A New Multi-objective Evolutionary Algorithm: Neighborhood Exploring Evolution Strategy

This paper proposes a new multi-objective evolutionary algorithm, called neighborhood exploring evolution strategy (NEES). This approach incorporates the idea of neighborhood exploration together with other techniques commonly used in the multi-objective evolutionary optimization literature (namely, non-dominated sorting and diversity preservation mechanisms). This idea of the proposed approach was derived from a single-objective evolutionary algorithm, called line-up competition algorithm (LCA). The main idea is to assign neighborhoods of different size to different solutions. Within each neighborhood, new solutions are generated using a (1+ λ )-ES (evolution strategy). This scheme naturally balances the effect of local search (which is done by the evolution strategy) with that of the global search performed by the algorithm, and gradually impels the population to progress towards the true Pareto-optimal front of the problem and to explore the extent of such front. Three versions of our proposal are studied: a (1+1)-NEES, a (1+2)-NEES and a (1+5)-NEES. Such approaches are validated on a set of standard test problems reported in the specialized literature. Simulation results indicate that, for continuous numerical optimization problems, our proposal (particularly the (1+1)-NEES) is competitive with respect to the NSGA-II, which is an algorithm representative of the state-of-the-art in evolutionary multi-objective optimization. Moreover, all the versions of our NEES improve on the results of the NSGA-II when dealing with a discrete optimization problem. Although preliminary, such results might indicate a potential application area in which our proposed approach could be particularly useful.