A primal-dual multiobjective evolutionary algorithm for approximating the efficient set

In this article, we present a novel evolutionary algorithm for approximating the efficient set of a multiobjective optimization problem (MOP) with continuous variables. The algorithm is based on populations of variable size and exploits new rules for selecting alternatives generated by mutation and recombination. A special feature of the algorithm is that it solves at the same time the original problem and a dual problem such that solutions converge towards the efficient border from two "sides", the feasible set and a subset of the infeasible set. Together with additional assumptions on the considered MOP and further specifications on the algorithm, theoretical results on the approximation quality and the convergence of both subpopulations, the feasible and the infeasible one, are derived.