A Pareto following variation operator for evolutionary dynamic multi-objective optimization

Tracking the Pareto-front in a dynamic multi-objective optimization problem (MOP) is a challenging task. Evolutionary algorithms are a representative meta-heuristic capable of meeting this challenge. Typically, the stochastic variation operators used in an evolutionary algorithm work in decision (or design) variable space, thus there are no guarantees that the new individuals produced are non-dominated and/or are unique in the population. In this paper, we introduce a novel variation operator that manipulates the values in both objective space and design variable space in such a way that it can avoid re-exploration of dominated solutions. The proposed operator, inspired by the theory of dynamic system identification, is based on integral transformation. Here, we approximate the next expected Pareto-front, and from this expected front, we generate corresponding correct decision variables. We show empirically that our algorithm can approximate the Pareto-optimal set for given static benchmark MOPpsilas and that it can track changes in the Pareto-front for particular dynamic MOPpsilas.