surrogate_based_global

Adaptive Global 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)	Sub-method 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		replace_points	(Recommended) Replace points in the surrogate training set, instead of appending
Optional		max_iterations	Number of iterations allowed for optimizers and adaptive UQ methods

Description

The surrogate_based_global method iteratively performs optimization on a global surrogate using the same bounds during each iteration.

• In one iteration, optimal solutions are found on the surrogate model, and a subset of these are passed to the next iteration.

• At the next iteration, these surrogate-optimal variable sets are evaluated with the “truth” model, and added to the set of points over which the next surrogate is constructed.

In this way, the optimization operates on a more accurate surrogate during each iteration, presumably driving to optimality quickly. In contrast to surrogate_based_local, this approach has no guarantee of convergence.

Usage Tips

Attention: This adaptive method is not recommended for “build-once” surrogates trained from (static) imported data or trained online using a single Dakota design of experiments. Instead, any Dakota optimization method can be used with a (build-once) global surrogate by specifying the id_model of a global surrogate model with the optimizer’s model_pointer keyword.

Configuring the method:

• The sub-method, specified with either method_pointer or method_name should typically be an optimizer that returns multiple final solutions, such as moga or soga.

• The model_pointer keyword must identify a surrogate model which includes an underlying truth model, typically via truth_model_pointer or dace_method_pointer

Workflow:

• One might first try a single minimization method coupled with a surrogate model prior to using this surrogate-based global method. This is essentially equivalent to setting max_iterations to 1 and will allow one to get a sense of what surrogate types are the most accurate to use for the problem.

• Consider starting with a small number of maximum iterations, such as 3–5, to get a sense of how the optimization evolves as the surrogate gets updated. If it is still changing significantly, then a larger number (used in combination with restart) may be needed.

• Surrogates can be built for all primary functions and constraints or for only a subset of these functions and constraints. This allows one to use a “truth” model directly for some of the response functions, perhaps due to them being much less expensive than other functions.

Known Issue: When using discrete variables, there have been sometimes significant differences in surrogate behavior observed across computing platforms in some cases. The cause has not yet been fully diagnosed and is currently under investigation. In addition, guidance on appropriate construction and use of surrogates with discrete variables is under development. In the meantime, users should therefore be aware that there is a risk of inaccurate results when using surrogates with discrete variables.

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)

Theory

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.

The surrogate_based_global method was originally designed for MOGA (a multi-objective genetic algorithm). Since genetic algorithms often need thousands or tens of thousands of points to produce optimal or near-optimal solutions, the use of surrogates can be helpful for reducing the truth model evaluations. Instead of creating one set of surrogates for the individual objectives and running the optimization algorithm on the surrogate once, the idea is to select points along the (surrogate) Pareto frontier, which can be used to supplement the existing points.

In this way, one does not need to use many points initially to get a very accurate surrogate. The surrogate becomes more accurate as the iterations progress.