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#!/usr/bin/env python
#
# Problem definition:
# A-R Hedar and M Fukushima, "Derivative-Free Filter Simulated Annealing
# Method for Constrained Continuous Global Optimization", Journal of
# Global Optimization, 35(4), 521-549 (2006).
#
# Original Matlab code written by A. Hedar (Nov. 23, 2005)
# http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/go.htm
# and ported to Python by Mike McKerns (December 2014)
#
# Author: Mike McKerns (mmckerns @caltech and @uqfoundation)
# Copyright (c) 1997-2016 California Institute of Technology.
# Copyright (c) 2016-2024 The Uncertainty Quantification Foundation.
# License: 3-clause BSD. The full license text is available at:
# - https://github.com/uqfoundation/mystic/blob/master/LICENSE
def objective(x):
from numpy import exp, prod as product
return exp(product(x))
bounds = [(-2.3,2.3)]*2 + [(-3.2,3.2)]*3
# with penalty='penalty' applied, solution is:
xs = [-1.717143, 1.595709, 1.827247, -0.7636413, -0.763645]
_xs = [-1.717143, 1.595709, 1.827247, 0.7636413, 0.763645]
x_s = [-1.717143, 1.595709, -1.827247, 0.7636413, -0.763645]
xs_ = [-1.717143, 1.595709, -1.827247, -0.7636413, 0.763645]
ys = 0.05394983
from mystic.symbolic import generate_constraint, generate_solvers, simplify
from mystic.symbolic import generate_penalty, generate_conditions
equations = """
x0**2 + x1**2 + x2**2 + x3**2 + x4**2 - 10.0 = 0.0
x1*x2 - 5.0*x3*x4 = 0.0
x0**3 + x1**3 + 1.0 = 0.0
"""
cf = generate_constraint(generate_solvers(simplify(equations))) # slow solve
pf = generate_penalty(generate_conditions(equations))
if __name__ == '__main__':
from mystic.solvers import lattice
from mystic.math import almostEqual
result = lattice(objective, 5, [2]*5, bounds=bounds, penalty=pf, ftol=1e-8, xtol=1e-8, disp=False, full_output=True)
assert almostEqual(result[0], xs, tol=5e-2) \
or almostEqual(result[0], _xs, tol=5e-2) \
or almostEqual(result[0], x_s, tol=5e-2) \
or almostEqual(result[0], xs_, tol=5e-2)
assert almostEqual(result[1], ys, rel=5e-2)
# EOF
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