asynch_pattern_search

Pattern search, derivative free optimization method

Topics

package_hopspack, global_optimization_methods

Specification

• Alias: coliny_apps

• Arguments: 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 a batch of concurrent function evaluations in a parallel algorithm
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 [GK06] 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:

• max_function_evaluations

• constraint_tolerance

• output

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:

• Best Parameters

• Best Objective Functions (when objective_functions) are specified)

• Best Nonlinear Constraints

• Calibration (when calibration_terms are specified)