Dakota Reference Manual  Version 6.2 Large-Scale Engineering Optimization and Uncertainty Analysis

Finds optimal variable values using adaptive mesh-based search

## Specification

Alias: none

Argument(s): none

Required/Optional Description of Group 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.

## Examples

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

method,
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_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