surrogate_based_local

Local Surrogate Based Optimization

Topics

surrogate_based_optimization_methods

Specification

• Alias: None

• Arguments: None

Child Keywords:

Required/Optional	Description of Group	Dakota Keyword	Dakota Keyword Description
Required (Choose One)	Subproblem Optimizer Selection	method_pointer	Pointer to sub-method to apply to a surrogate or branch-and-bound sub-problem
		method_name	Specify sub-method by name
Required		model_pointer	Identifier for model block to be used by a method
Optional		soft_convergence_limit	Limit number of iterations w/ little improvement
Optional		truth_surrogate_bypass	Bypass lower level surrogates when performing truth verifications on a top level surrogate
Optional		approx_subproblem	Identify functions to be included in surrogate merit function
Optional		merit_function	Select type of penalty or merit function
Optional		acceptance_logic	Set criteria for trusted surrogate
Optional		constraint_relax	Enable constraint relaxation
Optional		trust_region	Specification group for trust region model management
Optional		max_iterations	Number of iterations allowed for optimizers and adaptive UQ methods
Optional		convergence_tolerance	Stopping criterion based on objective function or statistics convergence
Optional		constraint_tolerance	Maximum allowable constraint violation still considered feasible

Description

In surrogate-based optimization (SBO) and surrogate-based nonlinear least squares (SBNLS), minimization occurs using a set of one or more approximations, defined from a surrogate model, that are built and periodically updated using data from a “truth” model. The surrogate model can be a global data fit (e.g., regression or interpolation of data generated from a design of computer experiments), a multipoint approximation, a local Taylor Series expansion, or a model hierarchy approximation (e.g., a low-fidelity simulation model), whereas the truth model involves a high-fidelity simulation model. The goals of surrogate-based methods are to reduce the total number of truth model simulations and, in the case of global data fit surrogates, to smooth noisy data with an easily navigated analytic function.

In the surrogate-based local method, a trust region approach is used to manage the minimization process to maintain acceptable accuracy between the surrogate model and the truth model (by limiting the range over which the surrogate model is trusted). The process involves a sequence of minimizations performed on the surrogate model and bounded by the trust region. At the end of each approximate minimization, the candidate optimum point is validated using the truth model. If sufficient decrease has been obtained in the truth model, the trust region is re-centered around the candidate optimum point and the trust region will either shrink, expand, or remain the same size depending on the accuracy with which the surrogate model predicted the truth model decrease. If sufficient decrease has not been attained, the trust region center is not updated and the entire trust region shrinks by a user-specified factor. The cycle then repeats with the construction of a new surrogate model, a minimization, and another test for sufficient decrease in the truth model. This cycle continues until convergence is attained.

Expected HDF5 Output

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

• hdf5_results-best_params

• hdf5_results-best_obj_fncs (when responses-objective_functions) are specified)

• hdf5_results-best_constraints

• hdf5_results-calibration (when responses-calibration_terms are specified)

Theory

For surrogate_based_local problems with nonlinear constraints, a number of algorithm formulations exist as described in [ED06] and as summarized in Surrogate-Based Local Minimization.