – Search range amplification factor

• c_r (Optional[float]) – Search range reduction factor

• epsilon (Optional[float]) – Small number.

See also

• niapy.algorithms.Algorithm.__init__()

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get algorithms information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize starting individual.

Parameters

task (Task) – Optimization task.

Returns

1. Initialized individual.

2. Initialized individual fitness/function value.

3. Additional arguments:

   • ki (int): Number of successful rho update.

Return type

Tuple[Individual, float, Dict[str, Any]]

mutate(x, rho)

Mutate individual.

Parameters

• x (numpy.ndarray) – Current individual.

• rho (float) – Current standard deviation.

Returns

Mutated individual.

Return type

Individual

run_iteration(task, c, population_fitness, best_x, best_fitness, **params)

Core function of EvolutionStrategy(1+1) algorithm.

Parameters

• task (Task) – Optimization task.

• c (Individual) – Current position.

• population_fitness (float) – Current position function/fitness value.

• best_x (numpy.ndarray) – Global best position.

• best_fitness (float) – Global best function/fitness value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. Initialized individual.

2. Initialized individual fitness/function value.

3. New global best solution.

4. New global best solutions fitness/objective value.

5. Additional arguments:

   • ki (int): Number of successful rho update.

Return type

Tuple[Individual, float, Individual, float, Dict[str, Any]]

set_parameters(mu=1, k=10, c_a=1.1, c_r=0.5, epsilon=1e-20, **kwargs)

Set the arguments of an algorithm.

Parameters

• mu (Optional[int]) – Number of parents

• k (Optional[int]) – Number of iterations before checking and fixing rho

• c_a (Optional[float]) – Search range amplification factor

• c_r (Optional[float]) – Search range reduction factor

• epsilon (Optional[float]) – Small number.

See also

• niapy.algorithms.Algorithm.set_parameters()

update_rho(rho, k)

Update standard deviation.

Parameters

• rho (float) – Current standard deviation.

• k (int) – Number of successful mutations.

Returns

New standard deviation.

Return type

float

class niapy.algorithms.basic.EvolutionStrategyML(lam=45, *args, **kwargs)

Bases: EvolutionStrategyMpL

Implementation of (mu, lambda) evolution strategy algorithm. Algorithm is good for dynamic environments. Mu individual create lambda children. Only best mu children go to new generation. Mu parents are discarded.

Algorithm:

(\(\mu + \lambda\)) Evolution Strategy Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

Reference paper:

Variables

Name (List[str]) – List of strings representing algorithm names

See also

• niapy.algorithm.basic.es.EvolutionStrategyMpL

Initialize EvolutionStrategyMpL.

Parameters

lam (int) – Number of new individual generated by mutation.

Name = ['EvolutionStrategyML', 'EvolutionStrategy(mu,lambda)', 'ES(m,l)']

static info()

Get algorithms information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize starting population.

Parameters

task (Task) – Optimization task.

Returns

1. Initialized population.

2. Initialized populations fitness/function values.

3. Additional arguments.

Return type

Tuple[numpy.ndarray[Individual], numpy.ndarray[float], Dict[str, Any]]

See also

• niapy.algorithm.basic.es.EvolutionStrategyMpL.init_population()

new_pop(pop)

Return new population.

Parameters

pop (numpy.ndarray) – Current population.

Returns

New population.

Return type

numpy.ndarray

run_iteration(task, c, population_fitness, best_x, best_fitness, **params)

Core function of EvolutionStrategyML algorithm.

Parameters

• task (Task) – Optimization task.

• c (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current population fitness/function values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best individuals fitness/function value.

• Dict[str (**params) – Additional arguments.

• Any] – Additional arguments.

Returns

1. New population.

2. New populations fitness/function values.

3. New global best solution.

4. New global best solutions fitness/objective value.

5. Additional arguments.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

class niapy.algorithms.basic.EvolutionStrategyMp1(mu=40, *args, **kwargs)

Bases: EvolutionStrategy1p1

Implementation of (mu + 1) evolution strategy algorithm. Algorithm creates mu mutants but into new generation goes only one individual.

Algorithm:

(\(\mu + 1\)) Evolution Strategy Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

Reference paper:

Variables

Name (List[str]) – List of strings representing algorithm names.

See also

• niapy.algorithms.basic.EvolutionStrategy1p1

Initialize EvolutionStrategyMp1.

Name = ['EvolutionStrategyMp1', 'EvolutionStrategy(mu+1)', 'ES(m+1)']

__init__(mu=40, *args, **kwargs)

Initialize EvolutionStrategyMp1.

static info()

Get algorithms information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

set_parameters(**kwargs)

Set core parameters of EvolutionStrategy(mu+1) algorithm.

See also

• niapy.algorithms.basic.EvolutionStrategy1p1.set_parameters()

class niapy.algorithms.basic.EvolutionStrategyMpL(lam=45, *args, **kwargs)

Bases: EvolutionStrategy1p1

Implementation of (mu + lambda) evolution strategy algorithm. Mutation creates lambda individual. Lambda individual compete with mu individuals for survival, so only mu individual go to new generation.

Algorithm:

(\(\mu + \lambda\)) Evolution Strategy Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

Reference paper:

Variables

• Name (List[str]) – List of strings representing algorithm names

• lam (int) – Lambda.

See also

• niapy.algorithms.basic.EvolutionStrategy1p1

Initialize EvolutionStrategyMpL.

Parameters

lam (int) – Number of new individual generated by mutation.

Name = ['EvolutionStrategyMpL', 'EvolutionStrategy(mu+lambda)', 'ES(m+l)']

__init__(lam=45, *args, **kwargs)

Initialize EvolutionStrategyMpL.

Parameters

lam (int) – Number of new individual generated by mutation.

static change_count(c, cn)

Update number of successful mutations for population.

Parameters

• c (numpy.ndarray[Individual]) – Current population.

• cn (numpy.ndarray[Individual]) – New population.

Returns

Number of successful mutations.

Return type

int

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get algorithms information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize starting population.

Parameters

task (Task) – Optimization task.

Returns

1. Initialized population.

2. Initialized populations function/fitness values.

3. Additional arguments:

   • ki (int): Number of successful mutations.

Return type

Tuple[numpy.ndarray[Individual], numpy.ndarray[float], Dict[str, Any]]

See also

• niapy.algorithms.algorithm.Algorithm.init_population()

mutate_rand(pop, task)

Mutate random individual form population.

Parameters

• pop (numpy.ndarray[Individual]) – Current population.

• task (Task) – Optimization task.

Returns

Random individual from population that was mutated.

Return type

numpy.ndarray

run_iteration(task, c, population_fitness, best_x, best_fitness, **params)

Core function of EvolutionStrategyMpL algorithm.

Parameters

• task (Task) – Optimization task.

• c (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current populations fitness/function values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best individuals fitness/function value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New population.

2. New populations function/fitness values.

3. New global best solution.

4. New global best solutions fitness/objective value.

5. Additional arguments:

   • ki (int): Number of successful mutations.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(lam=45, **kwargs)

Set the arguments of an algorithm.

Parameters

lam (int) – Number of new individual generated by mutation.

See also

• niapy.algorithms.basic.es.EvolutionStrategy1p1.set_parameters()

update_rho(pop, k)

Update standard deviation for population.

Parameters

• pop (numpy.ndarray[Individual]) – Current population.

• k (int) – Number of successful mutations.

class niapy.algorithms.basic.FireflyAlgorithm(population_size=20, alpha=1, beta0=1, gamma=0.01, theta=0.97, *args, **kwargs)

Bases: Algorithm

Implementation of Firefly algorithm.

Algorithm:

Firefly algorithm

Date:

2016

Authors:

Iztok Fister Jr, Iztok Fister and Klemen Berkovič

License:

MIT

Reference paper:

Fister, I., Fister Jr, I., Yang, X. S., & Brest, J. (2013). A comprehensive review of firefly algorithms. Swarm and Evolutionary Computation, 13, 34-46.

Variables

• Name (List[str]) – List of strings representing algorithm name.

• alpha (float) – Randomness strength.

• beta0 (float) – Attractiveness constant.

• gamma (float) – Absorption coefficient.

• theta (float) – Randomness reduction factor.

See also

• niapy.algorithms.Algorithm

Initialize FireflyAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• alpha (Optional[float]) – Randomness strength 0–1 (highly random).

• beta0 (Optional[float]) – Attractiveness constant.

• gamma (Optional[float]) – Absorption coefficient.

• theta (Optional[float]) – Randomness reduction factor.

See also

• niapy.algorithms.Algorithm.__init__()

Name = ['FireflyAlgorithm', 'FA']

__init__(population_size=20, alpha=1, beta0=1, gamma=0.01, theta=0.97, *args, **kwargs)

Initialize FireflyAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• alpha (Optional[float]) – Randomness strength 0–1 (highly random).

• beta0 (Optional[float]) – Attractiveness constant.

• gamma (Optional[float]) – Absorption coefficient.

• theta (Optional[float]) – Randomness reduction factor.

See also

• niapy.algorithms.Algorithm.__init__()

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get algorithms information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize the starting population.

Parameters

task (Task) – Optimization task

Returns

1. New population.

2. New population fitness/function values.

3. Additional arguments:

   • alpha (float): Randomness strength.

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], Dict[str, Any]]

See also

• niapy.algorithms.Algorithm.init_population()

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Firefly Algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current population function/fitness values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best individual fitness/function value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New population.

2. New population fitness/function values.

3. New global best solution

4. New global best solutions fitness/objective value

5. Additional arguments:

   • alpha (float): Randomness strength.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

See also

• niapy.algorithms.basic.FireflyAlgorithm.move_ffa()

set_parameters(population_size=20, alpha=1, beta0=1, gamma=0.01, theta=0.97, **kwargs)

Set the parameters of the algorithm.

Parameters

• population_size (Optional[int]) – Population size.

• alpha (Optional[float]) – Randomness strength 0–1 (highly random).

• beta0 (Optional[float]) – Attractiveness constant.

• gamma (Optional[float]) – Absorption coefficient.

• theta (Optional[float]) – Randomness reduction factor.

See also

• niapy.algorithms.Algorithm.set_parameters()

class niapy.algorithms.basic.FireworksAlgorithm(population_size=5, num_sparks=50, a=0.04, b=0.8, max_amplitude=40, num_gaussian=5, *args, **kwargs)

Bases: Algorithm

Implementation of fireworks algorithm.

Algorithm:

Fireworks Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

https://www.springer.com/gp/book/9783662463529

Reference paper:

Tan, Ying. “Fireworks algorithm.” Heidelberg, Germany: Springer 10 (2015): 978-3

Variables

Name (List[str]) – List of strings representing algorithm names.

Initialize FWA.

Parameters

• population_size (int) – Number of Fireworks

• num_sparks (int) – Number of sparks

• a (float) – Limitation of sparks

• b (float) – Limitation of sparks

• max_amplitude (float) – Initial amplitude.

• num_gaussian (int) – Number of sparks to apply gaussian mutation to.

Name = ['FireworksAlgorithm', 'FWA']

__init__(population_size=5, num_sparks=50, a=0.04, b=0.8, max_amplitude=40, num_gaussian=5, *args, **kwargs)

Initialize FWA.

Parameters

• population_size (int) – Number of Fireworks

• num_sparks (int) – Number of sparks

• a (float) – Limitation of sparks

• b (float) – Limitation of sparks

• max_amplitude (float) – Initial amplitude.

• num_gaussian (int) – Number of sparks to apply gaussian mutation to.

explosion_amplitudes(population_fitness, task=None)

Calculate explosion amplitude.

Parameters

• population_fitness (numpy.ndarray) – Population fitness values.

• task (Optional[Task]) – Optimization task (Unused in this version of the algorithm).

Returns

Explosion amplitude of sparks.

Return type

numpy.ndarray

explosion_spark(x, amplitude, task)

Explode a spark.

Parameters

• x (numpy.ndarray) – Individuals creating spark.

• amplitude (float) – Amplitude of spark.

• task (Task) – Optimization task.

Returns

Sparks exploded in with specified amplitude.

Return type

numpy.ndarray

gaussian_spark(x, task, best_x=None)

Create gaussian spark.

Parameters

• x (numpy.ndarray) – Individual creating a spark.

• task (Task) – Optimization task.

• best_x (numpy.ndarray) – Current best individual. Unused in this version of the algorithm.

Returns

Spark exploded based on gaussian amplitude.

Return type

numpy.ndarray

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get default information of algorithm.

Returns

Basic information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

mapping(x, task)

Fix value to bounds.

Parameters

• x (numpy.ndarray) – Individual to fix.

• task (Task) – Optimization task.

Returns

Individual in search range.

Return type

numpy.ndarray

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Fireworks algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray[float]) – Current populations function/fitness values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best individuals fitness/function value.

• **params (Dict[str, Any) – Additional arguments

Returns

1. Initialized population.

2. Initialized populations function/fitness values.

3. New global best solution.

4. New global best solutions fitness/objective value.

5. Additional arguments:

   • Ah (numpy.ndarray): Initialized amplitudes.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

See also

• FireworksAlgorithm.sparks_num().

• FireworksAlgorithm.explosion_amplitudes()

• FireworksAlgorithm.explosion_spark()

• FireworksAlgorithm.gaussian_spark()

• FireworksAlgorithm.selection()

selection(population, population_fitness, sparks, task)

Generate new generation of individuals.

Parameters

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray[float]) – Currents population fitness/function values.

• sparks (numpy.ndarray) – New population.

• task (Task) – Optimization task.

Returns

1. New population.

2. New populations fitness/function values.

3. New global best individual.

4. New global best fitness.

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], numpy.ndarray, float]

set_parameters(population_size=5, num_sparks=50, a=0.04, b=0.8, max_amplitude=40, num_gaussian=5, **kwargs)

Set the arguments of an algorithm.

Parameters

• population_size (int) – Number of Fireworks

• num_sparks (int) – Number of sparks

• a (float) – Limitation of sparks

• b (float) – Limitation of sparks

• max_amplitude (float) – Initial amplitude.

• num_gaussian (int) – Number of sparks to apply gaussian mutation to.

sparks_num(population_fitness)

Calculate number of sparks.

Parameters

population_fitness (numpy.ndarray) – Population fitness values.

Returns

Number of sparks that for all fireworks.

Return type

numpy.ndarray

class niapy.algorithms.basic.FishSchoolSearch(population_size=30, step_individual_init=0.1, step_individual_final=0.0001, step_volitive_init=0.01, step_volitive_final=0.001, min_w=1.0, w_scale=500.0, *args, **kwargs)

Bases: Algorithm

Implementation of Fish School Search algorithm.

Algorithm:

Fish School Search algorithm

Date:

2019

Authors:

Clodomir Santana Jr, Elliackin Figueredo, Mariana Maceds, Pedro Santos. Ported to niapy with small changes by Kristian Järvenpää (2018). Ported to niapy 2.0 by Klemen Berkovič (2019).

License:

MIT

Reference paper:

Bastos Filho, Lima Neto, Lins, D. O. Nascimento and P. Lima, “A novel search algorithm based on fish school behavior,” in 2008 IEEE International Conference on Systems, Man and Cybernetics, Oct 2008, pp. 2646–2651.

Variables

• Name (List[str]) – List of strings representing algorithm name.

• step_individual_init (float) – Length of initial individual step.

• step_individual_final (float) – Length of final individual step.

• step_volitive_init (float) – Length of initial volatile step.

• step_volitive_final (float) – Length of final volatile step.

• min_w (float) – Minimum weight of a fish.

• w_scale (float) – Maximum weight of a fish.

See also

• niapy.algorithms.algorithm.Algorithm

Initialize FishSchoolSearch.

Parameters

• population_size (Optional[int]) – Number of fishes in school.

• step_individual_init (Optional[float]) – Length of initial individual step.

• step_individual_final (Optional[float]) – Length of final individual step.

• step_volitive_init (Optional[float]) – Length of initial volatile step.

• step_volitive_final (Optional[float]) – Length of final volatile step.

• min_w (Optional[float]) – Minimum weight of a fish.

• w_scale (Optional[float]) – Maximum weight of a fish. Recommended value: max_iterations / 2

See also

• niapy.algorithms.Algorithm.__init__()

Name = ['FSS', 'FishSchoolSearch']

__init__(population_size=30, step_individual_init=0.1, step_individual_final=0.0001, step_volitive_init=0.01, step_volitive_final=0.001, min_w=1.0, w_scale=500.0, *args, **kwargs)

Initialize FishSchoolSearch.

Parameters

• population_size (Optional[int]) – Number of fishes in school.

• step_individual_init (Optional[float]) – Length of initial individual step.

• step_individual_final (Optional[float]) – Length of final individual step.

• step_volitive_init (Optional[float]) – Length of initial volatile step.

• step_volitive_final (Optional[float]) – Length of final volatile step.

• min_w (Optional[float]) – Minimum weight of a fish.

• w_scale (Optional[float]) – Maximum weight of a fish. Recommended value: max_iterations / 2

See also

• niapy.algorithms.Algorithm.__init__()

collective_instinctive_movement(school, task)

Perform collective instinctive movement.

Parameters

• school (numpy.ndarray) – Current population.

• task (Task) – Optimization task.

Returns

New population

Return type

numpy.ndarray

collective_volitive_movement(school, step_volitive, school_weight, xb, fxb, task)

Perform collective volitive movement.

Parameters

• school (numpy.ndarray) –

• step_volitive –

• school_weight –

• xb (numpy.ndarray) – Global best solution.

• fxb (float) – Global best solutions fitness/objective value.

• task (Task) – Optimization task.

Returns

1. New population.

2. New global best individual.

3. New global best fitness.

Return type

Tuple[numpy.ndarray, numpy.ndarray, float]

feeding(school)

Feed all fishes.

Parameters

school (numpy.ndarray) – Current school fish population.

Returns

New school fish population.

Return type

numpy.ndarray

get_parameters()

Get algorithm parameters.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

See also

• niapy.algorithms.Algorithm.set_parameters()

individual_movement(school, step_individual, xb, fxb, task)

Perform individual movement for each fish.

Parameters

• school (numpy.ndarray) – School fish population.

• step_individual (numpy.ndarray) – Current individual step.

• xb (numpy.ndarray) – Global best solution.

• fxb (float) – Global best solutions fitness/objective value.

• task (Task) – Optimization task.

Returns

1. New school of fishes.

2. New global best position.

3. New global best fitness.

Return type

Tuple[numpy.ndarray, numpy.ndarray, float]

static info()

Get default information of algorithm.

Returns

Basic information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize the school.

Parameters

task (Task) – Optimization task.

Returns

1. Population.

2. Population fitness.

3. Additional arguments:

   • step_individual (float): Current individual step.

   • step_volitive (float): Current volitive step.

   • school_weight (float): Current school weight.

Return type

Tuple[numpy.ndarray, numpy.ndarray, dict]

init_school(task)

Initialize fish school with uniform distribution.

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current population fitness.

• best_x (numpy.ndarray) – Current global best individual.

• best_fitness (float) – Current global best fitness.

• **params – Additional parameters.

Returns

1. New Population.

2. New Population fitness.

3. New global best individual.

4. New global best fitness.

5. Additional parameters:

   • step_individual (float): Current individual step.

   • step_volitive (float): Current volitive step.

   • school_weight (float): Current school weight.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, dict]

set_parameters(population_size=30, step_individual_init=0.1, step_individual_final=0.0001, step_volitive_init=0.01, step_volitive_final=0.001, min_w=1.0, w_scale=5000.0, **kwargs)

Set core arguments of FishSchoolSearch algorithm.

Parameters

• population_size (Optional[int]) – Number of fishes in school.

• step_individual_init (Optional[float]) – Length of initial individual step.

• step_individual_final (Optional[float]) – Length of final individual step.

• step_volitive_init (Optional[float]) – Length of initial volatile step.

• step_volitive_final (Optional[float]) – Length of final volatile step.

• min_w (Optional[float]) – Minimum weight of a fish.

• w_scale (Optional[float]) – Maximum weight of a fish. Recommended value: max_iterations / 2

See also

• niapy.algorithms.Algorithm.set_parameters()

update_steps(task)

Update step length for individual and volatile steps.

Parameters

task (Task) – Optimization task

Returns

1. New individual step.

2. New volitive step.

Return type

Tuple[numpy.ndarray, numpy.ndarray]

class niapy.algorithms.basic.FlowerPollinationAlgorithm(population_size=20, p=0.8, *args, **kwargs)

Bases: Algorithm

Implementation of Flower Pollination algorithm.

Algorithm:

Flower Pollination algorithm

Date:

2018

Authors:

Dusan Fister, Iztok Fister Jr. and Klemen Berkovič

License:

MIT

Reference paper:

Yang, Xin-She. “Flower pollination algorithm for global optimization. International conference on unconventional computing and natural computation. Springer, Berlin, Heidelberg, 2012.

References URL:

Implementation is based on the following MATLAB code: https://www.mathworks.com/matlabcentral/fileexchange/45112-flower-pollination-algorithm?requestedDomain=true

Variables

• Name (List[str]) – List of strings representing algorithm names.

• p (float) – Switch probability.

See also

• niapy.algorithms.Algorithm

Initialize FlowerPollinationAlgorithm.

Parameters

• population_size (int) – Population size.

• p (float) – Switch probability.

See also

• niapy.algorithms.Algorithm.__init__()

Name = ['FlowerPollinationAlgorithm', 'FPA']

__init__(population_size=20, p=0.8, *args, **kwargs)

Initialize FlowerPollinationAlgorithm.

Parameters

• population_size (int) – Population size.

• p (float) – Switch probability.

See also

• niapy.algorithms.Algorithm.__init__()

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get default information of algorithm.

Returns

Basic information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize population.

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of FlowerPollinationAlgorithm algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current population fitness/function values.

• best_x (numpy.ndarray) – Global best solution.

• best_fitness (float) – Global best solution function/fitness value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New population.

2. New populations fitness/function values.

3. New global best solution.

4. New global best solution fitness/objective value.

5. Additional arguments.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(population_size=25, p=0.8, **kwargs)

Set core parameters of FlowerPollinationAlgorithm algorithm.

Parameters

• population_size (int) – Population size.

• p (float) – Switch probability.

See also

• niapy.algorithms.Algorithm.set_parameters()

class niapy.algorithms.basic.ForestOptimizationAlgorithm(population_size=10, lifetime=3, area_limit=10, local_seeding_changes=1, global_seeding_changes=1, transfer_rate=0.3, *args, **kwargs)

Bases: Algorithm

Implementation of Forest Optimization Algorithm.

Algorithm:

Forest Optimization Algorithm

Date:

2019

Authors:

Luka Pečnik

License:

MIT

Reference paper:

Manizheh Ghaemi, Mohammad-Reza Feizi-Derakhshi, Forest Optimization Algorithm, Expert Systems with Applications, Volume 41, Issue 15, 2014, Pages 6676-6687, ISSN 0957-4174, https://doi.org/10.1016/j.eswa.2014.05.009.

References URL:

Implementation is based on the following MATLAB code: https://github.com/cominsys/FOA

Variables

• Name (List[str]) – List of strings representing algorithm name.

• lifetime (int) – Life time of trees parameter.

• area_limit (int) – Area limit parameter.

• local_seeding_changes (int) – Local seeding changes parameter.

• global_seeding_changes (int) – Global seeding changes parameter.

• transfer_rate (float) – Transfer rate parameter.

See also

• niapy.algorithms.Algorithm

Initialize ForestOptimizationAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• lifetime (Optional[int]) – Life time parameter.

• area_limit (Optional[int]) – Area limit parameter.

• local_seeding_changes (Optional[int]) – Local seeding changes parameter.

• global_seeding_changes (Optional[int]) – Global seeding changes parameter.

• transfer_rate (Optional[float]) – Transfer rate parameter.

See also

• niapy.algorithms.Algorithm.__init__()

Name = ['ForestOptimizationAlgorithm', 'FOA']

__init__(population_size=10, lifetime=3, area_limit=10, local_seeding_changes=1, global_seeding_changes=1, transfer_rate=0.3, *args, **kwargs)

Initialize ForestOptimizationAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• lifetime (Optional[int]) – Life time parameter.

• area_limit (Optional[int]) – Area limit parameter.

• local_seeding_changes (Optional[int]) – Local seeding changes parameter.

• global_seeding_changes (Optional[int]) – Global seeding changes parameter.

• transfer_rate (Optional[float]) – Transfer rate parameter.

See also

• niapy.algorithms.Algorithm.__init__()

get_parameters()

Get parameters values of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

global_seeding(task, candidates, size)

Global optimum search stage that should prevent getting stuck in a local optimum.

Parameters

• task (Task) – Optimization task.

• candidates (numpy.ndarray) – Candidate population for global seeding.

• size (int) – Number of trees to produce.

Returns

Resulting trees.

Return type

numpy.ndarray

static info()

Get algorithms information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize the starting population.

Parameters

task (Task) – Optimization task

Returns

1. New population.

2. New population fitness/function values.

3. Additional arguments:

   • age (numpy.ndarray[int32]): Age of trees.

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], Dict[str, Any]]

See also

• niapy.algorithms.Algorithm.init_population()

local_seeding(task, trees)

Local optimum search stage.

Parameters

• task (Task) – Optimization task.

• trees (numpy.ndarray) – Zero age trees for local seeding.

Returns

Resulting zero age trees.

Return type

numpy.ndarray

remove_lifetime_exceeded(trees, age)

Remove dead trees.

Parameters

• trees (numpy.ndarray) – Population to test.

• age (numpy.ndarray[int32]) – Age of trees.

Returns

1. Alive trees.

2. New candidate population.

3. Age of trees.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray[int32]]

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Forest Optimization Algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray[float]) – Current population function/fitness values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best individual fitness/function value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New population.

2. New population fitness/function values.

3. Additional arguments:

   • age (numpy.ndarray[int32]): Age of trees.

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], Dict[str, Any]]

set_parameters(population_size=10, lifetime=3, area_limit=10, local_seeding_changes=1, global_seeding_changes=1, transfer_rate=0.3, **kwargs)

Set the parameters of the algorithm.

Parameters

• population_size (Optional[int]) – Population size.

• lifetime (Optional[int]) – Life time parameter.

• area_limit (Optional[int]) – Area limit parameter.

• local_seeding_changes (Optional[int]) – Local seeding changes parameter.

• global_seeding_changes (Optional[int]) – Global seeding changes parameter.

• transfer_rate (Optional[float]) – Transfer rate parameter.

See also

• niapy.algorithms.Algorithm.set_parameters()

survival_of_the_fittest(task, trees, candidates, age)

Evaluate and filter current population.

Parameters

• task (Task) – Optimization task.

• trees (numpy.ndarray) – Population to evaluate.

• candidates (numpy.ndarray) – Candidate population array to be updated.

• age (numpy.ndarray[int32]) – Age of trees.

Returns

1. Trees sorted by fitness value.

2. Updated candidate population.

3. Population fitness values.

4. Age of trees

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray[float], numpy.ndarray[int32]]

class niapy.algorithms.basic.GeneticAlgorithm(population_size=25, tournament_size=5, mutation_rate=0.25, crossover_rate=0.25, selection=<function tournament_selection>, crossover=<function uniform_crossover>, mutation=<function uniform_mutation>, *args, **kwargs)

Bases: Algorithm

Implementation of Genetic Algorithm.

Algorithm:

Genetic algorithm

Date:

2018

Author:

Klemen Berkovič

Reference paper:

Goldberg, David (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Reading, MA: Addison-Wesley Professional.

License:

MIT

Variables

• Name (List[str]) – List of strings representing algorithm name.

• tournament_size (int) – Tournament size.

• mutation_rate (float) – Mutation rate.

• crossover_rate (float) – Crossover rate.

• selection (Callable[[numpy.ndarray[Individual], int, int, Individual, numpy.random.Generator], Individual]) – selection operator.

• crossover (Callable[[numpy.ndarray[Individual], int, float, numpy.random.Generator], Individual]) – Crossover operator.

• mutation (Callable[[numpy.ndarray[Individual], int, float, Task, numpy.random.Generator], Individual]) – Mutation operator.

See also

• niapy.algorithms.Algorithm

Initialize GeneticAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• tournament_size (Optional[int]) – Tournament selection.

• mutation_rate (Optional[int]) – Mutation rate.

• crossover_rate (Optional[float]) – Crossover rate.

• selection (Optional[Callable[[numpy.ndarray[Individual], int, int, Individual, numpy.random.Generator], Individual]]) – Selection operator.

• crossover (Optional[Callable[[numpy.ndarray[Individual], int, float, numpy.random.Generator], Individual]]) – Crossover operator.

• mutation (Optional[Callable[[numpy.ndarray[Individual], int, float, Task, numpy.random.Generator], Individual]]) – Mutation operator.

See also

• niapy.algorithms.Algorithm.set_parameters()

• selection:

  • niapy.algorithms.basic.tournament_selection()

  • niapy.algorithms.basic.roulette_selection()

• Crossover:

  • niapy.algorithms.basic.uniform_crossover()

  • niapy.algorithms.basic.two_point_crossover()

  • niapy.algorithms.basic.multi_point_crossover()

  • niapy.algorithms.basic.crossover_uros()

• Mutations:

  • niapy.algorithms.basic.uniform_mutation()

  • niapy.algorithms.basic.creep_mutation()

  • niapy.algorithms.basic.mutation_uros()

Name = ['GeneticAlgorithm', 'GA']

__init__(population_size=25, tournament_size=5, mutation_rate=0.25, crossover_rate=0.25, selection=<function tournament_selection>, crossover=<function uniform_crossover>, mutation=<function uniform_mutation>, *args, **kwargs)

Initialize GeneticAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• tournament_size (Optional[int]) – Tournament selection.

• mutation_rate (Optional[int]) – Mutation rate.

• crossover_rate (Optional[float]) – Crossover rate.

• selection (Optional[Callable[[numpy.ndarray[Individual], int, int, Individual, numpy.random.Generator], Individual]]) – Selection operator.

• crossover (Optional[Callable[[numpy.ndarray[Individual], int, float, numpy.random.Generator], Individual]]) – Crossover operator.

• mutation (Optional[Callable[[numpy.ndarray[Individual], int, float, Task, numpy.random.Generator], Individual]]) – Mutation operator.

See also

• niapy.algorithms.Algorithm.set_parameters()

• selection:

  • niapy.algorithms.basic.tournament_selection()

  • niapy.algorithms.basic.roulette_selection()

• Crossover:

  • niapy.algorithms.basic.uniform_crossover()

  • niapy.algorithms.basic.two_point_crossover()

  • niapy.algorithms.basic.multi_point_crossover()

  • niapy.algorithms.basic.crossover_uros()

• Mutations:

  • niapy.algorithms.basic.uniform_mutation()

  • niapy.algorithms.basic.creep_mutation()

  • niapy.algorithms.basic.mutation_uros()

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get basic information of algorithm.

Returns

Basic information of algorithm.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of GeneticAlgorithm algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current populations fitness/function values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best individuals function/fitness value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New population.

2. New populations function/fitness values.

3. New global best solution

4. New global best solutions fitness/objective value

5. Additional arguments.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(population_size=25, tournament_size=5, mutation_rate=0.25, crossover_rate=0.25, selection=<function tournament_selection>, crossover=<function uniform_crossover>, mutation=<function uniform_mutation>, **kwargs)

Set the parameters of the algorithm.

Parameters

• population_size (Optional[int]) – Population size.

• tournament_size (Optional[int]) – Tournament selection.

• mutation_rate (Optional[int]) – Mutation rate.

• crossover_rate (Optional[float]) – Crossover rate.

• selection (Optional[Callable[[numpy.ndarray[Individual], int, int, Individual, numpy.random.Generator], Individual]]) – selection operator.

• crossover (Optional[Callable[[numpy.ndarray[Individual], int, float, numpy.random.Generator], Individual]]) – Crossover operator.

• mutation (Optional[Callable[[numpy.ndarray[Individual], int, float, Task, numpy.random.Generator], Individual]]) – Mutation operator.

See also

• niapy.algorithms.Algorithm.set_parameters()

• selection:

  • niapy.algorithms.basic.tournament_selection()

  • niapy.algorithms.basic.roulette_selection()

• Crossover:

  • niapy.algorithms.basic.uniform_crossover()

  • niapy.algorithms.basic.two_point_crossover()

  • niapy.algorithms.basic.multi_point_crossover()

  • niapy.algorithms.basic.crossover_uros()

• Mutations:

  • niapy.algorithms.basic.uniform_mutation()

  • niapy.algorithms.basic.creep_mutation()

  • niapy.algorithms.basic.mutation_uros()

class niapy.algorithms.basic.GlowwormSwarmOptimization(population_size=25, l0=5, nt=5, rho=0.4, gamma=0.6, beta=0.08, s=0.03, distance=<function euclidean>, *args, **kwargs)

Bases: Algorithm

Implementation of glowworm swarm optimization.

Algorithm:

Glowworm Swarm Optimization Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

https://www.springer.com/gp/book/9783319515946

Reference paper:

Kaipa, Krishnanand N., and Debasish Ghose. Glowworm swarm optimization: theory, algorithms, and applications. Vol. 698. Springer, 2017.

Variables

• Name (List[str]) – List of strings representing algorithm name.

• l0 (float) – Initial luciferin quantity for each glowworm.

• nt (float) – Number of neighbors.

• rho (float) – Luciferin decay constant.

• gamma (float) – Luciferin enhancement constant.

• beta (float) – Constant.

• s (float) – Step size.

• distance (Callable[[numpy.ndarray, numpy.ndarray], float]]) – Measure distance between two individuals.

See also

• NiaPy.algorithms.algorithm.Algorithm

Initialize GlowwormSwarmOptimization.

Parameters

• population_size (Optional[int]) – Number of glowworms in population.

• l0 (Optional[float]) – Initial luciferin quantity for each glowworm.

• nt (Optional[int]) – Number of neighbors.

• rho (Optional[float]) – Luciferin decay constant.

• gamma (Optional[float]) – Luciferin enhancement constant.

• beta (Optional[float]) – Constant.

• s (Optional[float]) – Step size.

• distance (Optional[Callable[[numpy.ndarray, numpy.ndarray], float]]]) – Measure distance between two individuals.

Name = ['GlowwormSwarmOptimization', 'GSO']

__init__(population_size=25, l0=5, nt=5, rho=0.4, gamma=0.6, beta=0.08, s=0.03, distance=<function euclidean>, *args, **kwargs)

Initialize GlowwormSwarmOptimization.

Parameters

• population_size (Optional[int]) – Number of glowworms in population.

• l0 (Optional[float]) – Initial luciferin quantity for each glowworm.

• nt (Optional[int]) – Number of neighbors.

• rho (Optional[float]) – Luciferin decay constant.

• gamma (Optional[float]) – Luciferin enhancement constant.

• beta (Optional[float]) – Constant.

• s (Optional[float]) – Step size.

• distance (Optional[Callable[[numpy.ndarray, numpy.ndarray], float]]]) – Measure distance between two individuals.

calculate_luciferin(luciferin, fitness)

get_neighbors(i, r, glowworms, luciferin)

Get neighbours of glowworm.

Parameters

• i (int) – Index of glowworm.

• r (float) – Neighborhood distance.

• glowworms (numpy.ndarray) –

• luciferin (numpy.ndarray[float]) – Luciferin value of glowworm.

Returns

Indexes of neighborhood glowworms.

Return type

numpy.ndarray[int]

get_parameters()

Get algorithms parameters values.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get basic information of algorithm.

Returns

Basic information.

Return type

str

init_population(task)

Initialize population.

Parameters

task (Task) – Optimization task.

Returns

1. Initialized population of glowworms.

2. Initialized populations function/fitness values.

3. Additional arguments:

   • luciferin (numpy.ndarray): Luciferin values of glowworms.

   • ranges (numpy.ndarray): Ranges.

   • sensing_range (float): Sensing range.

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], Dict[str, Any]]

move_select(pb, i)

Get move index for the i-th glowworm.

Parameters

• pb (numpy.ndarray) – Probabilities.

• i (int) – Index of the glowworm.

Returns

Index i-th glowworm will move towards.

Return type

int

probabilities(i, neighbors, luciferin)

Calculate probabilities for glowworm to movement.

Parameters

• i (int) – Index of glowworm to search for probable movement.

• neighbors (numpy.ndarray[float]) –

• luciferin (numpy.ndarray[float]) –

Returns

Probabilities for each glowworm in swarm.

Return type

numpy.ndarray[float]

range_update(range_, neighbors, sensing_range)

Update range.

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of GlowwormSwarmOptimization algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current populations fitness/function values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best individuals function/fitness value.

• Dict[str (**params) – Additional arguments.

• Any] – Additional arguments.

Returns

1. Initialized population of glowworms.

2. Initialized populations function/fitness values.

3. New global best solution

4. New global best solutions fitness/objective value.

5. Additional arguments:

   • luciferin (numpy.ndarray): Luciferin values of glowworms.

   • ranges (numpy.ndarray): Ranges.

   • sensing_range (float): Sensing range.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(population_size=25, l0=5, nt=5, rho=0.4, gamma=0.6, beta=0.08, s=0.03, distance=<function euclidean>, **kwargs)

Set the arguments of an algorithm.

Parameters

• population_size (Optional[int]) – Number of glowworms in population.

• l0 (Optional[float]) – Initial luciferin quantity for each glowworm.

• nt (Optional[int]) – Number of neighbors.

• rho (Optional[float]) – Luciferin decay constant.

• gamma (Optional[float]) – Luciferin enhancement constant.

• beta (Optional[float]) – Constant.

• s (Optional[float]) – Step size.

• distance (Optional[Callable[[numpy.ndarray, numpy.ndarray], float]]]) – Measure distance between two individuals.

class niapy.algorithms.basic.GlowwormSwarmOptimizationV1(population_size=25, l0=5, nt=5, rho=0.4, gamma=0.6, beta=0.08, s=0.03, distance=<function euclidean>, *args, **kwargs)

Bases: GlowwormSwarmOptimization

Implementation of glowworm swarm optimization.

Algorithm:

Glowworm Swarm Optimization Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

https://www.springer.com/gp/book/9783319515946

Reference paper:

Kaipa, Krishnanand N., and Debasish Ghose. Glowworm swarm optimization: theory, algorithms, and applications. Vol. 698. Springer, 2017.

Variables

Name (List[str]) – List of strings representing algorithm names.

See also

• NiaPy.algorithms.basic.GlowwormSwarmOptimization

Initialize GlowwormSwarmOptimization.

Parameters

• population_size (Optional[int]) – Number of glowworms in population.

• l0 (Optional[float]) – Initial luciferin quantity for each glowworm.

• nt (Optional[int]) – Number of neighbors.

• rho (Optional[float]) – Luciferin decay constant.

• gamma (Optional[float]) – Luciferin enhancement constant.

• beta (Optional[float]) – Constant.

• s (Optional[float]) – Step size.

• distance (Optional[Callable[[numpy.ndarray, numpy.ndarray], float]]]) – Measure distance between two individuals.

Name = ['GlowwormSwarmOptimizationV1', 'GSOv1']

calculate_luciferin(luciferin, fitness)

static info()

Get basic information of algorithm.

Returns

Basic information.

Return type

str

range_update(range_, neighbors, sensing_range)

Update range.

class niapy.algorithms.basic.GlowwormSwarmOptimizationV2(alpha=0.2, *args, **kwargs)

Bases: GlowwormSwarmOptimization

Implementation of glowworm swarm optimization.

Algorithm:

Glowworm Swarm Optimization Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

https://www.springer.com/gp/book/9783319515946

Reference paper:

Kaipa, Krishnanand N., and Debasish Ghose. Glowworm swarm optimization: theory, algorithms, and applications. Vol. 698. Springer, 2017.

Variables

• Name (List[str]) – List of strings representing algorithm names.

• alpha (float) –

  –

See also

• NiaPy.algorithms.basic.GlowwormSwarmOptimization

Initialize GlowwormSwarmOptimizationV2.

Parameters

alpha (Optional[float]) – Alpha parameter.

Name = ['GlowwormSwarmOptimizationV2', 'GSOv2']

__init__(alpha=0.2, *args, **kwargs)

Initialize GlowwormSwarmOptimizationV2.

Parameters

alpha (Optional[float]) – Alpha parameter.

static info()

Get basic information of algorithm.

Returns

Basic information.

Return type

str

range_update(range_, neighbors, sensing_range)

Update range.

set_parameters(alpha=0.2, **kwargs)

Set core parameters for GlowwormSwarmOptimizationV2 algorithm.

Parameters

alpha (Optional[float]) – Alpha parameter.

See also

• NiaPy.algorithms.basic.GlowwormSwarmOptimization.set_parameters()

class niapy.algorithms.basic.GlowwormSwarmOptimizationV3(beta1=0.2, *args, **kwargs)

Bases: GlowwormSwarmOptimization

Implementation of glowworm swarm optimization.

Algorithm:

Glowworm Swarm Optimization Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

https://www.springer.com/gp/book/9783319515946

Reference paper:

Kaipa, Krishnanand N., and Debasish Ghose. Glowworm swarm optimization: theory, algorithms, and applications. Vol. 698. Springer, 2017.

Variables

• Name (List[str]) – List of strings representing algorithm names.

• beta1 (float) –

  –

See also

• NiaPy.algorithms.basic.GlowwormSwarmOptimization

Initialize GlowwormSwarmOptimizationV3.

Parameters

beta1 (Optional[float]) – Beta1 parameter.

Name = ['GlowwormSwarmOptimizationV3', 'GSOv3']

__init__(beta1=0.2, *args, **kwargs)

Initialize GlowwormSwarmOptimizationV3.

Parameters

beta1 (Optional[float]) – Beta1 parameter.

static info()

Get basic information of algorithm.

Returns

Basic information.

Return type

str

range_update(range_, neighbors, sensing_range)

Update range.

set_parameters(beta1=0.2, **kwargs)

Set core parameters for GlowwormSwarmOptimizationV3 algorithm.

Parameters

beta1 (Optional[float]) – Beta1 parameter.

See also

• NiaPy.algorithms.basic.GlowwormSwarmOptimization.set_parameters()

class niapy.algorithms.basic.GravitationalSearchAlgorithm(population_size=40, g0=2.467, epsilon=1e-17, *args, **kwargs)

Bases: Algorithm

Implementation of Gravitational Search Algorithm.

Algorithm:

Gravitational Search Algorithm

Date:

2018

Author:

Klemen Berkovič

License:

MIT

Reference URL:

https://doi.org/10.1016/j.ins.2009.03.004

Reference paper:

Esmat Rashedi, Hossein Nezamabadi-pour, Saeid Saryazdi, GSA: A Gravitational Search Algorithm, Information Sciences, Volume 179, Issue 13, 2009, Pages 2232-2248, ISSN 0020-0255

Variables

Name (List[str]) – List of strings representing algorithm name.

See also

• niapy.algorithms.algorithm.Algorithm

Initialize GravitationalSearchAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• g0 (Optional[float]) – Starting gravitational constant.

• epsilon (Optional[float]) – Small number.

See also

• niapy.algorithms.algorithm.Algorithm.__init__()

Name = ['GravitationalSearchAlgorithm', 'GSA']

__init__(population_size=40, g0=2.467, epsilon=1e-17, *args, **kwargs)

Initialize GravitationalSearchAlgorithm.

Parameters

• population_size (Optional[int]) – Population size.

• g0 (Optional[float]) – Starting gravitational constant.

• epsilon (Optional[float]) – Small number.

See also

• niapy.algorithms.algorithm.Algorithm.__init__()

get_parameters()

Get algorithm parameters values.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

See also

• niapy.algorithms.algorithm.Algorithm.get_parameters()

gravity(t)

Get new gravitational constant.

Parameters

t (int) – Time (Current iteration).

Returns

New gravitational constant.

Return type

float

static info()

Get algorithm information.

Returns

Algorithm information.

Return type

str

init_population(task)

Initialize staring population.

Parameters

task (Task) – Optimization task.

Returns

1. Initialized population.

2. Initialized populations fitness/function values.

3. Additional arguments:

   • velocities (numpy.ndarray[float]): Velocities

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], Dict[str, Any]]

See also

• niapy.algorithms.algorithm.Algorithm.init_population()

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of GravitationalSearchAlgorithm algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current populations fitness/function values.

• best_x (numpy.ndarray) – Global best solution.

• best_fitness (float) – Global best fitness/function value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New population.

2. New populations fitness/function values.

3. New global best solution

4. New global best solutions fitness/objective value

5. Additional arguments:

   • velocities (numpy.ndarray): Velocities.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(population_size=40, g0=2.467, epsilon=1e-17, **kwargs)

Set the algorithm parameters.

Parameters

• population_size (Optional[int]) – Population size.

• g0 (Optional[float]) – Starting gravitational constant.

• epsilon (Optional[float]) – Small number.

See also

• niapy.algorithms.algorithm.Algorithm.set_parameters()

class niapy.algorithms.basic.GreyWolfOptimizer(population_size=50, initialization_function=<function default_numpy_init>, individual_type=None, seed=None, *args, **kwargs)

Bases: Algorithm

Implementation of Grey wolf optimizer.

Algorithm:

Grey wolf optimizer

Date:

2018

Author:

Iztok Fister Jr. and Klemen Berkovič

License:

MIT

Reference paper:

• Mirjalili, Seyedali, Seyed Mohammad Mirjalili, and Andrew Lewis. “Grey wolf optimizer.” Advances in engineering software 69 (2014): 46-61.

• Grey Wolf Optimizer (GWO) source code version 1.0 (MATLAB) from MathWorks

Variables

Name (List[str]) – List of strings representing algorithm names.

See also

• niapy.algorithms.Algorithm

Initialize algorithm and create name for an algorithm.

Parameters

• population_size (Optional[int]) – Population size.

• initialization_function (Optional[Callable[[int, Task, numpy.random.Generator, Dict[str, Any]], Tuple[numpy.ndarray, numpy.ndarray[float]]]]) – Population initialization function.

• individual_type (Optional[Type[Individual]]) – Individual type used in population, default is Numpy array.

• seed (Optional[int]) – Starting seed for random generator.

See also

• niapy.algorithms.Algorithm.set_parameters()

Name = ['GreyWolfOptimizer', 'GWO']

static info()

Get algorithm information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize population.

Parameters

task (Task) – Optimization task.

Returns

1. Initialized population.

2. Initialized populations fitness/function values.

3. Additional arguments:

   • alpha (numpy.ndarray): Alpha of the pack (Best solution)

   • alpha_fitness (float): Best fitness.

   • beta (numpy.ndarray): Beta of the pack (Second best solution)

   • beta_fitness (float): Second best fitness.

   • delta (numpy.ndarray): Delta of the pack (Third best solution)

   • delta_fitness (float): Third best fitness.

Return type

Tuple[numpy.ndarray, numpy.ndarray, Dict[str, Any]]

See also

• niapy.algorithms.Algorithm.init_population()

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of GreyWolfOptimizer algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current populations function/fitness values.

• best_x (numpy.ndarray) –

• best_fitness (float) –

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New population

2. New population fitness/function values

3. Additional arguments:

   • alpha (numpy.ndarray): Alpha of the pack (Best solution)

   • alpha_fitness (float): Best fitness.

   • beta (numpy.ndarray): Beta of the pack (Second best solution)

   • beta_fitness (float): Second best fitness.

   • delta (numpy.ndarray): Delta of the pack (Third best solution)

   • delta_fitness (float): Third best fitness.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

class niapy.algorithms.basic.HarmonySearch(population_size=30, r_accept=0.7, r_pa=0.35, b_range=1.42, *args, **kwargs)

Bases: Algorithm

Implementation of Harmony Search algorithm.

Algorithm:

Harmony Search Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

https://journals.sagepub.com/doi/10.1177/003754970107600201

Reference paper:

Geem, Z. W., Kim, J. H., & Loganathan, G. V. (2001). A new heuristic optimization algorithm: harmony search. Simulation, 76(2), 60-68.

Variables

• Name (List[str]) – List of strings representing algorithm names

• r_accept (float) – Probability of accepting new bandwidth into harmony.

• r_pa (float) – Probability of accepting random bandwidth into harmony.

• b_range (float) – Range of bandwidth.

See also

• niapy.algorithms.algorithm.Algorithm

Initialize HarmonySearch.

Parameters

• population_size (Optional[int]) – Number of harmony in the memory.

• r_accept (Optional[float]) – Probability of accepting new bandwidth to harmony.

• r_pa (Optional[float]) – Probability of accepting random bandwidth into harmony.

• b_range (Optional[float]) – Bandwidth range.

Name = ['HarmonySearch', 'HS']

__init__(population_size=30, r_accept=0.7, r_pa=0.35, b_range=1.42, *args, **kwargs)

Initialize HarmonySearch.

Parameters

• population_size (Optional[int]) – Number of harmony in the memory.

• r_accept (Optional[float]) – Probability of accepting new bandwidth to harmony.

• r_pa (Optional[float]) – Probability of accepting random bandwidth into harmony.

• b_range (Optional[float]) – Bandwidth range.

adjustment(x, task)

Adjust value based on bandwidth.

Parameters

• x (Union[int, float]) – Current position.

• task (Task) – Optimization task.

Returns

New position.

Return type

float

bw(task)

Get bandwidth.

Parameters

task (Task) – Optimization task.

Returns

Bandwidth.

Return type

float

get_parameters()

Get algorithm parameters.

improvise(harmonies, task)

Create new individual.

Parameters

• harmonies (numpy.ndarray) – Current population.

• task (Task) – Optimization task.

Returns

New individual.

Return type

numpy.ndarray

static info()

Get basic information about the algorithm.

Returns

Basic information.

Return type

str

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of HarmonySearch algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray) – Current populations function/fitness values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best fitness/function value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New harmony/population.

2. New populations function/fitness values.

3. New global best solution

4. New global best solution fitness/objective value

5. Additional arguments.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(population_size=30, r_accept=0.7, r_pa=0.35, b_range=1.42, **kwargs)

Set the arguments of the algorithm.

Parameters

• population_size (Optional[int]) – Number of harmony in the memory.

• r_accept (Optional[float]) – Probability of accepting new bandwidth to harmony.

• r_pa (Optional[float]) – Probability of accepting random bandwidth into harmony.

• b_range (Optional[float]) – Bandwidth range.

See also

• niapy.algorithms.algorithm.Algorithm.set_parameters()

class niapy.algorithms.basic.HarmonySearchV1(bw_min=1, bw_max=2, *args, **kwargs)

Bases: HarmonySearch

Implementation of harmony search algorithm.

Algorithm:

Harmony Search Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

https://link.springer.com/chapter/10.1007/978-3-642-00185-7_1

Reference paper:

Yang, Xin-She. “Harmony search as a metaheuristic algorithm.” Music-inspired harmony search algorithm. Springer, Berlin, Heidelberg, 2009. 1-14.

Variables

• Name (List[str]) – List of strings representing algorithm name.

• bw_min (float) – Minimal bandwidth.

• bw_max (float) – Maximal bandwidth.

See also

• niapy.algorithms.basic.hs.HarmonySearch

Initialize HarmonySearchV1.

Parameters

• bw_min (Optional[float]) – Minimal bandwidth.

• bw_max (Optional[float]) – Maximal bandwidth.

Name = ['HarmonySearchV1', 'HSv1']

__init__(bw_min=1, bw_max=2, *args, **kwargs)

Initialize HarmonySearchV1.

Parameters

• bw_min (Optional[float]) – Minimal bandwidth.

• bw_max (Optional[float]) – Maximal bandwidth.

bw(task)

Get new bandwidth.

Parameters

task (Task) – Optimization task.

Returns

New bandwidth.

Return type

float

get_parameters()

Get algorithm parameters.

static info()

Get basic information about algorithm.

Returns

Basic information.

Return type

str

set_parameters(bw_min=1, bw_max=2, **kwargs)

Set the parameters of the algorithm.

Parameters

• bw_min (Optional[float]) – Minimal bandwidth

• bw_max (Optional[float]) – Maximal bandwidth

See also

• niapy.algorithms.basic.hs.HarmonySearch.set_parameters()

class niapy.algorithms.basic.HarrisHawksOptimization(population_size=40, levy=0.01, *args, **kwargs)

Bases: Algorithm

Implementation of Harris Hawks Optimization algorithm.

Algorithm:

Harris Hawks Optimization

Date:

2020

Authors:

Francisco Jose Solis-Munoz

License:

MIT

Reference paper:

Heidari et al. “Harris hawks optimization: Algorithm and applications”. Future Generation Computer Systems. 2019. Vol. 97. 849-872.

Variables

• Name (List[str]) – List of strings representing algorithm name.

• levy (float) – Levy factor.

See also

• niapy.algorithms.Algorithm

Initialize HarrisHawksOptimization.

Parameters

• population_size (Optional[int]) – Population size.

• levy (Optional[float]) – Levy factor.

Name = ['HarrisHawksOptimization', 'HHO']

__init__(population_size=40, levy=0.01, *args, **kwargs)

Initialize HarrisHawksOptimization.

Parameters

• population_size (Optional[int]) – Population size.

• levy (Optional[float]) – Levy factor.

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get algorithms information.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Harris Hawks Optimization.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population

• population_fitness (numpy.ndarray[float]) – Current population fitness/function values

• best_x (numpy.ndarray) – Current best individual

• best_fitness (float) – Current best individual function/fitness value

• params (Dict[str, Any]) – Additional algorithm arguments

Returns

1. New population

2. New population fitness/function values

3. New global best solution

4. New global best fitness/objective value

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(population_size=40, levy=0.01, **kwargs)

Set the parameters of the algorithm.

Parameters

• population_size (Optional[int]) – Population size.

• levy (Optional[float]) – Levy factor.

See also

• niapy.algorithms.Algorithm.set_parameters()

class niapy.algorithms.basic.KrillHerd(population_size=50, n_max=0.01, foraging_speed=0.02, diffusion_speed=0.002, c_t=0.93, w_neighbor=0.42, w_foraging=0.38, d_s=2.63, max_neighbors=5, crossover_rate=0.2, mutation_rate=0.05, *args, **kwargs)

Bases: Algorithm

Implementation of krill herd algorithm.

Algorithm:

Krill Herd Algorithm

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

http://www.sciencedirect.com/science/article/pii/S1007570412002171

Reference paper:

Amir Hossein Gandomi, Amir Hossein Alavi, Krill herd: A new bio-inspired optimization algorithm, Communications in Nonlinear Science and Numerical Simulation, Volume 17, Issue 12, 2012, Pages 4831-4845, ISSN 1007-5704, https://doi.org/10.1016/j.cnsns.2012.05.010.

Variables

• Name (List[str]) – List of strings representing algorithm names.

• population_size (Optional[int]) – Number of krill herds in population.

• n_max (Optional[float]) – Maximum induced speed.

• foraging_speed (Optional[float]) – Foraging speed.

• diffusion_speed (Optional[float]) – Maximum diffusion speed.

• c_t (Optional[float]) – Constant $in [0, 2]$.

• w_neighbor (Optional[Union[int, float, numpy.ndarray]]) – Inertia weights of the motion induced from neighbors \(\in [0, 1]\).

• w_foraging (Optional[Union[int, float, numpy.ndarray]]) – Inertia weights of the motion induced from foraging \(\in [0, 1]\).

• d_s (Optional[float]) – Maximum euclidean distance for neighbors.

• max_neighbors (Optional[int]) – Maximum neighbors for neighbors effect.

• crossover_rate (Optional[float]) – Crossover probability.

• mutation_rate (Optional[float]) – Mutation probability.

See also

• niapy.algorithms.algorithm.Algorithm

Initialize KrillHerd.

Parameters

• population_size (Optional[int]) – Number of krill herds in population.

• n_max (Optional[float]) – Maximum induced speed.

• foraging_speed (Optional[float]) – Foraging speed.

• diffusion_speed (Optional[float]) – Maximum diffusion speed.

• c_t (Optional[float]) – Constant $in [0, 2]$.

• w_neighbor (Optional[Union[int, float, numpy.ndarray]]) – Inertia weights of the motion induced from neighbors \(\in [0, 1]\).

• w_foraging (Optional[Union[int, float, numpy.ndarray]]) – Inertia weights of the motion induced from foraging \(\in [0, 1]\).

• d_s (Optional[float]) – Maximum euclidean distance for neighbors.

• max_neighbors (Optional[int]) – Maximum neighbors for neighbors effect.

• cr (Optional[float]) – Crossover probability.

• mutation_rate (Optional[float]) – Mutation probability.

See also

• niapy.algorithms.algorithm.Algorithm.__init__()

Name = ['KrillHerd', 'KH']

__init__(population_size=50, n_max=0.01, foraging_speed=0.02, diffusion_speed=0.002, c_t=0.93, w_neighbor=0.42, w_foraging=0.38, d_s=2.63, max_neighbors=5, crossover_rate=0.2, mutation_rate=0.05, *args, **kwargs)

Initialize KrillHerd.

Parameters

• population_size (Optional[int]) – Number of krill herds in population.

• n_max (Optional[float]) – Maximum induced speed.

• foraging_speed (Optional[float]) – Foraging speed.

• diffusion_speed (Optional[float]) – Maximum diffusion speed.

• c_t (Optional[float]) – Constant $in [0, 2]$.

• w_neighbor (Optional[Union[int, float, numpy.ndarray]]) – Inertia weights of the motion induced from neighbors \(\in [0, 1]\).

• w_foraging (Optional[Union[int, float, numpy.ndarray]]) – Inertia weights of the motion induced from foraging \(\in [0, 1]\).

• d_s (Optional[float]) – Maximum euclidean distance for neighbors.

• max_neighbors (Optional[int]) – Maximum neighbors for neighbors effect.

• cr (Optional[float]) – Crossover probability.

• mutation_rate (Optional[float]) – Mutation probability.

See also

• niapy.algorithms.algorithm.Algorithm.__init__()

crossover(x, xo, crossover_rate)

Crossover operator.

Parameters

• x (numpy.ndarray) – Krill/individual being applied with operator.

• xo (numpy.ndarray) – Krill/individual being used in conjunction within operator.

• crossover_rate (float) – Crossover probability.

Returns

New krill/individual.

Return type

numpy.ndarray

crossover_rate(xf, yf, xf_best, xf_worst)

Get crossover probability.

Parameters

• xf (float) –

• yf (float) –

• xf_best (float) –

• xf_worst (float) –

Returns

New crossover probability.

Return type

float

delta_t(task)

Get new delta for all dimensions.

Parameters

task (Task) – Optimization task.

Returns

–

Return type

numpy.ndarray

get_food_location(population, population_fitness, task)

Get food location for krill heard.

Parameters

• population (numpy.ndarray) – Current heard/population.

• population_fitness (numpy.ndarray[float]) – Current heard/populations function/fitness values.

• task (Task) – Optimization task.

Returns

1. Location of food.

2. Foods function/fitness value.

Return type

Tuple[numpy.ndarray, float]

get_k(x, y, b, w)

Get k values.

Parameters

• x (float) – First krill/individual.

• y (float) – Second krill/individual.

• b (float) – Best krill/individual.

• w (float) – Worst krill/individual.

Returns

Return type

numpy.ndarray

get_neighbours(i, ids, population)

Get neighbours.

Parameters

• i (int) – Individual looking for neighbours.

• ids (float) – Maximal distance for being a neighbour.

• population (numpy.ndarray) – Current population.

Returns

Neighbours of krill heard.

Return type

numpy.ndarray

get_parameters()

Get parameter values for the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

get_x(x, y)

Get x values.

Parameters

• x (numpy.ndarray) – First krill/individual.

• y (numpy.ndarray) – Second krill/individual.

Returns

–

Return type

numpy.ndarray

induce_foraging_motion(i, x, x_f, f, weights, population, population_fitness, best_index, worst_index, task)

Induced foraging motion operator.

Parameters

• i (int) – Index of current krill being operated.

• x (numpy.ndarray) – Position of food.

• x_f (float) – Fitness/function values of food.

• f –

• weights (numpy.ndarray[float]) – Weights for this operator.

• population (numpy.ndarray) – Current population/heard.

• population_fitness (numpy.ndarray[float]) – Current heard/populations function/fitness values.

• best_index (numpy.ndarray) – Index of current best krill in heard.

• worst_index (numpy.ndarray) – Index of current worst krill in heard.

• task (Task) – Optimization task.

Returns

Moved krill.

Return type

numpy.ndarray

induce_neighbors_motion(i, n, weights, population, population_fitness, best_index, worst_index, task)

Induced neighbours motion operator.

Parameters

• i (int) – Index of individual being applied with operator.

• n –

• weights (numpy.ndarray[float]) – Weights for this operator.

• population (numpy.ndarray) – Current heard/population.

• population_fitness (numpy.ndarray[float]) – Current populations/heard function/fitness values.

• best_index (numpy.ndarray) – Current best krill in heard/population.

• worst_index (numpy.ndarray) – Current worst krill in heard/population.

• task (Task) – Optimization task.

Returns

Moved krill.

Return type

numpy.ndarray

induce_physical_diffusion(task)

Induced physical diffusion operator.

Parameters

task (Task) – Optimization task.

Return type

numpy.ndarray

static info()

Get basic information of algorithm.

Returns

Basic information of algorithm.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize stating population.

Parameters

task (Task) – Optimization task.

Returns

1. Initialized population.

2. Initialized populations function/fitness values.

3. Additional arguments:

   • w_neighbor (numpy.ndarray): Weights neighborhood.

   • w_foraging (numpy.ndarray): Weights foraging.

   • induced_speed (numpy.ndarray): Induced speed.

   • foraging_speed (numpy.ndarray): Foraging speed.

Return type

Tuple[numpy.ndarray, numpy.ndarray, Dict[str, Any]]

See also

• niapy.algorithms.algorithm.Algorithm.init_population()

init_weights(task)

Initialize weights.

Parameters

task (Task) – Optimization task.

Returns

1. Weights for neighborhood.

2. Weights for foraging.

Return type

Tuple[numpy.ndarray, numpy.ndarray]

mutate(x, x_b, mutation_rate)

Mutate operator.

Parameters

• x (numpy.ndarray) – Individual being mutated.

• x_b (numpy.ndarray) – Global best individual.

• mutation_rate (float) – Probability of mutations.

Returns

Mutated krill.

Return type

numpy.ndarray

mutation_rate(xf, yf, xf_best, xf_worst)

Get mutation probability.

Parameters

• xf (float) –

• yf (float) –

• xf_best (float) –

• xf_worst (float) –

Returns

New mutation probability.

Return type

float

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of KrillHerd algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current heard/population.

• population_fitness (numpy.ndarray[float]) – Current heard/populations function/fitness values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best individuals function fitness values.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New herd/population

2. New herd/populations function/fitness values.

3. New global best solution.

4. New global best solutions fitness/objective value.

5. Additional arguments:

   • w_neighbor (numpy.ndarray): –

   • w_foraging (numpy.ndarray): –

   • induced_speed (numpy.ndarray): –

   • foraging_speed (numpy.ndarray): –

Return type

Tuple [numpy.ndarray, numpy.ndarray, numpy.ndarray, float Dict[str, Any]]

sense_range(ki, population)

Calculate sense range for selected individual.

Parameters

• ki (int) – Selected individual.

• population (numpy.ndarray) – Krill heard population.

Returns

Sense range for krill.

Return type

float

set_parameters(population_size=50, n_max=0.01, foraging_speed=0.02, diffusion_speed=0.002, c_t=0.93, w_neighbor=0.42, w_foraging=0.38, d_s=2.63, max_neighbors=5, crossover_rate=0.2, mutation_rate=0.05, **kwargs)

Set the arguments of an algorithm.

Parameters

• population_size (Optional[int]) – Number of krill herds in population.

• n_max (Optional[float]) – Maximum induced speed.

• foraging_speed (Optional[float]) – Foraging speed.

• diffusion_speed (Optional[float]) – Maximum diffusion speed.

• c_t (Optional[float]) – Constant $in [0, 2]$.

• w_neighbor (Optional[Union[int, float, numpy.ndarray]]) – Inertia weights of the motion induced from neighbors \(\in [0, 1]\).

• w_foraging (Optional[Union[int, float, numpy.ndarray]]) – Inertia weights of the motion induced from foraging \(\in [0, 1]\).

• d_s (Optional[float]) – Maximum euclidean distance for neighbors.

• max_neighbors (Optional[int]) – Maximum neighbors for neighbors effect.

• crossover_rate (Optional[float]) – Crossover probability.

• mutation_rate (Optional[float]) – Mutation probability.

See also

• niapy.algorithms.algorithm.Algorithm.set_parameters()

class niapy.algorithms.basic.LionOptimizationAlgorithm(population_size=50, nomad_ratio=0.2, num_of_prides=5, female_ratio=0.8, roaming_factor=0.2, mating_factor=0.3, mutation_factor=0.2, immigration_factor=0.4, *args, **kwargs)

Bases: Algorithm

Implementation of lion optimization algorithm.

Algorithm:

Lion Optimization algorithm

Date:

2021

Authors:

Aljoša Mesarec

License:

MIT

Reference URL:

https://doi.org/10.1016/j.jcde.2015.06.003

Reference paper:

Yazdani, Maziar, Jolai, Fariborz. Lion Optimization Algorithm (LOA): A nature-inspired metaheuristic algorithm. Journal of Computational Design and Engineering, Volume 3, Issue 1, Pages 24-36. 2016.

Variables

• Name (List[str]) – List of strings representing name of the algorithm.

• population_size (Optional[int]) – Population size \(\in [1, \infty)\).

• nomad_ratio (Optional[float]) – Ratio of nomad lions \(\in [0, 1]\).

:ivar num_of_prides = Number of prides \(\in [1, \infty)\).: :ivar female_ratio = Ratio of female lions in prides \(\in [0, 1]\).: :ivar roaming_factor = Roaming factor \(\in [0, 1]\).: :ivar mating_factor = Mating factor \(\in [0, 1]\).: :ivar mutation_factor = Mutation factor \(\in [0, 1]\).: :ivar immigration_factor = Immigration factor \(\in [0, 1]\).:

See also

• niapy.algorithms.Algorithm

Initialize LionOptimizationAlgorithm.

Parameters

• population_size (Optional[int]) – Population size \(\in [1, \infty)\).

• nomad_ratio (Optional[float]) – Ratio of nomad lions \(\in [0, 1]\).

:param num_of_prides = Number of prides \(\in [1: :param \infty)\).: :param female_ratio = Ratio of female lions in prides \(\in [0: :param 1]\).: :param roaming_factor = Roaming factor \(\in [0: :param 1]\).: :param mating_factor = Mating factor \(\in [0: :param 1]\).: :param mutation_factor = Mutation factor \(\in [0: :param 1]\).: :param immigration_factor = Immigration factor \(\in [0: :param 1]\).:

See also

• niapy.algorithms.Algorithm.__init__()

Name = ['LionOptimizationAlgorithm', 'LOA']

__init__(population_size=50, nomad_ratio=0.2, num_of_prides=5, female_ratio=0.8, roaming_factor=0.2, mating_factor=0.3, mutation_factor=0.2, immigration_factor=0.4, *args, **kwargs)

Initialize LionOptimizationAlgorithm.

Parameters

• population_size (Optional[int]) – Population size \(\in [1, \infty)\).

• nomad_ratio (Optional[float]) – Ratio of nomad lions \(\in [0, 1]\).

:param num_of_prides = Number of prides \(\in [1: :param \infty)\).: :param female_ratio = Ratio of female lions in prides \(\in [0: :param 1]\).: :param roaming_factor = Roaming factor \(\in [0: :param 1]\).: :param mating_factor = Mating factor \(\in [0: :param 1]\).: :param mutation_factor = Mutation factor \(\in [0: :param 1]\).: :param immigration_factor = Immigration factor \(\in [0: :param 1]\).:

See also

• niapy.algorithms.Algorithm.__init__()

data_correction(population, pride_size, task)

Update lion’s data if his position has improved since last iteration.

Parameters

• population (numpy.ndarray[Lion]) – Lion population.

• pride_size (numpy.ndarray[int]) – Pride and nomad sizes.

• task (Task) – Optimization task.

Returns

Lion population with corrected data.

Return type

population (numpy.ndarray[Lion])

defense(population, pride_size, gender_distribution, excess_lion_gender_quantities, task)

Male lions attack other lions in pride.

Parameters

• population (numpy.ndarray[Lion]) – Lion population.

• pride_size (numpy.ndarray[int]) – Pride and nomad sizes.

• gender_distribution (numpy.ndarray[int]) – Pride and nomad gender distribution.

• excess_lion_gender_quantities (numpy.ndarray[int]) – Pride and nomad excess members.

• task (Task) – Optimization task.

Returns

1. Lion population that finished with defending.

2. Pride and nomad excess gender quantities.

Return type

Tuple[numpy.ndarray[Lion], numpy.ndarray[int])

get_parameters()

Get parameters of the algorithm.

Returns

Algorithm Parameters.

Return type

Dict[str, Any]

hunting(population, pride_size, task)

Pride female hunters go hunting.

Parameters

• population (numpy.ndarray[Lion]) – Lion population.

• pride_size (numpy.ndarray[int]) – Pride and nomad sizes.

• task (Task) – Optimization task.

Returns

Lion population that finished with hunting.

Return type

population (numpy.ndarray[Lion])

static info()

Get information about algorithm.

Returns

Algorithm information

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Initialize starting population.

Parameters

task (Task) – Optimization task.

Returns

1. Initialized population of lions.

2. Initialized populations function/fitness values.

3. Additional arguments:

   • pride_size (numpy.ndarray): Pride and nomad sizes.

   • gender_distribution (numpy.ndarray): Pride and nomad gender distributions.

Return type

Tuple[numpy.ndarray[Lion], numpy.ndarray[float], Dict[str, Any]]

init_population_data(pop, d)

Initialize data of starting population.

Parameters

• (numpy.ndarray[Lion] (pop) – Starting lion population

• d (Dict[str, Any]) – Additional arguments

Returns

1. Initialized population of lions.

2. Additional arguments:

   • pride_size (numpy.ndarray): Pride and nomad sizes.

   • gender_distribution (numpy.ndarray): Pride and nomad gender distributions.

Return type

Tuple[numpy.ndarray[Lion], Dict[str, Any]]

mating(population, pride_size, gender_distribution, task)

Female lions mate with male lions to produce offspring.

Parameters

• population (numpy.ndarray[Lion]) – Lion population.

• pride_size (numpy.ndarray[int]) – Pride and nomad sizes.

• gender_distribution (numpy.ndarray[int]) – Pride and nomad gender distribution.

• task (Task) – Optimization task.

Returns

1. Lion population that finished with mating.

2. Pride and nomad excess gender quantities.

Return type

Tuple[numpy.ndarray[Lion], numpy.ndarray[int])

migration(population, pride_size, gender_distribution, excess_lion_gender_quantities, task)

Female lions randomly become nomad.

Parameters

• population (numpy.ndarray[Lion]) – Lion population.

• pride_size (numpy.ndarray[int]) – Pride and nomad sizes.

• gender_distribution (numpy.ndarray[int]) – Pride and nomad gender distribution.

• excess_lion_gender_quantities (numpy.ndarray[int]) – Pride and nomad excess members.

• task (Task) – Optimization task.

Returns

1. Lion population that finished with migration.

2. Pride and nomad excess gender quantities.

Return type

Tuple[numpy.ndarray[Lion], numpy.ndarray[int])

move_to_safe_place(population, pride_size, task)

Female pride lions move towards position with good fitness.

Parameters

• population (numpy.ndarray[Lion]) – Lion population.

• pride_size (numpy.ndarray[int]) – Pride and nomad sizes.

• task (Task) – Optimization task.

Returns

Lion population that finished with moving to safe place.

Return type

population (numpy.ndarray[Lion])

population_equilibrium(population, pride_size, gender_distribution, excess_lion_gender_quantities, task)

Remove extra nomad lions.

Parameters

• population (numpy.ndarray[Lion]) – Lion population.

• pride_size (numpy.ndarray[int]) – Pride and nomad sizes.

• gender_distribution (numpy.ndarray[int]) – Pride and nomad gender distribution.

• excess_lion_gender_quantities (numpy.ndarray[int]) – Pride and nomad excess members.

• task (Task) – Optimization task.

Returns

Lion population with removed extra nomads.

Return type

final_population (numpy.ndarray[Lion])

roaming(population, pride_size, task)

Male lions move towards new position.

Parameters

• population (numpy.ndarray[Lion]) – Lion population.

• pride_size (numpy.ndarray[int]) – Pride and nomad sizes.

• task (Task) – Optimization task.

Returns

Lion population that finished with roaming.

Return type

population (numpy.ndarray[Lion])

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core functionality of algorithm.

This function is called on every algorithm iteration.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population coordinates.

• population_fitness (numpy.ndarray) – Current population fitness value.

• best_x (numpy.ndarray) – Current generation best individuals coordinates.

• best_fitness (float) – current generation best individuals fitness value.

• **params (Dict[str, Any]) – Additional arguments for algorithms.

Returns

1. New populations coordinates.

2. New populations fitness values.

3. New global best position/solution

4. New global best fitness/objective value

5. Additional arguments of the algorithm.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

See also

• niapy.algorithms.Algorithm.iteration_generator()

set_parameters(population_size=50, nomad_ratio=0.2, num_of_prides=5, female_ratio=0.8, roaming_factor=0.2, mating_factor=0.3, mutation_factor=0.2, immigration_factor=0.4, **kwargs)

Set the arguments of an algorithm.

Parameters

• population_size (Optional[int]) – Population size \(\in [1, \infty)\).

• nomad_ratio (Optional[float]) – Ratio of nomad lions \(\in [0, 1]\).

:param num_of_prides = Number of prides \(\in [1: :param \infty)\).: :param female_ratio = Ratio of female lions in prides \(\in [0: :param 1]\).: :param roaming_factor = Roaming factor \(\in [0: :param 1]\).: :param mating_factor = Mating factor \(\in [0: :param 1]\).: :param mutation_factor = Mutation factor \(\in [0: :param 1]\).: :param immigration_factor = Immigration factor \(\in [0: :param 1]\).:

See also

• niapy.algorithms.Algorithm.set_parameters()

class niapy.algorithms.basic.MonarchButterflyOptimization(population_size=20, partition=0.4166666666666667, period=1.2, *args, **kwargs)

Bases: Algorithm

Implementation of Monarch Butterfly Optimization.

Algorithm:

Monarch Butterfly Optimization

Date:

2019

Authors:

Jan Banko

License:

MIT

Reference paper:

Wang, G. G., Deb, S., & Cui, Z. (2019). Monarch butterfly optimization. Neural computing and applications, 31(7), 1995-2014.

Variables

• Name (List[str]) – List of strings representing algorithm name.

• PAR (float) – Partition.

• PER (float) – Period.

See also

• niapy.algorithms.Algorithm

Initialize MonarchButterflyOptimization.

Parameters

• population_size (Optional[int]) – Population size.

• partition (Optional[int]) – Partition.

• period (Optional[int]) – Period.

See also

• niapy.algorithms.Algorithm.__init__()

Name = ['MonarchButterflyOptimization', 'MBO']

__init__(population_size=20, partition=0.4166666666666667, period=1.2, *args, **kwargs)

Initialize MonarchButterflyOptimization.

Parameters

• population_size (Optional[int]) – Population size.

• partition (Optional[int]) – Partition.

• period (Optional[int]) – Period.

See also

• niapy.algorithms.Algorithm.__init__()

adjusting_operator(t, max_t, dimension, np1, np2, butterflies, best)

Apply the adjusting operator.

Parameters

• t (int) – Current generation.

• max_t (int) – Maximum generation.

• dimension (int) – Number of dimensions.

• np1 (int) – Number of butterflies in Land 1.

• np2 (int) – Number of butterflies in Land 2.

• butterflies (numpy.ndarray) – Current butterfly population.

• best (numpy.ndarray) – The best butterfly currently.

Returns

Adjusted butterfly population.

Return type

numpy.ndarray

static evaluate_and_sort(task, butterflies)

Evaluate and sort the butterfly population.

Parameters

• task (Task) – Optimization task

• butterflies (numpy.ndarray) – Current butterfly population.

Returns

Tuple[numpy.ndarray, float, numpy.ndarray]:

1. Best butterfly according to the evaluation.

2. The best fitness value.

3. Butterfly population.

Return type

numpy.ndarray

get_parameters()

Get parameters values for the algorithm.

Returns

Algorithm parameters.

Return type

Dict[str, Any]

static info()

Get information of the algorithm.

Returns

Algorithm information.

Return type

str

See also

• niapy.algorithms.algorithm.Algorithm.info()

init_population(task)

Initialize the starting population.

Parameters

task (Task) – Optimization task

Returns

1. New population.

2. New population fitness/function values.

3. Additional arguments:

   • current_best (numpy.ndarray): Current generation’s best individual.

Return type

Tuple[numpy.ndarray, numpy.ndarray[float], Dict[str, Any]]

See also

• niapy.algorithms.Algorithm.init_population()

levy(_step_size, dimension)

Calculate levy flight.

Parameters

• _step_size (float) – Size of the walk step.

• dimension (int) – Number of dimensions.

Returns

Calculated values for levy flight.

Return type

numpy.ndarray

migration_operator(dimension, np1, np2, butterflies)

Apply the migration operator.

Parameters

• dimension (int) – Number of dimensions.

• np1 (int) – Number of butterflies in Land 1.

• np2 (int) – Number of butterflies in Land 2.

• butterflies (numpy.ndarray) – Current butterfly population.

Returns

Adjusted butterfly population.

Return type

numpy.ndarray

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Forest Optimization Algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray) – Current population.

• population_fitness (numpy.ndarray[float]) – Current population function/fitness values.

• best_x (numpy.ndarray) – Global best individual.

• best_fitness (float) – Global best individual fitness/function value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. New population.

2. New population fitness/function values.

3. New global best solution.

4. New global best solutions fitness/objective value.

5. Additional arguments:

   • current_best (numpy.ndarray): Current generation’s best individual.

Return type

Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, float, Dict[str, Any]]

set_parameters(population_size=20, partition=0.4166666666666667, period=1.2, **kwargs)

Set the parameters of the algorithm.

Parameters

• population_size (Optional[int]) – Population size.

• partition (Optional[int]) – Partition.

• period (Optional[int]) – Period.

See also

• niapy.algorithms.Algorithm.set_parameters()

class niapy.algorithms.basic.MonkeyKingEvolutionV1(population_size=40, fluctuation_coeff=0.7, population_rate=0.3, c=3, fc=0.5, *args, **kwargs)

Bases: Algorithm

Implementation of monkey king evolution algorithm version 1.

Algorithm:

Monkey King Evolution version 1

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

https://www.sciencedirect.com/science/article/pii/S0950705116000198

Reference paper:

Zhenyu Meng, Jeng-Shyang Pan, Monkey King Evolution: A new memetic evolutionary algorithm and its application in vehicle fuel consumption optimization, Knowledge-Based Systems, Volume 97, 2016, Pages 144-157, ISSN 0950-7051, https://doi.org/10.1016/j.knosys.2016.01.009.

Variables

• Name (List[str]) – List of strings representing algorithm names.

• fluctuation_coeff (float) – Scale factor for normal particles.

• population_rate (float) – Percent value of now many new particle Monkey King particle creates.

• c (int) – Number of new particles generated by Monkey King particle.

• fc (float) – Scale factor for Monkey King particles.

See also

• niapy.algorithms.algorithm.Algorithm

Initialize MonkeyKingEvolutionV1.

Parameters

• population_size (int) – Population size.

• fluctuation_coeff (float) – Scale factor for normal particle.

• population_rate (float) – Percent value of now many new particle Monkey King particle creates. Value in rage [0, 1].

• c (int) – Number of new particles generated by Monkey King particle.

• fc (float) – Scale factor for Monkey King particles.

See also

• niapy.algorithms.algorithm.Algorithm.__init__()

Name = ['MonkeyKingEvolutionV1', 'MKEv1']

__init__(population_size=40, fluctuation_coeff=0.7, population_rate=0.3, c=3, fc=0.5, *args, **kwargs)

Initialize MonkeyKingEvolutionV1.

Parameters

• population_size (int) – Population size.

• fluctuation_coeff (float) – Scale factor for normal particle.

• population_rate (float) – Percent value of now many new particle Monkey King particle creates. Value in rage [0, 1].

• c (int) – Number of new particles generated by Monkey King particle.

• fc (float) – Scale factor for Monkey King particles.

See also

• niapy.algorithms.algorithm.Algorithm.__init__()

get_parameters()

Get algorithms parameters values.

Returns

Dict[str, Any]

See also

• niapy.algorithms.Algorithm.get_parameters()

static info()

Get basic information of algorithm.

Returns

Basic information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

init_population(task)

Init population.

Parameters

task (Task) – Optimization task

Returns

1. Initialized solutions

2. Fitness/function values of solution

3. Additional arguments

Return type

Tuple(numpy.ndarray[MkeSolution], numpy.ndarray[float], Dict[str, Any]]

move_mk(x, task)

Move Monkey King particle.

For moving Monkey King particles algorithm uses next formula: \(\mathbf{x} + \mathit{fc} \odot \mathbf{population_rate} \odot \mathbf{x}\) where \(\mathbf{population_rate}\) is two dimensional array with shape {c * D, D}. Components of this array are in range [0, 1]

Parameters

• x (numpy.ndarray) – Monkey King patricle position.

• task (Task) – Optimization task.

Returns

New particles generated by Monkey King particle.

Return type

numpy.ndarray

move_monkey_king_particle(p, task)

Move Monkey King Particles.

Parameters

• p (MkeSolution) – Monkey King particle to apply this function on.

• task (Task) – Optimization task.

move_p(x, x_pb, x_b, task)

Move normal particle in search space.

For moving particles algorithm uses next formula: \(\mathbf{x_{pb} - \mathit{differential_weight} \odot \mathbf{r} \odot (\mathbf{x_b} - \mathbf{x})\) where \(\mathbf{r}\) is one dimension array with D components. Components in this vector are in range [0, 1].

Parameters

• x (numpy.ndarray) – Particle position.

• x_pb (numpy.ndarray) – Particle best position.

• x_b (numpy.ndarray) – Best particle position.

• task (Task) – Optimization task.

Returns

Particle new position.

Return type

numpy.ndarray

move_particle(p, p_b, task)

Move particles.

Parameters

• p (MkeSolution) – Monkey particle.

• p_b (numpy.ndarray) – Population best particle.

• task (Task) – Optimization task.

move_population(pop, xb, task)

Move population.

Parameters

• pop (numpy.ndarray[MkeSolution]) – Current population.

• xb (numpy.ndarray) – Current best solution.

• task (Task) – Optimization task.

Returns

New particles.

Return type

numpy.ndarray[MkeSolution]

run_iteration(task, population, population_fitness, best_x, best_fitness, **params)

Core function of Monkey King Evolution v1 algorithm.

Parameters

• task (Task) – Optimization task.

• population (numpy.ndarray[MkeSolution]) – Current population.

• population_fitness (numpy.ndarray[float]) – Current population fitness/function values.

• best_x (numpy.ndarray) – Current best solution.

• best_fitness (float) – Current best solutions function/fitness value.

• **params (Dict[str, Any]) – Additional arguments.

Returns

1. Initialized solutions.

2. Fitness/function values of solution.

3. Additional arguments.

Return type

Tuple(numpy.ndarray[MkeSolution], numpy.ndarray[float], Dict[str, Any]]

set_parameters(population_size=40, fluctuation_coeff=0.7, population_rate=0.3, c=3, fc=0.5, **kwargs)

Set Monkey King Evolution v1 algorithms static parameters.

Parameters

• population_size (int) – Population size.

• fluctuation_coeff (float) – Scale factor for normal particle.

• population_rate (float) – Percent value of now many new particle Monkey King particle creates. Value in rage [0, 1].

• c (int) – Number of new particles generated by Monkey King particle.

• fc (float) – Scale factor for Monkey King particles.

See also

• niapy.algorithms.algorithm.Algorithm.set_parameters()

class niapy.algorithms.basic.MonkeyKingEvolutionV2(population_size=40, fluctuation_coeff=0.7, population_rate=0.3, c=3, fc=0.5, *args, **kwargs)

Bases: MonkeyKingEvolutionV1

Implementation of monkey king evolution algorithm version 2.

Algorithm:

Monkey King Evolution version 2

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

https://www.sciencedirect.com/science/article/pii/S0950705116000198

Reference paper:

Zhenyu Meng, Jeng-Shyang Pan, Monkey King Evolution: A new memetic evolutionary algorithm and its application in vehicle fuel consumption optimization, Knowledge-Based Systems, Volume 97, 2016, Pages 144-157, ISSN 0950-7051, https://doi.org/10.1016/j.knosys.2016.01.009.

Variables

Name (List[str]) – List of strings representing algorithm names.

See also

• niapy.algorithms.basic.mke.MonkeyKingEvolutionV1

Initialize MonkeyKingEvolutionV1.

Parameters

• population_size (int) – Population size.

• fluctuation_coeff (float) – Scale factor for normal particle.

• population_rate (float) – Percent value of now many new particle Monkey King particle creates. Value in rage [0, 1].

• c (int) – Number of new particles generated by Monkey King particle.

• fc (float) – Scale factor for Monkey King particles.

See also

• niapy.algorithms.algorithm.Algorithm.__init__()

Name = ['MonkeyKingEvolutionV2', 'MKEv2']

static info()

Get basic information of algorithm.

Returns

Basic information.

Return type

str

See also

• niapy.algorithms.Algorithm.info()

move_mk(x, task, dx=None)

Move Monkey King particle.

For movement of particles algorithm uses next formula: \(\mathbf{x} - \mathit{fc} \odot \mathbf{dx}\)

Parameters

• x (numpy.ndarray) – Particle to apply movement on.

• task (Task) – Optimization task.

• dx (numpy.ndarray) – Difference between to random particles in population.

Returns

Moved particles.

Return type

numpy.ndarray

move_monkey_king_particle(p, task, pop=None)

Move Monkey King particles.

Parameters

• p (MkeSolution) – Monkey King particle to move.

• task (Task) – Optimization task.

• pop (numpy.ndarray[MkeSolution]) – Current population.

move_population(pop, xb, task)

Move population.

Parameters

• pop (numpy.ndarray[MkeSolution]) – Current population.

• xb (numpy.ndarray) – Current best solution.

• task (Task) – Optimization task.

Returns

Moved population.

Return type

numpy.ndarray[MkeSolution]

class niapy.algorithms.basic.MonkeyKingEvolutionV3(*args, **kwargs)

Bases: MonkeyKingEvolutionV1

Implementation of monkey king evolution algorithm version 3.

Algorithm:

Monkey King Evolution version 3

Date:

2018

Authors:

Klemen Berkovič

License:

MIT

Reference URL:

https://www.sciencedirect.com/science/article/pii/S0950705116000198

Reference paper:

Zhenyu Meng, Jeng-Shyang Pan, Monkey King Evolution: A new memetic evolutionary algorithm and its application in vehicle fuel consumption optimization, Knowledge-Based Systems, Volume 97, 2016, Pages 144-157, ISSN 0950-7051, https://doi.org/10.1016/j.knosys.2016.01.009.

Variables

Name (List[str]) – List of strings that represent algorithm names.

See also

• niapy.algorithms.basic.mke.MonkeyKingEvolutionV1

Initialize MonkeyKingEvolutionV3.

Name = ['MonkeyKingEvolutionV3', 'MKEv3']

__init__(*args, **kwargs)

Initialize MonkeyKingEvolutionV3.