Stochastic Global Optimization Techniques

Abstract

In this research, a novel population-based global optimization method has been studied. The method is called Electromagnetism-like Mechanism or in short EM. The proposed method mimicks the behavior of electrically charged particles. In other words, a set of points is sampled from the feasible region and these points imitate the role of the charged particles in basic electromagnetism. The underlying idea of the method is directing sample points toward local optimizers, which point out attractive regions of the feasible space.The proposed method has been applied to different test problems from the literature. Moreover, the viability of the method has been tested by comparing its results with other reported results from the literature. Without using the higher order information, EM has converged rapidly (in terms of the number of function evaluations) to the global optimum and produced highly efficient results for problems of varying degree of difficulty.After a systematic study of the underlying stochastic process, the proof of convergence to the global optimum has been given for the proposed method. The thrust of the proof has been to show that in the limit, at least one of the points in the population moves to the neighborhood of the global optimum with probability one.The structure of the proposed method is very flexible permitting the easy development of variations. Capitalizing on this, several variants of the proposed method has been developed and compared with the other methods from the literature. These variants of EM have been able to provide accurate answers to selected problems and in many cases have been able to outperform other well-known methods.