#!/usr/bin/env python
# Created by "Thieu" at 17:22, 22/07/2022 ----------%
# Email: nguyenthieu2102@gmail.com %
# Github: https://github.com/thieu1995 %
# --------------------------------------------------%
import numpy as np
from opfunu.benchmark import Benchmark
[docs]class FreudensteinRoth(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.
"""
name = "Freudenstein Roth Function"
latex_formula = r'f(x) = \left\{x_1 - 13 + \left[(5 - x_2) x_2' +\
r'- 2 \right] x_2 \right\}^2 + \left \{x_1 - 29 + \left[(x_2 + 1) x_2 - 14 \right] x_2 \right\}^2'
latex_formula_dimension = r'd = 2'
latex_formula_bounds = r'x_i \in [-10, 10], \forall i \in \llbracket 1, d\rrbracket'
latex_formula_global_optimum = r'f(5, 4) = 0'
continuous = True
linear = False
convex = True
unimodal = False
separable = False
differentiable = True
scalable = False
randomized_term = False
parametric = False
modality = False # 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 = 0.
self.x_global = np.array([5., 4.])
[docs] def evaluate(self, x, *args):
self.check_solution(x)
self.n_fe += 1
f1 = (-13.0 + x[0] + ((5.0 - x[1]) * x[1] - 2.0) * x[1]) ** 2
f2 = (-29.0 + x[0] + ((x[1] + 1.0) * x[1] - 14.0) * x[1]) ** 2
return f1 + f2