# encoding=utf8
import logging
import numpy as np
from niapy.algorithms.algorithm import Algorithm
from niapy.util import full_array, euclidean
logging.basicConfig()
logger = logging.getLogger('niapy.algorithms.basic')
logger.setLevel('INFO')
__all__ = ['KrillHerd']
[docs]class KrillHerd(Algorithm):
r"""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.
Attributes:
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 :math:`\in [0, 1]`.
w_foraging (Optional[Union[int, float, numpy.ndarray]]): Inertia weights of the motion induced from foraging :math:`\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:
* :class:`niapy.algorithms.algorithm.Algorithm`
"""
Name = ['KrillHerd', 'KH']
[docs] @staticmethod
def info():
r"""Get basic information of algorithm.
Returns:
str: Basic information of algorithm.
See Also:
* :func:`niapy.algorithms.Algorithm.info`
"""
return r"""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."""
[docs] def __init__(self, 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):
r"""Initialize KrillHerd.
Args:
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 :math:`\in [0, 1]`.
w_foraging (Optional[Union[int, float, numpy.ndarray]]): Inertia weights of the motion induced from foraging :math:`\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:
* :func:`niapy.algorithms.algorithm.Algorithm.__init__`
"""
super().__init__(population_size, *args, **kwargs)
self.n_max = n_max
self.foraging_speed = foraging_speed
self.diffusion_speed = diffusion_speed
self.c_t = c_t
self.w_neighbor = w_neighbor
self.w_foraging = w_foraging
self.d_s = d_s
self.max_neighbors = max_neighbors
self.cr = crossover_rate
self.mr = mutation_rate
self.epsilon = np.finfo(float).eps
[docs] def set_parameters(self, 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):
r"""Set the arguments of an algorithm.
Args:
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 :math:`\in [0, 1]`.
w_foraging (Optional[Union[int, float, numpy.ndarray]]): Inertia weights of the motion induced from foraging :math:`\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:
* :func:`niapy.algorithms.algorithm.Algorithm.set_parameters`
"""
super().set_parameters(population_size=population_size, **kwargs)
self.n_max = n_max
self.foraging_speed = foraging_speed
self.diffusion_speed = diffusion_speed
self.c_t = c_t
self.w_neighbor = w_neighbor
self.w_foraging = w_foraging
self.d_s = d_s
self.max_neighbors = max_neighbors
self.cr = crossover_rate
self.mr = mutation_rate
self.epsilon = np.finfo(float).eps
[docs] def get_parameters(self):
r"""Get parameter values for the algorithm.
Returns:
Dict[str, Any]: Algorithm parameters.
"""
d = Algorithm.get_parameters(self)
d.update({
'n_max': self.n_max,
'foraging_speed': self.foraging_speed,
'diffusion_speed': self.diffusion_speed,
'c_t': self.c_t,
'w_neighbor': self.w_neighbor,
'w_foraging': self.w_foraging,
'd_s': self.d_s,
'max_neighbors': self.max_neighbors,
'crossover_rate': self.cr,
'mutation_rate': self.mr
})
return d
[docs] def init_weights(self, task):
r"""Initialize weights.
Args:
task (Task): Optimization task.
Returns:
Tuple[numpy.ndarray, numpy.ndarray]:
1. Weights for neighborhood.
2. Weights for foraging.
"""
return full_array(self.w_neighbor, task.dimension), full_array(self.w_foraging, task.dimension)
[docs] def sense_range(self, ki, population):
r"""Calculate sense range for selected individual.
Args:
ki (int): Selected individual.
population (numpy.ndarray): Krill heard population.
Returns:
float: Sense range for krill.
"""
return np.sum([euclidean(population[ki], population[i]) for i in range(self.population_size)]) / (self.max_neighbors * self.population_size)
[docs] def get_neighbours(self, i, ids, population):
r"""Get neighbours.
Args:
i (int): Individual looking for neighbours.
ids (float): Maximal distance for being a neighbour.
population (numpy.ndarray): Current population.
Returns:
numpy.ndarray: Neighbours of krill heard.
"""
neighbors = list()
for j in range(self.population_size):
if j != i and ids > euclidean(population[i], population[j]):
neighbors.append(j)
if not neighbors:
neighbors.append(self.integers(self.population_size))
return np.asarray(neighbors)
[docs] def get_x(self, x, y):
r"""Get x values.
Args:
x (numpy.ndarray): First krill/individual.
y (numpy.ndarray): Second krill/individual.
Returns:
numpy.ndarray: --
"""
return ((y - x) + self.epsilon) / (euclidean(y, x) + self.epsilon)
[docs] def get_k(self, x, y, b, w):
r"""Get k values.
Args:
x (float): First krill/individual.
y (float): Second krill/individual.
b (float): Best krill/individual.
w (float): Worst krill/individual.
Returns:
numpy.ndarray: K.
"""
return ((x - y) + self.epsilon) / ((w - b) + self.epsilon)
[docs] def induce_neighbors_motion(self, i, n, weights, population, population_fitness, best_index, worst_index, task):
r"""Induced neighbours motion operator.
Args:
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:
numpy.ndarray: Moved krill.
"""
neighbor_i = self.get_neighbours(i, self.sense_range(i, population), population)
neighbor_x, neighbor_f, f_b, f_w = population[neighbor_i], population_fitness[neighbor_i], population_fitness[best_index], population_fitness[worst_index]
alpha_l = np.sum(
np.asarray([self.get_k(population_fitness[i], j, f_b, f_w) for j in neighbor_f]) * np.asarray([self.get_x(population[i], j) for j in neighbor_x]).T)
alpha_t = 2 * (1 + self.random() * (task.iters + 1) / task.max_iters)
return self.n_max * (alpha_l + alpha_t) + weights * n
[docs] def induce_foraging_motion(self, i, x, x_f, f, weights, population, population_fitness, best_index, worst_index, task):
r"""Induced foraging motion operator.
Args:
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:
numpy.ndarray: Moved krill.
"""
beta_f = 2 * (1 - (task.iters + 1) / task.max_iters) * self.get_k(population_fitness[i], x_f, population_fitness[best_index], population_fitness[worst_index]) * self.get_x(
population[i], x) if population_fitness[best_index] < population_fitness[i] else 0
beta_b = self.get_k(population_fitness[i], population_fitness[best_index], population_fitness[best_index], population_fitness[worst_index]) * self.get_x(population[i], population[best_index])
return self.foraging_speed * (beta_f + beta_b) + weights * f
[docs] def induce_physical_diffusion(self, task):
r"""Induced physical diffusion operator.
Args:
task (Task): Optimization task.
Returns:
numpy.ndarray:
"""
return self.diffusion_speed * (1 - (task.iters + 1) / task.max_iters) * self.uniform(-1, 1, task.dimension)
[docs] def delta_t(self, task):
r"""Get new delta for all dimensions.
Args:
task (Task): Optimization task.
Returns:
numpy.ndarray: --
"""
return self.c_t * np.sum(task.range)
[docs] def crossover(self, x, xo, crossover_rate):
r"""Crossover operator.
Args:
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:
numpy.ndarray: New krill/individual.
"""
return [xo[i] if self.random() < crossover_rate else x[i] for i in range(len(x))]
[docs] def mutate(self, x, x_b, mutation_rate):
r"""Mutate operator.
Args:
x (numpy.ndarray): Individual being mutated.
x_b (numpy.ndarray): Global best individual.
mutation_rate (float): Probability of mutations.
Returns:
numpy.ndarray: Mutated krill.
"""
return [x[i] if self.random() < mutation_rate else (x_b[i] + self.random()) for i in range(len(x))]
[docs] def get_food_location(self, population, population_fitness, task):
r"""Get food location for krill heard.
Args:
population (numpy.ndarray): Current heard/population.
population_fitness (numpy.ndarray[float]): Current heard/populations function/fitness values.
task (Task): Optimization task.
Returns:
Tuple[numpy.ndarray, float]:
1. Location of food.
2. Foods function/fitness value.
"""
x_food = task.repair(np.asarray([np.sum(population[:, i] / population_fitness) for i in range(task.dimension)]) / np.sum(1 / population_fitness),
rng=self.rng)
x_food_f = task.eval(x_food)
return x_food, x_food_f
[docs] def mutation_rate(self, xf, yf, xf_best, xf_worst):
r"""Get mutation probability.
Args:
xf (float):
yf (float):
xf_best (float):
xf_worst (float):
Returns:
float: New mutation probability.
"""
return self.mr / (self.get_k(xf, yf, xf_best, xf_worst) + 1e-31)
[docs] def crossover_rate(self, xf, yf, xf_best, xf_worst):
r"""Get crossover probability.
Args:
xf (float):
yf (float):
xf_best (float):
xf_worst (float):
Returns:
float: New crossover probability.
"""
return self.cr * self.get_k(xf, yf, xf_best, xf_worst)
[docs] def init_population(self, task):
r"""Initialize stating population.
Args:
task (Task): Optimization task.
Returns:
Tuple[numpy.ndarray, numpy.ndarray, Dict[str, Any]]:
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.
See Also:
* :func:`niapy.algorithms.algorithm.Algorithm.init_population`
"""
krill_herd, krill_herd_fitness, d = Algorithm.init_population(self, task)
w_neighbor, w_foraging = self.init_weights(task)
induced_speed, foraging_speed = np.zeros(self.population_size), np.zeros(self.population_size)
d.update({'w_neighbor': w_neighbor, 'w_foraging': w_foraging, 'induced_speed': induced_speed, 'foraging_speed': foraging_speed})
return krill_herd, krill_herd_fitness, d
[docs] def run_iteration(self, task, population, population_fitness, best_x, best_fitness, **params):
r"""Core function of KrillHerd algorithm.
Args:
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:
Tuple [numpy.ndarray, numpy.ndarray, numpy.ndarray, float Dict[str, Any]]:
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): --
"""
w_neighbor = params.pop('w_neighbor')
w_foraging = params.pop('w_foraging')
induced_speed = params.pop('induced_speed')
foraging_speed = params.pop('foraging_speed')
ikh_b, ikh_w = np.argmin(population_fitness), np.argmax(population_fitness)
x_food, x_food_f = self.get_food_location(population, population_fitness, task)
if x_food_f < best_fitness:
best_x, best_fitness = x_food, x_food_f # noqa: F841
induced_speed = np.asarray([self.induce_neighbors_motion(i, induced_speed[i], w_neighbor, population, population_fitness, ikh_b, ikh_w, task) for i in range(self.population_size)])
foraging_speed = np.asarray([self.induce_foraging_motion(i, x_food, x_food_f, foraging_speed[i], w_foraging, population, population_fitness, ikh_b, ikh_w, task) for i in range(self.population_size)])
diffusion = np.asarray([self.induce_physical_diffusion(task) for _ in range(self.population_size)])
new_herd = population + (self.delta_t(task) * (induced_speed + foraging_speed + diffusion))
crossover_rates = np.asarray([self.crossover_rate(population_fitness[i], population_fitness[ikh_b], population_fitness[ikh_b], population_fitness[ikh_w]) for i in range(self.population_size)])
new_herd = np.asarray([self.crossover(new_herd[i], population[i], crossover_rates[i]) for i in range(self.population_size)])
mutation_rates = np.asarray([self.mutation_rate(population_fitness[i], population_fitness[ikh_b], population_fitness[ikh_b], population_fitness[ikh_w]) for i in range(self.population_size)])
new_herd = np.asarray([self.mutate(new_herd[i], population[ikh_b], mutation_rates[i]) for i in range(self.population_size)])
population = np.apply_along_axis(task.repair, 1, new_herd, rng=self.rng)
population_fitness = np.apply_along_axis(task.eval, 1, population)
best_x, best_fitness = self.get_best(population, population_fitness, best_x, best_fitness)
return population, population_fitness, best_x, best_fitness, {'w_neighbor': w_neighbor, 'w_foraging': w_foraging, 'induced_speed': induced_speed, 'foraging_speed': foraging_speed}
