#!/usr/bin/env python
# Created by "Thieu" at 17:32, 30/07/2022 ----------%
# Email: nguyenthieu2102@gmail.com %
# Github: https://github.com/thieu1995 %
# --------------------------------------------------%
import numpy as np
from opfunu.benchmark import Benchmark
[docs]class XinSheYang01(Benchmark):
"""
.. [1] Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions For Global Optimization Problems
Int. Journal of Mathematical Modelling and Numerical Optimisation, 2013, 4, 150-194.
.. math::
f(x) = \sum_{i=1}^{n} \epsilon_i \lvert x_i \rvert^i
The variable :math:`\epsilon_i, (i = 1, ..., n)` is a random variable uniformly distributed in :math:`[0, 1]`.
Here, :math:`n` represents the number of dimensions and :math:`x_i \in [-5, 5]` for :math:`i = 1, ..., n`.
*Global optimum*: :math:`f(x) = 0` for :math:`x_i = 0` for :math:`i = 1, ..., n`
"""
name = "Xin-She Yang 1 Function"
latex_formula = r'f(x) = \sum_{i=1}^{n} \epsilon_i \lvert x_i \rvert^i'
latex_formula_dimension = r'd = n'
latex_formula_bounds = r'x_i \in [-10, 10, ..., 10]'
latex_formula_global_optimum = r'f(0, 0, ...,0) = 1.0'
continuous = True
linear = False
convex = True
unimodal = False
separable = True
differentiable = False
scalable = True
randomized_term = False
parametric = False
modality = True # Number of ambiguous peaks, unknown # peaks
def __init__(self, ndim=None, bounds=None):
super().__init__()
self.dim_changeable = True
self.dim_default = 2
self.check_ndim_and_bounds(ndim, bounds, np.array([[-5., 5.] for _ in range(self.dim_default)]))
self.f_global = 0.
self.x_global = np.zeros(self.ndim)
[docs] def evaluate(self, x, *args):
self.check_solution(x)
self.n_fe += 1
i = np.arange(1.0, self.ndim + 1.0)
return np.sum(np.random.random(self.ndim) * (np.abs(x) ** i))