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
limax_iterations
liconvergence_tolerance
lisolution_target
limax_boxsize_limit
limin_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)