mesh_adaptive_search

Finds optimal variable values using adaptive mesh-based search

Specification

• Alias: None

• Arguments: None

Child Keywords:

Required/Optional	Description of Group	Dakota Keyword	Dakota Keyword Description
Optional		initial_delta	Initial step size for derivative-free optimizers
Optional		variable_tolerance	Step length-based stopping criteria for derivative-free optimizers
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		use_surrogate	Surrogate model usage mode for mesh adaptive search
Optional		max_iterations	Number of iterations allowed for optimizers and adaptive UQ methods
Optional		max_function_evaluations	Number of function evaluations allowed for optimizers
Optional		scaling	Turn on scaling for variables, responses, and constraints
Optional		model_pointer	Identifier for model block to be used by a method

Description

The mesh adaptive direct search algorithm [ALeDigabelT09] 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 by default, with the option to control the method’s output through Dakota’s output level. It also generates a history file containing a list of all function evaluations done.

Expected HDF5 Output

If Dakota was built with HDF5 support and run with the hdf5 keyword, this method writes the following results to HDF5:

• Best Parameters

• Best Objective Functions (when objective_functions) are specified)

• Best Nonlinear Constraints

• Calibration (when calibration_terms are specified)

Additional Discussion

The mesh adaptive direct search method is made available in Dakota through the NOMAD software [AAC+], 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

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

<<<<< 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 evaluation ID: 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