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
57
58
59
60
61
62
63
64
65
|
#!/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 abs, sum, cos, prod as product, sqrt
sum_jx = 0.0
for j in range(len(x)): sum_jx = sum_jx + (j+1) * x[j]**2
return -abs((sum(cos(x)**4) - 2.*product(cos(x)**2))/sqrt(sum_jx))
def bounds(len=3):
return [(0.0,10.0)]*len
# with penalty='penalty' applied, solution is:
xs = [ 3.04295933, 1.48286963, 0.16618875]
ys = -0.51578987
"""
for len(x) = 10,
xs ~ [3.12388714, 3.06913834, 3.01426760, 2.95755412, 1.46603517,
0.36802963, 0.36346912, 0.35912472, 0.35493945, 0.35095372]
ys ~ -0.74732020
"""
bounds = bounds(len(xs))
from mystic.constraints import and_
from mystic.symbolic import (generate_constraint, generate_solvers,
generate_penalty, generate_conditions,
simplify, symbolic_bounds)
equations = """
-prod([x0, x1, x2]) + 0.75 <= 0.0
sum([x0, x1, x2]) - 7.5*3 <= 0.0
"""
equations += symbolic_bounds(*zip(*bounds))
cf = generate_constraint(generate_solvers(simplify(equations)), join=and_)
pf = generate_penalty(generate_conditions(equations))
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=80, disp=False, full_output=True, gtol=100)
assert almostEqual(result[0], xs, rel=1e-1)
assert almostEqual(result[1], ys, rel=1e-1)
# EOF
|
