1Blurb::
2Finds optimal variable values using adaptive mesh-based search
3
4Description::
5The mesh adaptive direct search algorithm \cite AuLeTr09a
6is a derivative-free generalized pattern
7search in which the set of points evaluated becomes increasingly
8dense, leading to good convergence properties.  It can handle
9unconstrained problems as well as those with bound constraints and
10general nonlinear constraints. Furthermore, it can handle continuous,
11discrete, and categorical variables.
12
13<b> Default Behavior </b>
14
15By default, \c mesh_adaptive_search operates on design variables.  The
16types of variables can be expanded through the use of the \c active
17keyword in the \ref variables block in the %Dakota input file.
18Categorical variables, however, must be limited to design variables.
19
20<b> Expected Outputs </b>
21
22The best objective function value achieved and associated parameter
23and constraint values can be found at the end of the %Dakota output.
24The method's internally summarized iteration history will appear in
25the screen output by default, with the option to control the method's
26output through Dakota's output level.  It also generates a history
27file containing a list of all function evaluations done.
28
29<b>Expected HDF5 Output</b>
30
31If Dakota was built with HDF5 support and run with the
32\ref environment-results_output-hdf5 keyword, this method
33writes the following results to HDF5:
34
35- \ref hdf5_results-best_params
36- \ref hdf5_results-best_obj_fncs (when \ref responses-objective_functions) are specified)
37- \ref hdf5_results-best_constraints
38- \ref hdf5_results-calibration (when \ref responses-calibration_terms are specified)
39
40<b> Additional Discussion </b>
41
42The mesh adaptive direct search method is made available in %Dakota
43through the NOMAD software \cite Nomad,
44available to the public under the
45GNU LGPL from http://www.gerad.ca/nomad.
46
47Topics::
48
49Examples::
50
51The following is an example of a %Dakota input file that makes use of
52\c mesh_adaptive_search to optimize the textbook function.
53
54\verbatim
55method,
56        mesh_adaptive_search
57        seed = 1234
58
59variables,
60        continuous_design = 3
61          initial_point   -1.0    1.5   2.0
62          upper_bounds    10.0   10.0  10.0
63          lower_bounds   -10.0  -10.0 -10.0
64          descriptors      'x1'  'x2'  'x3'
65
66interface,
67       direct
68          analysis_driver = 'text_book'
69
70responses,
71        objective_functions = 1
72        no_gradients
73        no_hessians
74\endverbatim
75
76The best function value and associated parameters are found at the end
77of the %Dakota output.
78
79\verbatim
80<<<<< Function evaluation summary: 674 total (674 new, 0 duplicate)
81<<<<< Best parameters          =
82                      1.0000000000e+00 x1
83                      1.0000000000e+00 x2
84                      1.0000000000e+00 x3
85<<<<< Best objective function  =
86                      1.0735377280e-52
87<<<<< Best data captured at function evaluation 658
88\endverbatim
89
90A NOMAD-generated iteration summary is also printed to the screen.
91
92\verbatim
93MADS run {
94
95	BBE	OBJ
96
97	   1	17.0625000000
98	   2	1.0625000000
99	  13	0.0625000000
100	  24	0.0002441406
101	  41	0.0000314713
102	  43	0.0000028610
103	  54	0.0000000037
104	  83	0.0000000000
105	 105	0.0000000000
106	 112	0.0000000000
107	 114	0.0000000000
108	 135	0.0000000000
109	 142	0.0000000000
110	 153	0.0000000000
111	 159	0.0000000000
112	 171	0.0000000000
113	 193	0.0000000000
114	 200	0.0000000000
115	 207	0.0000000000
116	 223	0.0000000000
117	 229	0.0000000000
118	 250	0.0000000000
119	 266	0.0000000000
120	 282	0.0000000000
121	 288	0.0000000000
122	 314	0.0000000000
123	 320	0.0000000000
124	 321	0.0000000000
125	 327	0.0000000000
126	 354	0.0000000000
127	 361	0.0000000000
128	 372	0.0000000000
129	 373	0.0000000000
130	 389	0.0000000000
131	 400	0.0000000000
132	 417	0.0000000000
133	 444	0.0000000000
134	 459	0.0000000000
135	 461	0.0000000000
136	 488	0.0000000000
137	 492	0.0000000000
138	 494	0.0000000000
139	 501	0.0000000000
140	 518	0.0000000000
141	 530	0.0000000000
142	 537	0.0000000000
143	 564	0.0000000000
144	 566	0.0000000000
145	 583	0.0000000000
146	 590	0.0000000000
147	 592	0.0000000000
148	 604	0.0000000000
149	 606	0.0000000000
150	 629	0.0000000000
151	 636	0.0000000000
152	 658	0.0000000000
153	 674	0.0000000000
154
155} end of run (mesh size reached NOMAD precision)
156
157blackbox evaluations                     : 674
158best feasible solution                   : ( 1 1 1 ) h=0 f=1.073537728e-52
159\endverbatim
160
161Theory::
162Faq::
163See_Also::
164