Multi-objective variable neighborhood search: an application to combinatorial optimization problems

Abstract

Solutions to real-life optimization problems usually have to be evaluated considering multiple conflicting objectives. These kind of problems, known as multi-objective optimization problems, have been mainly solved in the past by using evolutionary algorithms. In this paper, we explore the adaptation of the Variable Neighborhood Search (VNS) metaheuristic to solve multi-objective combinatorial optimization problems. In particular, we describe how to design the shake procedure, the improvement method and the acceptance criterion within different VNS schemas (Reduced VNS, Variable Neighborhood Descent and General VNS), when two or more objectives are considered. We validate these proposals over two multi-objective combinatorial optimization problems.