#!/usr/bin/env python
# Created by "Thieu" at 17:31, 30/07/2022 ----------%
# Email: nguyenthieu2102@gmail.com %
# Github: https://github.com/thieu1995 %
# --------------------------------------------------%
import numpy as np
from opfunu.benchmark import Benchmark
[docs]class TestTubeHolder(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_{\text{TestTubeHolder}}(x) = - 4 \left | {e^{\left|{\cos \left(\frac{1}{200} x_{1}^{2} +
\frac{1}{200} x_{2}^{2}\right)} \right|}\sin\left(x_{1}\right) \cos\left(x_{2}\right)}\right|
with :math:`x_i \in [-10, 10]` for :math:`i = 1, 2`.
*Global optimum*: :math:`f(x) = -10.872299901558` for :math:`x= [-\pi/2, 0]`
"""
name = "Qing Function"
latex_formula = r'f_{\text{TestTubeHolder}}(x)='
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 = True
scalable = False
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 = False
self.dim_default = 2
self.check_ndim_and_bounds(ndim, bounds, np.array([[-10., 10.] for _ in range(self.dim_default)]))
self.f_global = -10.87229990155800
self.x_global = np.array([-np.pi / 2, 0.0])
[docs] def evaluate(self, x, *args):
self.check_solution(x)
self.n_fe += 1
u = np.sin(x[0]) * np.cos(x[1])
v = (x[0] ** 2 + x[1] ** 2) / 200
return -4 * np.abs(u * np.exp(np.abs(np.cos(v))))