Additive approximations of Pareto-optimal sets by evolutionary multi-objective algorithms

Abstract

Often the Pareto front of a multi-objective optimization problem grows exponentially with the problem size. In this case, it is not possible to compute the whole Pareto front efficiently and one is interested in good approximations. We consider how evolutionary algorithms can achieve such approximations by using different diversity mechanisms. We discuss some well-known approaches such as the density estimator and the "-dominance approach and point out how and when such mechanisms provably help to obtain good additive approximations of the Pareto-optimal set.