Stochastic Approximation and Brownian Repulsion based Evolutionary Search

Abstract: Many global optimization algorithms of the memetic variety rely on some form of stochastic search, and yet they often lack a sound probabilistic basis. Without a recourse to the powerful tools of stochastic calculus, treading the fine balance between exploration and exploitation could be tricky. In this work, we propose an evolutionary algorithm (EA) comprising two types of additive updates. The primary update utilizes stochastic approximation to guide a population of randomly initialized particles towards an optimum. We incorporate derivative-free Robbins-Monro type gains in the first update so as to provide a directional guidance to the candidate solutions. The secondary update leverages stochastic conditioning to apply random perturbations for a controlled yet efficient exploration. Specifically, conceptualized on a change of measures, the perturbation strategy discourages two or more trajectories exploring the same region of the search space. Our optimization algorithm, dubbed as SABRES (Stochastic Approximation and Brownian Repulsion based Evolutionary Search), is applied to CEC-2022 benchmark functions on global optimization. Numerical results are indicative of the potentialities of SABRES in solving a variety of challenging multi-modal, non-separable, and asymmetrical benchmark functions.