A new hybrid metaheuristic for equality constrained bi-objective optimization problems

Abstract

The recently proposed Pareto Tracer method is an effective numerical continuation technique which allows performing movements along the set of KKT points of a given multi-objective optimization problem. The nature of this predictor-corrector method leads to constructing solutions along the Pareto set/front numerically; it applies to higher dimensions and can handle box and equality constraints. We argue that the right hybridization of multi-objective evolutionary algorithms together with specific continuation methods leads to fast and reliable algorithms. Moreover, due to the continuation technique, the resulting hybrid algorithm could have a certain advantage when handling, in particular, equality constraints. In this paper, we make the first effort to hybridize NSGA-II with the Pareto Tracer. To support our claims, we present some numerical results on continuously differentiable equality constrained bi-objective optimization test problems, to show that the resulting hybrid NSGAII/PT is highly competitive against some state-of-the-art algorithms for constrained optimization. Finally, we stress that the chosen approach could be applied to a more significant number of objectives with some adaptations of the algorithm, leading to a very promising research topic.