Source code for niapy.problems.step

# encoding=utf8

"""Implementations of Step functions."""

import numpy as np
from niapy.problems.problem import Problem

__all__ = ['Step', 'Step2', 'Step3']

[docs]class Step(Problem):
r"""Implementation of Step function.

Date: 2018

Author: Lucija Brezočnik

Function: **Step function**

:math:f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor \left |
x_i \right | \rfloor \right)

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-100, 100], for all :math:i = 1, 2,..., D.

**Global minimum:** :math:f(x^*) = 0, at :math:x^* = (0,...,0)

LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor \left | x_i \right | \rfloor \right)$

Equation:
f(\mathbf{x}) = \sum_{i=1}^D \left(
\lfloor \left | x_i \right | \rfloor \right)

Domain:
$-100 \leq x_i \leq 100$

Reference paper:
Jamil, M., and Yang, X. S. (2013).
A literature survey of benchmark functions for global optimisation problems.
International Journal of Mathematical Modelling and Numerical Optimisation,
4(2), 150-194.

"""

[docs]    def __init__(self, dimension=4, lower=-100.0, upper=100.0, *args, **kwargs):
r"""Initialize Step problem..

Args:
dimension (Optional[int]): Dimension of the problem.
lower (Optional[Union[float, Iterable[float]]]): Lower bounds of the problem.
upper (Optional[Union[float, Iterable[float]]]): Upper bounds of the problem.

:func:niapy.problems.Problem.__init__

"""
super().__init__(dimension, lower, upper, *args, **kwargs)

[docs]    @staticmethod
def latex_code():
r"""Return the latex code of the problem.

Returns:
str: Latex code.

"""
return r'''$f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor \left | x_i \right | \rfloor \right)$'''

def _evaluate(self, x):
return np.sum(np.floor(np.abs(x)))

[docs]class Step2(Problem):
r"""Step2 function implementation.

Date: 2018

Author: Lucija Brezočnik

Licence: MIT

Function: **Step2 function**

:math:f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor x_i + 0.5 \rfloor \right)^2

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-100, 100], for all :math:i = 1, 2,..., D.

**Global minimum:** :math:f(x^*) = 0, at :math:x^* = (-0.5,...,-0.5)

LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor x_i + 0.5 \rfloor \right)^2$

Equation:
f(\mathbf{x}) = \sum_{i=1}^D \left(
\lfloor x_i + 0.5 \rfloor \right)^2

Domain:
$-100 \leq x_i \leq 100$

Reference paper:
Jamil, M., and Yang, X. S. (2013).
A literature survey of benchmark functions for global optimisation problems.
International Journal of Mathematical Modelling and Numerical Optimisation,
4(2), 150-194.

"""

[docs]    def __init__(self, dimension=4, lower=-100.0, upper=100.0, *args, **kwargs):
r"""Initialize Step2 problem..

Args:
dimension (Optional[int]): Dimension of the problem.
lower (Optional[Union[float, Iterable[float]]]): Lower bounds of the problem.
upper (Optional[Union[float, Iterable[float]]]): Upper bounds of the problem.

:func:niapy.problems.Problem.__init__

"""
super().__init__(dimension, lower, upper, *args, **kwargs)

[docs]    @staticmethod
def latex_code():
r"""Return the latex code of the problem.

Returns:
str: Latex code.

"""
return r'''$f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor x_i + 0.5 \rfloor \right)^2$'''

def _evaluate(self, x):
return np.sum(np.floor(x + 0.5) ** 2)

[docs]class Step3(Problem):
r"""Step3 function implementation.

Date: 2018

Author: Lucija Brezočnik

Licence: MIT

Function: **Step3 function**

:math:f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor x_i^2 \rfloor \right)

**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:x_i ∈ [-100, 100], for all :math:i = 1, 2,..., D.

**Global minimum:** :math:f(x^*) = 0, at :math:x^* = (0,...,0)

LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor x_i^2 \rfloor \right)$

Equation:
f(\mathbf{x}) = \sum_{i=1}^D \left(
\lfloor x_i^2 \rfloor \right)

Domain:
$-100 \leq x_i \leq 100$

Reference paper:
Jamil, M., and Yang, X. S. (2013).
A literature survey of benchmark functions for global optimisation problems.
International Journal of Mathematical Modelling and Numerical Optimisation,
4(2), 150-194.

"""

[docs]    def __init__(self, dimension=4, lower=-100.0, upper=100.0, *args, **kwargs):
r"""Initialize Step3 problem..

Args:
dimension (Optional[int]): Dimension of the problem.
lower (Optional[Union[float, Iterable[float]]]): Lower bounds of the problem.
upper (Optional[Union[float, Iterable[float]]]): Upper bounds of the problem.

:func:niapy.problems.Problem.__init__

"""
super().__init__(dimension, lower, upper, *args, **kwargs)

[docs]    @staticmethod
def latex_code():
r"""Return the latex code of the problem.

Returns:
str: Latex code.

"""
return r'''$f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor x_i^2 \rfloor \right)$'''

def _evaluate(self, x):
return np.sum(np.floor(x ** 2))