A new algorithm for identifying all global maximizers based on simulated annealing

Abstract

In this work we consider the problem of finding all the global maximizers of a given nonlinear optimization problem. We propose a new algorithm that combines the simulated annealing (SA) method with a function stretching technique, to generate a sequence of global maximization problems that are defined whenever a new maximizer is identified. To find the global maximizers, we apply the SA algorithm to the sequence of maximization problems. Results of numerical experiments with a set of well-known test problems show that the proposed method is effective. We also compare the performance of our algorithm with other multi-global optimizers.