# coliny_direct

DIviding RECTangles method

**Topics**

package_scolib, package_coliny, global_optimization_methods

**Specification**

*Alias:*None*Arguments:*None

**Child Keywords:**

Required/Optional |
Description of Group |
Dakota Keyword |
Dakota Keyword Description |
---|---|---|---|

Optional |
Determine how rectangles are subdivided |
||

Optional |
Tolerance for whether a subregion is worth dividing |
||

Optional |
Tolerance for whether a subregion is worth dividing |
||

Optional |
Stopping Criterion based on longest edge of hyperrectangle |
||

Optional |
Stopping Criterion based on shortest edge of hyperrectangle |
||

Optional |
Multiplier for the penalty function |
||

Optional |
Stopping criteria based on objective function value |
||

Optional |
Seed of the random number generator |
||

Optional |
Show algorithm parameters not exposed in Dakota input |
||

Optional |
Set method options not available through Dakota spec |
||

Optional |
Number of iterations allowed for optimizers and adaptive UQ methods |
||

Optional |
Stopping criterion based on objective function or statistics convergence |
||

Optional |
Number of function evaluations allowed for optimizers |
||

Optional |
Turn on scaling for variables, responses, and constraints |
||

Optional |
Identifier for model block to be used by a method |

**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
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

`max_function_evaluations`

li`max_iterations`

li`convergence_tolerance`

li`solution_target`

li`max_boxsize_limit`

li`min_boxsize_limit`

- most effective in practice

*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 Objective Functions (when

`objective_functions`

) are specified)Calibration (when

`calibration_terms`

are specified)