1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
|
#!/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 = x
return (x0-10)**2 + 5*(x1-12)**2 + x2**4 + 3*(x3-11)**2 + \
10*x4**6 + 7*x5**2 + x6**4 - 4*x5*x6 - 10*x5 - 8*x6
bounds = [(-10.,10.)]*7
# with penalty='penalty' applied, solution is:
xs = [2.330499, 1.951372, -0.4775414, 4.365726, -0.6244870, 1.038131, 1.594227]
ys = 680.6300573
from mystic.symbolic import (generate_constraint, generate_solvers,
generate_penalty, generate_conditions,
simplify, symbolic_bounds)
equations = """
2.0*x0**2 + 3.0*x1**4 + x2 + 4.0*x3**2 + 5.0*x4 - 127.0 <= 0.0
7.0*x0 + 3.0*x1 + 10.0*x2**2 + x3 - x4 - 282.0 <= 0.0
23.0*x0 + x1**2 + 6.0*x5**2 - 8.0*x6 - 196.0 <= 0.0
4.0*x0**2 + x1**2 - 3.0*x0*x1 + 2.0*x2**2 + 5.0*x5 - 11.0*x6 <= 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
result = diffev2(objective, x0=bounds, bounds=bounds, constraints=cf, penalty=pf, npop=40, gtol=200, disp=False, full_output=True)
assert almostEqual(result[0], xs, rel=1e-2)
assert almostEqual(result[1], ys, rel=1e-2)
# EOF
|
