Dynamic resizing for grid-based archiving in evolutionary multi objective optimization

Archival of elite solutions is widespread practice in evolutionary multi-objective optimization. Grid-based archiving presents a compromise between accuracy and computational cost. Most grid-based archiving algorithms require apriori knowledge of the span of the Pareto front for pre-setting of the grid length or the associated parameter, grid number. Unfortunately the knowledge is often unavailable beforehand in practice. The quality of the attained non-dominated front can be very sensitive to the dimension of the grids. This paper presents a dynamic grid resizing strategy, capable of shrinking or expanding hyper grids as necessity dictates. Empirical study on two- and three-objective test functions demonstrates robust performance with respect to the initial grid sizes. Applied in the context of PAES, the adaptive archiving strategy performed well for initial grid sizes determined from a uniform random distribution. In comparison to AGA, the dynamic strategy presents improved non-dominated solutions in terms of proximity to the Pareto front and diversity for selected test problems.

1. Introduction

Multi-Objective optimization involves multiple conflicting, incomparable and non-commensurable objectives. The generic Multi-Objective Evolutionary Algorithm (MOEA) aims to attain a well-distributed set of efficient solutions which map to the Pareto front in the objective space. Besides appropriate ranking and selection strategy, elitism is important for MOEAs for obtaining a good approximation of the Pareto front [1].