Dakota Reference Manual  Version 6.12
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asynch_pattern_search


Pattern search, derivative free optimization method

Topics

This keyword is related to the topics:

Specification

Alias: coliny_apps

Argument(s): none

Child Keywords:

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
Optional initial_delta

Initial step size for derivative-free optimizers

Optional contraction_factor Amount by which step length is rescaled
Optional variable_tolerance

Step length-based stopping criteria for derivative-free optimizers

Optional solution_target Stopping criteria based on objective function value
Optional synchronization Select how Dakota schedules function evaluations in a pattern search
Optional merit_function Balance goals of reducing objective function and satisfying constraints
Optional constraint_penalty Multiplier for the penalty function
Optional smoothing_factor Smoothing value for smoothed penalty functions
Optional constraint_tolerance

Maximum allowable constraint violation still considered feasible

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

Description

The asynchronous parallel pattern search (APPS) algorithm [36] is a fully asynchronous pattern search technique in that the search along each offset direction continues without waiting for searches along other directions to finish.

Currently, APPS only supports coordinate bases with a total of 2n function evaluations in the pattern, and these patterns may only contract.

Concurrency

APPS exploits parallelism through the use of Dakota's concurrent function evaluations. The variant of the algorithm that is currently exposed, however, limits the amount of concurrency that can be exploited. In particular, APPS can leverage an evaluation concurrency level of at most twice the number of variables. More options that allow for greater evaluation concurrency may be exposed in future releases.

Algorithm Behavior

  • initial_delta: the initial step length, must be positive
  • variable_tolerance: step length used to determine convergence, must be greater than or equal to 4.4e-16
  • contraction_factor: amount by which step length is rescaled after unsuccesful iterates, must be strictly between 0 and 1

Merit Functions

APPS solves nonlinearly constrained problems by solving a sequence of linearly constrained merit function-base subproblems. There are several exact and smoothed exact penalty functions that can be specified with the merit_function control. The options are as follows:

  • merit_max: based on $ \ell_\infty$ norm
  • merit_max_smooth: based on smoothed $ \ell_\infty$ norm
  • merit1: based on $ \ell_1$ norm
  • merit1_smooth: based on smoothed $ \ell_1$ norm
  • merit2: based on $ \ell_2$ norm
  • merit2_smooth: based on smoothed $ \ell_2$ norm
  • merit2_squared: based on $ \ell_2^2$ norm

The user can also specify the following to affect the merit functions:

  • constraint_penalty
  • smoothing_parameter

Method Independent Controls

The only method independent controls that are currently mapped to APPS are:

Note that while APPS treats the constraint tolerance separately for linear and nonlinear constraints, we apply the same value to both if the user specifies constraint_tolerance.

The APPS internal display level is mapped to the Dakota output settings as follows:

  • debug: display final solution, all input parameters, variable and constraint info, trial points, search directions, and execution details
  • verbose: display final solution, all input parameters, variable and constraint info, and trial points
  • normal: display final solution, all input parameters, variable and constraint summaries, and new best points
  • quiet: display final solution and all input parameters
  • silent: display final solution

Expected HDF5 Output

If Dakota was built with HDF5 support and run with the hdf5 keyword, this method writes the following results to HDF5: