A Multi-objective Version of the Lin-Kernighan Heuristic for the Traveling Salesman Problem

Abstract: The Lin and Kernighan’s algorithm (LK) for the single objective Traveling Salesman Problem (TSP) is one of the most efficient heuristics for the symmetric case. Although many algorithms for the TSP were extended to the multi-objective version of the problem (MTSP), the LK was still not fully explored. Works that applied the LK for the MTSP were driven to weighted sum versions of the problem. We investigate the LK from a Pareto dominance perspective. The multi-objective LK was implemented within two local search schemes and applied to 2 to 4-objective instances. The results showed that the proposed algorithmic variants obtained better results than a state-of-the-art algorithm.