Finds optimal variable values using adaptive mesh-based search

Specification

Alias: none

Argument(s): none

Required/Optional	Dakota Keyword	Dakota Keyword Description
Optional	function_precision	Specify the maximum precision of the analysis code responses
Optional	seed	Seed of the random number generator
Optional	history_file	Name of file where mesh adaptive search records all evaluation points.
Optional	display_format	Information to be reported from mesh adaptive search's internal records.
Optional	variable_neighborhood_search	Percentage of evaluations to do to escape local minima.
Optional	neighbor_order	Number of dimensions in which to perturb categorical variables.
Optional	display_all_evaluations	Shows mesh adaptive search's internally held list of all evaluations
Optional	linear_inequality_constraint_matrix	Define coefficients of the linear inequality constraints
Optional	linear_inequality_lower_bounds	Define lower bounds for the linear inequality constraint
Optional	linear_inequality_upper_bounds	Define upper bounds for the linear inequality constraint
Optional	linear_inequality_scale_types	Specify how each linear inequality constraint is scaled
Optional	linear_inequality_scales	Define the characteristic values to scale linear inequalities
Optional	linear_equality_constraint_matrix	Define coefficients of the linear equalities
Optional	linear_equality_targets	Define target values for the linear equality constraints
Optional	linear_equality_scale_types	Specify how each linear equality constraint is scaled
Optional	linear_equality_scales	Define the characteristic values to scale linear equalities
Optional	model_pointer	Identifier for model block to be used by a method

Description

The mesh adaptive direct search algorithm[8] is a derivative-free generalized pattern search in which the set of points evaluated becomes increasingly dense, leading to good convergence properties. It can handle unconstrained problems as well as those with bound constraints and general nonlinear constraints. Furthermore, it can handle continuous, discrete, and categorical variables.

Default Behavior

By default, mesh_adaptive_search operates on design variables. The types of variables can be expanded through the use of the active keyword in the variables block in the Dakota input file. Categorical variables, however, must be limited to design variables.

Expected Outputs

The best objective function value achieved and associated parameter and constraint values can be found at the end of the Dakota output. The method's internally summarized iteration history will appear in the screen output. It also generates a history file containing a list of all function evaluations done.

Additional Discussion

The mesh adaptive direct search method is made available in Dakota through the NOMAD software[1], available to the public under the GNU LGPL from http://www.gerad.ca/nomad.

Examples

The following is an example of a Dakota input file that makes use of mesh_adaptive_search to optimize the textbook function.

method,
        mesh_adaptive_search
        seed = 1234

variables,
        continuous_design = 3                                   
          initial_point   -1.0    1.5   2.0                     
          upper_bounds    10.0   10.0  10.0                     
          lower_bounds   -10.0  -10.0 -10.0                     
          descriptors      'x1'  'x2'  'x3'                     

interface,
       direct                                                   
          analysis_driver = 'text_book'                         

responses,
        objective_functions = 1
        no_gradients
        no_hessians
\end verbatim

The best function value and associated parameters are found at the end
of the %Dakota output.

\verbatim
<<<<< Function evaluation summary: 674 total (674 new, 0 duplicate)
<<<<< Best parameters          =
                      1.0000000000e+00 x1
                      1.0000000000e+00 x2
                      1.0000000000e+00 x3
<<<<< Best objective function  =
                      1.0735377280e-52
<<<<< Best data captured at function evaluation 658

A NOMAD-generated iteration summary is also printed to the screen.

MADS run {

    BBE OBJ

       1    17.0625000000
       2    1.0625000000
      13    0.0625000000
      24    0.0002441406
      41    0.0000314713
      43    0.0000028610
      54    0.0000000037
      83    0.0000000000
     105    0.0000000000
     112    0.0000000000
     114    0.0000000000
     135    0.0000000000
     142    0.0000000000
     153    0.0000000000
     159    0.0000000000
     171    0.0000000000
     193    0.0000000000
     200    0.0000000000
     207    0.0000000000
     223    0.0000000000
     229    0.0000000000
     250    0.0000000000
     266    0.0000000000
     282    0.0000000000
     288    0.0000000000
     314    0.0000000000
     320    0.0000000000
     321    0.0000000000
     327    0.0000000000
     354    0.0000000000
     361    0.0000000000
     372    0.0000000000
     373    0.0000000000
     389    0.0000000000
     400    0.0000000000
     417    0.0000000000
     444    0.0000000000
     459    0.0000000000
     461    0.0000000000
     488    0.0000000000
     492    0.0000000000
     494    0.0000000000
     501    0.0000000000
     518    0.0000000000
     530    0.0000000000
     537    0.0000000000
     564    0.0000000000
     566    0.0000000000
     583    0.0000000000
     590    0.0000000000
     592    0.0000000000
     604    0.0000000000
     606    0.0000000000
     629    0.0000000000
     636    0.0000000000
     658    0.0000000000
     674    0.0000000000

} end of run (mesh size reached NOMAD precision)

blackbox evaluations                     : 674
best feasible solution                   : ( 1 1 1 ) h=0 f=1.073537728e-52