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
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
|
% STK_TESTFUN_HARTMAN6 computes the "Hartman6" function
%
% The Hartman6 function is a test function in dimension 6, which is
% part of the famous Dixon & Szego benchmark [1] in global optimization.
%
% It is usually minimized over [0, 1]^6.
%
% HISTORICAL REMARKS
%
% This function belongs to a general class of test functions
% introduced by Hartman [2], hence the name.
%
% The particular set of coefficients used in the definition of the
% "Hartman6" function, however, seems to have been introduced by [1].
%
% GLOBAL MINIMUM
%
% According to [4], the function has one global minimum at
%
% x = [0.20169 0.150011 0.476874 0.275332 0.311652 0.657300].
%
% The corresponding function value is:
%
% f(x) = -3.322368011391339
%
% A slightly lower value is attained [5] at
%
% x = [0.20168952 0.15001069 0.47687398 ...
% 0.27533243 0.31165162 0.65730054]
%
% The corresponding function value is:
%
% f(x) = -3.322368011415512
%
% The exact global optimum does not appear to be known.
%
% REFERENCES
%
% [1] L. C. W. Dixon & G. P. Szego (1978). Towards Global
% Optimization 2, North-Holland, Amsterdam, The Netherlands
%
% [2] J. K. Hartman (1973). Some experiments in global optimization.
% Naval Research Logistics Quarterly, 20(3):569-576.
%
% [3] V. Picheny, T. Wagner & D. Ginsbourger (2013). A benchmark
% of kriging-based infill criteria for noisy optimization.
% Structural and Multidisciplinary Optimization, 48:607-626.
%
% [4] S. Surjanovic & D. Bingham. Virtual Library of Simulation
% Experiments: Test Functions and Datasets. Retrieved March 3,
% 2022, https://www.sfu.ca/~ssurjano/hart4.html.
%
% [5] O. Roustant, D. Ginsbourger & Y. Deville (2012).
% DiceKriging package, version 1.6.0 from 2021-02-23
% URL: https://cran.r-project.org/web/packages/DiceKriging/index.html
% Author
%
% Julien Bect <julien.bect@centralesupelec.fr>
% Copying Permission Statement (this file)
%
% To the extent possible under law, CentraleSupelec has waived all
% copyright and related or neighboring rights to
% stk_testfun_hartman6.m. This work is published from France.
%
% License: CC0 <http://creativecommons.org/publicdomain/zero/1.0/>
% Copying Permission Statement (STK toolbox as a whole)
%
% This file is part of
%
% STK: a Small (Matlab/Octave) Toolbox for Kriging
% (https://github.com/stk-kriging/stk/)
%
% STK is free software: you can redistribute it and/or modify it under
% the terms of the GNU General Public License as published by the Free
% Software Foundation, either version 3 of the License, or (at your
% option) any later version.
%
% STK is distributed in the hope that it will be useful, but WITHOUT
% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
% or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
% License for more details.
%
% You should have received a copy of the GNU General Public License
% along with STK. If not, see <http://www.gnu.org/licenses/>.
function y = stk_testfun_hartman6 (x)
a = [ ...
[ 10.00 0.05 3.00 17.00 ]; ...
[ 3.00 10.00 3.50 8.00 ]; ...
[ 17.00 17.00 1.70 0.05 ]; ...
[ 3.50 0.10 10.00 10.00 ]; ...
[ 1.70 8.00 17.00 0.10 ]; ...
[ 8.00 14.00 8.00 14.00 ]];
p = [ ...
[ 0.1312 0.2329 0.2348 0.4047 ]; ...
[ 0.1696 0.4135 0.1451 0.8828 ]; ...
[ 0.5569 0.8307 0.3522 0.8732 ]; ...
[ 0.0124 0.3736 0.2883 0.5743 ]; ...
[ 0.8283 0.1004 0.3047 0.1091 ]; ...
[ 0.5886 0.9991 0.6650 0.0381 ]];
c = [1.0 1.2 3.0 3.2];
y = stk_testfun_hartman_generic (x, a, p, c);
end % function
%!test
%! x1 = [0.20169 0.150011 0.476874 0.275332 0.311652 0.657300];
%! y1 = -3.322368011391339;
%!
%! x2 = [0.20168952 0.15001069 0.47687398 0.27533243 0.31165162 0.65730054];
%! y2 = -3.322368011415512;
%!
%! y = stk_testfun_hartman6 ([x1; x2]);
%! assert (stk_isequal_tolabs (y, [y1; y2], 1e-15))
|
