Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

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.
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:
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