Studies of multi‐start clustering for global optimization

Global/multi-modal optimization problems arise in many engineering applications. Owing to the existence of multiple minima, it is a challenge to solve the multi-modal optimization problem and to identify the global minimum especially if efficiency is a concern. In this paper, variants of the multi-start with clustering strategy are developed and studied for identifying multiple local minima in nonlinear global optimization problems. The study considers the sampling procedure, the use of Hessian information in forming clusters, the technique for cluster analysis and the local search procedure. Variations of multi-start with clustering are applied to 15 multi-modal problems. A comparative study focuses on the overall search effectiveness in terms of the number of local searches performed, local minima found and required function evaluations. The performance of these multi-start clustering algorithms ranges from very efficient to very robust. Copyright © 2002 John Wiley & Sons, Ltd.