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

Abstract

The Lin and Kernighan’s algorithm 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 Lin and Kernighan’s algorithm was still not fully explored. Works that applied the Lin and Kernighan’s algorithm 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.