In global optimization, a typical population-based stochastic search method works on a set of sample points from the feasible region. In this paper, we study a recently proposed method of this sort. The method utilizes an attraction-repulsion mechanism to move sample points toward optimality and is thus referred to as electromagnetism-like method (EM). The computational results showed that EM is robust in practice, so we further investigate the theoretical structure. After reviewing the original method, we present some necessary modifications for the convergence proof. We show that in the limit, the modified method converges to the vicinity of global optimum with probability one.

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Journal of Global Optimization
Erasmus Research Institute of Management

Birbil, I., Fang, S.-C., & Sheu, R.-L. (2004). On the convergence of a population-based global optimization algorithm. In Journal of Global Optimization (Vol. 30, pp. 301–318). doi:10.1007/s10898-004-8270-3