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