Refined EM Method for Solving Linearly Constrained Global Optimization Problems

Abstract

The Electromagnetism-like Mechanism (EM) has been widely used for solving global optimization problems with box-constrained variables. It is a population-based stochastic search method. Since the method uses function evaluations only at each step, it does not require any special information or structure of the objective function. In this article, we extend the original EM for solving optimization problems with linear constraints. The proposed method mimics the behavior of electrically charged particles that are restricted in the feasible region formed by the linear constraints. The underlying idea is to direct the sample points to some attractive regions of the feasible domain. In refined EM, the major steps of the original EM are redesigned to handle the explicit linear constraints in an efficient manner to find global optimal solutions. The proposed method is evaluated using many known test problems and is compared with some existing methods. Computational results show that without using the higher-order information, refined EM converges rapidly (in terms of the number of functions evaluations) to the global optimal solutions and produces better results than other known methods in solving problems of a varying degree of difficulty.