.. _method-coliny_direct:

"""""""""""""
coliny_direct
"""""""""""""


DIviding RECTangles method



**Topics**


package_scolib, package_coliny, global_optimization_methods


.. toctree::
   :hidden:
   :maxdepth: 1

   method-coliny_direct-division
   method-coliny_direct-global_balance_parameter
   method-coliny_direct-local_balance_parameter
   method-coliny_direct-max_boxsize_limit
   method-coliny_direct-min_boxsize_limit
   method-coliny_direct-constraint_penalty
   method-coliny_direct-solution_target
   method-coliny_direct-seed
   method-coliny_direct-show_misc_options
   method-coliny_direct-misc_options
   method-coliny_direct-max_iterations
   method-coliny_direct-convergence_tolerance
   method-coliny_direct-max_function_evaluations
   method-coliny_direct-scaling
   method-coliny_direct-model_pointer


**Specification**

- *Alias:* None

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+------------------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword               | Dakota Keyword Description                    |
|                         | Group              |                              |                                               |
+=========================+====================+==============================+===============================================+
| Optional                                     | `division`__                 | Determine how rectangles are subdivided       |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `global_balance_parameter`__ | Tolerance for whether a subregion is worth    |
|                                              |                              | dividing                                      |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `local_balance_parameter`__  | Tolerance for whether a subregion is worth    |
|                                              |                              | dividing                                      |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `max_boxsize_limit`__        | Stopping Criterion based on longest edge of   |
|                                              |                              | hyperrectangle                                |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `min_boxsize_limit`__        | Stopping Criterion based on shortest edge of  |
|                                              |                              | hyperrectangle                                |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `constraint_penalty`__       | Multiplier for the penalty function           |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `solution_target`__          | Stopping criteria based on objective function |
|                                              |                              | value                                         |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `seed`__                     | Seed of the random number generator           |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `show_misc_options`__        | Show algorithm parameters not exposed in      |
|                                              |                              | Dakota input                                  |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `misc_options`__             | Set method options not available through      |
|                                              |                              | Dakota spec                                   |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `max_iterations`__           | Number of iterations allowed for optimizers   |
|                                              |                              | and adaptive UQ methods                       |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `convergence_tolerance`__    | Stopping criterion based on objective         |
|                                              |                              | function or statistics convergence            |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| 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-coliny_direct-division.html
__ method-coliny_direct-global_balance_parameter.html
__ method-coliny_direct-local_balance_parameter.html
__ method-coliny_direct-max_boxsize_limit.html
__ method-coliny_direct-min_boxsize_limit.html
__ method-coliny_direct-constraint_penalty.html
__ method-coliny_direct-solution_target.html
__ method-coliny_direct-seed.html
__ method-coliny_direct-show_misc_options.html
__ method-coliny_direct-misc_options.html
__ method-coliny_direct-max_iterations.html
__ method-coliny_direct-convergence_tolerance.html
__ method-coliny_direct-max_function_evaluations.html
__ method-coliny_direct-scaling.html
__ method-coliny_direct-model_pointer.html



**Description**


The DIviding RECTangles (DIRECT) optimization algorithm is a
derivative free global optimization method that balances local search
in promising regions of the design space with global search in
unexplored regions. As shown in Figure 5.1, DIRECT adaptively
subdivides the space of feasible design points so as to guarantee that
iterates are generated in the neighborhood of a global minimum in
finitely many iterations.

\image html direct1.jpg "Figure 5.1 Design space partitioning with
DIRECT" \image latex direct1.eps "Design space partitioning with
DIRECT" width=10cm

In practice, DIRECT has proven an effective heuristic for engineering
design applications, for which it is able to quickly identify
candidate solutions that can be further refined with fast local
optimizers.

*See the page :ref:`topic-package_scolib` for important information
regarding all SCOLIB methods*

The DIRECT algorithm supports concurrency up to twice the number of
variables being optimized.

DIRECT uses the ``solution_target``, ``constraint_penalty`` and
``show_misc_options`` specifications that are described in
:ref:`topic-package_scolib`. Note, however, that DIRECT uses a fixed penalty
value for constraint violations (i.e. it is not dynamically adapted as
is done in ``coliny_pattern_search``).

*Search Parameters*

The ``global_balance_parameter`` controls how much global search is
performed by only allowing a subregion to be subdivided if the size of
the subregion divided by the size of the largest subregion is at least
``global_balance_parameter``.  Intuitively, this forces large
subregions to be subdivided before the smallest subregions are
refined. The ``local_balance_parameter`` provides a tolerance for
estimating whether the smallest subregion can provide a sufficient
decrease to be worth subdividing; the default value is a small value
that is suitable for most applications.

*Stopping Critieria*

DIRECT can be terminated with:
 \li :dakkw:`method-coliny_direct-max_function_evaluations`
 \li :dakkw:`method-coliny_direct-max_iterations`
 \li :dakkw:`method-coliny_direct-convergence_tolerance`
 \li :dakkw:`method-coliny_direct-solution_target`
 \li :dakkw:`method-coliny_direct-max_boxsize_limit`
 \li :dakkw:`method-coliny_direct-min_boxsize_limit` - most effective in practice


*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)


