Combining Two Search Paradigms for Multi-objective Optimization: Two-Phase and Pareto Local Search

In this chapter, we review metaheuristics for solving multi-objective combinatorial optimization problems, when no information about the decision maker’s preferences is available, that is, when problems are tackled in the sense of Pareto optimization. Most of these metaheuristics follow one of the two main paradigms to tackle such problems in a heuristic way. The first paradigm is to rely on Pareto dominance when exploring the search space. The second paradigm is to tackle several single-objective problems to find several solutions that are non-dominated for the original problem; in this case, one may exploit existing, efficient single-objective algorithms, but the performance depends on the definition of the set of scalarized problems. There are also a number of approaches in the literature that combine both paradigms. However, this is usually done in a relatively ad-hoc way. In this chapter, we review two conceptually simple methods representative of each paradigm: Pareto local search and Two-phase local search. The hybridization of these two strategies provides a general framework for engineering stochastic local search algorithms that can be used to improve over the state-of-the-art for several, widely studied problems.