Neutral but a Winner! How Neutrality Helps Multiobjective Local Search Algorithms

Abstract

This work extends the concept of neutrality used in single-objective optimization to the multi-objective context and investigates its effects on the performance of multi-objective dominance-based local search methods. We discuss neutrality in single-objective optimization and fitness assignment in multi-objective algorithms to provide a general definition for neutrality applicable to multi-objective landscapes. We also put forward a definition of neutrality when Pareto dominance is used to compute fitness of solutions. Then, we focus on dedicated local search approaches that have shown good results in multi-objective combinatorial optimization. In such methods, particular attention is paid to the set of solutions selected for exploration, the way the neighborhood is explored, and how the candidate set to update the archive is defined. We investigate the last two of these three important steps from the perspective of neutrality in multi-objective landscapes, propose new strategies that take into account neutrality, and show that exploiting neutrality allows to improve the performance of dominance-based local search methods on bi-objective permutation flowshop scheduling problems.