On the implementation of a global optimization method for mixed-variable problems

TL;DR

This paper presents an enhanced global optimization algorithm for mixed-variable problems, integrating novel modifications into existing radial basis and response surface methods, and demonstrates its effectiveness through numerical experiments.

Contribution

It introduces several improvements to existing algorithms, including categorical variable handling, local refinement, flexible interpolation models, and parallel evaluation support.

Findings

Effective handling of categorical variables

Improved optimization performance demonstrated

Parallel evaluation accelerates convergence

Abstract

We describe the optimization algorithm implemented in the open-source derivative-free solver RBFOpt. The algorithm is based on the radial basis function method of Gutmann and the metric stochastic response surface method of Regis and Shoemaker. We propose several modifications aimed at generalizing and improving these two algorithms: (i) the use of an extended space to represent categorical variables in unary encoding; (ii) a refinement phase to locally improve a candidate solution; (iii) interpolation models without the unisolvence condition, to both help deal with categorical variables, and initiate the optimization before a uniquely determined model is possible; (iv) a master-worker framework to allow asynchronous objective function evaluations in parallel. Numerical experiments show the effectiveness of these ideas.