Source code for NiaPy.benchmarks.pinter

# encoding=utf8

"""Implementation of Pinter function."""

import math
from NiaPy.benchmarks.benchmark import Benchmark

__all__ = ['Pinter']


[docs]class Pinter(Benchmark): r"""Implementation of Pintér function. Date: 2018 Author: Lucija Brezočnik License: MIT Function: **Pintér function** :math:`f(\mathbf{x}) = \sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i \log_{10} (1 + iB^2);` :math:`A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad` :math:`B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1)` **Input domain:** The function can be defined on any input domain but it is usually evaluated on the hypercube :math:`x_i ∈ [-10, 10]`, for all :math:`i = 1, 2,..., D`. **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)` LaTeX formats: Inline: $f(\mathbf{x}) = \sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i \log_{10} (1 + iB^2); A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1)$ Equation: \begin{equation} f(\mathbf{x}) = \sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i \log_{10} (1 + iB^2); A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1) \end{equation} Domain: $-10 \leq x_i \leq 10$ 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. """ Name = ['Pinter']
[docs] def __init__(self, Lower=-10.0, Upper=10.0): r"""Initialize of Pinter benchmark. Args: Lower (Optional[float]): Lower bound of problem. Upper (Optional[float]): Upper bound of problem. See Also: :func:`NiaPy.benchmarks.Benchmark.__init__` """ Benchmark.__init__(self, Lower, Upper)
[docs] @staticmethod def latex_code(): r"""Return the latex code of the problem. Returns: str: Latex code """ return r''' $f(\mathbf{x}) = \sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i \log_{10} (1 + iB^2); A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1)$'''
[docs] def function(self): r"""Return benchmark evaluation function. Returns: Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function """ def evaluate(D, sol): r"""Fitness function. Args: D (int): Dimensionality of the problem sol (Union[int, float, List[int, float], numpy.ndarray]): Solution to check. Returns: float: Fitness value for the solution. """ val1 = 0.0 val2 = 0.0 val3 = 0.0 for i in range(D): if i == 0: sub = sol[D - 1] add = sol[i + 1] elif i == D - 1: sub = sol[i - 1] add = sol[0] else: sub = sol[i - 1] add = sol[i + 1] A = (sub * math.sin(sol[i]) + math.sin(add)) B = (math.pow(sub, 2) - 2.0 * sol[i] + 3.0 * add - math.cos(sol[i]) + 1.0) val1 += (i + 1.0) * math.pow(sol[i], 2) val2 += 20.0 * (i + 1.0) * math.pow(math.sin(A), 2) val3 += (i + 1.0) * math.log10(1.0 + (i + 1.0) * math.pow(B, 2)) return val1 + val2 + val3 return evaluate