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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
"Pressure Vessel Design"
def objective(x):
x0,x1,x2,x3 = x
return 0.6224*x0*x2*x3 + 1.7781*x1*x2**2 + 3.1661*x0**2*x3 + 19.84*x0**2*x2
bounds = [(0,1e6)]*4
# with penalty='penalty' applied, solution is:
xs = [0.72759093, 0.35964857, 37.69901188, 240.0]
ys = 5804.3762083
from mystic.symbolic import (generate_constraint, generate_solvers,
generate_penalty, generate_conditions,
simplify, symbolic_bounds)
equations = """
-x0 + 0.0193*x2 <= 0.0
-x1 + 0.00954*x2 <= 0.0
-pi*x2**2*x3 - (4/3.)*pi*x2**3 + 1296000.0 <= 0.0
x3 - 240.0 <= 0.0
"""
equations += symbolic_bounds(*zip(*bounds))
cf = generate_constraint(generate_solvers(simplify(equations)))
pf = generate_penalty(generate_conditions(equations), k=1e12)
if __name__ == '__main__':
from mystic.solvers import diffev2
from mystic.math import almostEqual
from mystic.monitors import VerboseMonitor
mon = VerboseMonitor(10)
result = diffev2(objective, x0=bounds, bounds=bounds, constraints=cf, penalty=pf, npop=40, gtol=50, disp=False, full_output=True, itermon=mon)
assert almostEqual(result[0], xs, rel=1e-2)
assert almostEqual(result[1], ys, rel=1e-2)
# EOF
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