Pattern Search Methods

Overview

Pattern search methods are a class of direct search optimizers that have recently received a lot of attention because of new convergence proofs that guarantee weak first order stationary point convergence [DenTor94,Tor89,Tor97,Tor91].

The GPSOpt class provides a generic framework for defining generalized pattern search algorithms. This class implements the framework used by Torczon [Tor97] to define generalized pattern search methods. The class PatternSearch provides a specific implementation of several types of pattern search methods that perform a rather local search about the best current iterate. This includes randomized variants of these methods, which randomize the order of the steps taken in the deterministic algorithm; these methods have the same convergence properties as their deterministic counterparts.

The PatternSearch class defines a variety of pattern search algorithms. Although these algorithms could have been defined with seperate classes, it has proved easier to maintain these algorithms within a single class, using a switch to select which algorithm is executed.

For each of these pattern search algorithms, a single expansion and contraction factor is used. The default expansion factor is 2.0 and the default contraction factor is 0.5. None of these methods explicitly maintains a pattern matrix, so the UpdateMatrix method is not defined. The variable em_case is used to select amongst the following pattern search algorithms:

Current Status

The code in GPSOpt is rather stable. The code defining the various pattern search methods continues to be refined.

\subsection psparams Solver Parameters