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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):
x0,x1,x2,x3,x4,x5,x6,x7,x8,x9 = x
return x0**2 + x1**2 + x0*x1 - 14*x0 - 16*x1 + (x2-10)**2 + \
4*(x3-5)**2 + (x4-3)**2 + 2*(x5-1)**2 + 5*x6**2 + \
7*(x7-11)**2 + 2*(x8-10)**2 + (x9-7)**2 + 45.0
bounds = [(-10,10)]*10
# with penalty='penalty' applied, solution is:
xs = [2.171996, 2.363683, 8.773926, 5.095984, 0.9906548,
1.430574, 1.321644, 9.828726, 8.280092, 8.375927]
ys = 24.3062091
from mystic.symbolic import generate_constraint, generate_solvers, simplify
from mystic.symbolic import generate_penalty, generate_conditions
equations = """
4.0*x0 + 5.0*x1 - 3.0*x6 + 9.0*x7 - 105.0 <= 0.0
10.0*x0 - 8.0*x1 - 17.0*x6 + 2.0*x7 <= 0.0
-8.0*x0 + 2.0*x1 + 5.0*x8 - 2.0*x9 - 12.0 <= 0.0
3.0*(x0-2)**2 + 4.0*(x1-3)**2 + 2.0*x2**2 - 7.0*x3 - 120.0 <= 0.0
5.0*x0**2 + 8.0*x1 + (x2-6)**2 - 2.0*x3 - 40.0 <= 0.0
0.5*(x0-8)**2 + 2.0*(x1-4)**2 + 3.0*x4**2 - x5 - 30.0 <= 0.0
x0**2 + 2.0*(x1-2)**2 - 2.0*x0*x1 + 14.0*x4 - 6.0*x5 <= 0.0
-3.0*x0 + 6.0*x1 + 12.0*(x8-8)**2 - 7.0*x9 <= 0.0
"""
cf = generate_constraint(generate_solvers(simplify(equations, target=['x5','x3'])))
pf = generate_penalty(generate_conditions(equations))
if __name__ == '__main__':
x = [0]*len(xs)
from mystic.solvers import fmin_powell
from mystic.math import almostEqual
from mystic.monitors import VerboseMonitor
mon = VerboseMonitor(10)
result = fmin_powell(objective, x0=x, bounds=bounds, penalty=pf, maxiter=1000, maxfun=100000, ftol=1e-12, xtol=1e-12, gtol=10, disp=False, full_output=True)
assert almostEqual(result[0], xs, tol=1e-2)
assert almostEqual(result[1], ys, rel=1e-2)
# EOF
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