Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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DIviding RECTangles method


This keyword is related to the topics:


Alias: none

Argument(s): none

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
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

Stopping criterion based on number of iterations

Optional convergence_tolerance

Stopping criterion based on convergence of the objective function or statistics

Optional max_function_evaluations Stopping criteria based on number of function evaluations
Optional scaling Turn on scaling for variables, responses, and constraints
Optional model_pointer

Identifier for model block to be used by a method


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.

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 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:

See Also

These keywords may also be of interest: