.. _method-mesh_adaptive_search:
""""""""""""""""""""
mesh_adaptive_search
""""""""""""""""""""
Finds optimal variable values using adaptive mesh-based search
.. toctree::
:hidden:
:maxdepth: 1
method-mesh_adaptive_search-initial_delta
method-mesh_adaptive_search-variable_tolerance
method-mesh_adaptive_search-function_precision
method-mesh_adaptive_search-seed
method-mesh_adaptive_search-history_file
method-mesh_adaptive_search-display_format
method-mesh_adaptive_search-variable_neighborhood_search
method-mesh_adaptive_search-neighbor_order
method-mesh_adaptive_search-display_all_evaluations
method-mesh_adaptive_search-use_surrogate
method-mesh_adaptive_search-max_iterations
method-mesh_adaptive_search-max_function_evaluations
method-mesh_adaptive_search-scaling
method-mesh_adaptive_search-model_pointer
**Specification**
- *Alias:* None
- *Arguments:* None
**Child Keywords:**
+-------------------------+--------------------+----------------------------------+-----------------------------------------------+
| Required/Optional | Description of | Dakota Keyword | Dakota Keyword Description |
| | Group | | |
+=========================+====================+==================================+===============================================+
| 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 |
+----------------------------------------------+----------------------------------+-----------------------------------------------+
.. __: method-mesh_adaptive_search-initial_delta.html
__ method-mesh_adaptive_search-variable_tolerance.html
__ method-mesh_adaptive_search-function_precision.html
__ method-mesh_adaptive_search-seed.html
__ method-mesh_adaptive_search-history_file.html
__ method-mesh_adaptive_search-display_format.html
__ method-mesh_adaptive_search-variable_neighborhood_search.html
__ method-mesh_adaptive_search-neighbor_order.html
__ method-mesh_adaptive_search-display_all_evaluations.html
__ method-mesh_adaptive_search-use_surrogate.html
__ method-mesh_adaptive_search-max_iterations.html
__ method-mesh_adaptive_search-max_function_evaluations.html
__ method-mesh_adaptive_search-scaling.html
__ method-mesh_adaptive_search-model_pointer.html
**Description**
The mesh adaptive direct search algorithm :cite:p:`AuLeTr09a`
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 :dakkw:`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
:dakkw:`environment-results_output-hdf5` keyword, this method
writes the following results to HDF5:
- :ref:`hdf5_results-best_params`
- :ref:`hdf5_results-best_obj_fncs` (when :dakkw:`responses-objective_functions`) are specified)
- :ref:`hdf5_results-best_constraints`
- :ref:`hdf5_results-calibration` (when :dakkw:`responses-calibration_terms` are specified)
*Additional Discussion*
The mesh adaptive direct search method is made available in Dakota
through the NOMAD software :cite:p:`Nomad`,
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.
.. code-block::
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.
.. code-block::
<<<<< 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.
.. code-block::
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