A surrogate-model based multi-modal optimization algorithm

Abstract

In this article a new algorithm for optimization of multi-modal, nonlinear, black-box objective functions is introduced. It extends the recently-introduced adaptive multi-modal optimization by incorporating surrogate modelling features similar to response surface methods. The resulting algorithm has reduced computational intensity and is well-suited for optimization of expensive objective functions. It relies on an adaptive, multi-resolution mesh to obtain an initial estimation of the objective function surface. Local surrogate models are then constructed and used to generate additional trial points around the local minima discovered. The steps of mesh refinement and surrogate modelling continue until convergence is achieved. The algorithm produces progressively accurate surrogate models, which can be used for post-optimization studies such as sensitivity and tolerance analyses with minimal computational effort. This article demonstrates the effectiveness of the algorithm using comparative optimization of several multi-modal objective functions, and shows an engineering application of the design of a power electronic converter.

Keywords:

• multi-modal optimization
• response surface methodology
• surrogate modelling
• black-box optimization
• simulation-based design