On the choice of neighborhood sampling to build effective search operators for constrained MOPs

For the treatment of multi-objective optimization problems (MOPs) sto-chas-tic search algorithms such as multi-objective evolutionary algorithms (MOEAs) are very popular due to their global set based approach. Multi-objective stochastic local search (MOSLS) represents a powerful tool within MOEAs which is crucial for the guidance of the populations’ individuals. The success of variation operators in evolutionary algorithms is related to survival chances of their new generated individuals. Though individual feasibility determines directly the survival chances, in MOEAs, regular variation operators do not consider any information from the constraints. Recently, an initial study has been done for unconstrained MOPs revealing that a pressure both toward and along the Pareto front is inherent in MOSLS by which the behavior of many MOEAs in different stages of the search could be explained to a certain extent. In the present paper we go further to study the implications of MOSLS for the constrained case and propose the construction of subspace based movements during the search; we identify how neighborhood samples have to be chosen such that a movement along the Pareto front is achieved, for points near the Pareto set of a given constrained MOP. Next, we present two applications of these insights, namely (i) to explore the behavior of a population based algorithm that is merely using this proposed neighborhood sampling and (ii) to build a specialized mutation operator for effectively explore search regions on constrained MOPs, where the constraints are given explicitly. Numerical results indicate that these ideas yield competitive results in most cases. We conjecture that these insights are valuable for the future design of specialized search operators for memetic algorithms dealing with constrained multi-objective search spaces.