# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
"""Implementations of Step functions."""
import math
__all__ = ['Step', 'Step2', 'Step3']
[docs]class Step:
r"""Implementation of Step function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
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:
\begin{equation} f(\mathbf{x}) = \sum_{i=1}^D \left(
\lfloor \left | x_i \right | \rfloor \right) \end{equation}
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.
"""
def __init__(self, Lower=-100.0, Upper=100.0):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
val = 0.0
for i in range(D):
val += math.floor(abs(sol[i]))
return val
return evaluate
[docs]class Step2:
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`.
**lobal 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:
\begin{equation}f(\mathbf{x}) = \sum_{i=1}^D \left(
\lfloor x_i + 0.5 \rfloor \right)^2 \end{equation}
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.
"""
def __init__(self, Lower=-100.0, Upper=100.0):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
val = 0.0
for i in range(D):
val += math.pow(math.floor(sol[i] + 0.5), 2)
return val
return evaluate
[docs]class Step3:
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:
\begin{equation}f(\mathbf{x}) = \sum_{i=1}^D \left(
\lfloor x_i^2 \rfloor \right)\end{equation}
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.
"""
def __init__(self, Lower=-100.0, Upper=100.0):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
val = 0.0
for i in range(D):
val += math.floor(math.pow(sol[i], 2))
return val
return evaluate