Decomposition-Based Lin–Kernighan Heuristic With Neighborhood Structure Transfer for Multi/Many-Objective Traveling Salesman Problem

Abstract

The multi/many-objective traveling salesman problem (MOTSP), which is NP-hard, can be found in many real-world applications. The Lin-Kernighan (LK) algorithm, as one of the most successful local search methods for single-objective TSP, adopts a variable neighborhood local search. However, LK cannot be directly applied to the decomposition-based multiobjective optimization framework due to its incapability of effective knowledge transfer among different subproblems, especially for problems with more than two objectives. In this paper, we propose an algorithm, called Decomposition-based Multiobjective Lin-Kernighan Heuristic with Neighborhood Structure Transfer (NST-MOLK) for MOTSP. In NST-MOLK, the knowledge of neighborhood structure has been transferred to enhance the efficiency and effectiveness of LK. The experimental studies have been conducted on both benchmark and real-world instances constructed based on the flight prices of 7 airlines and 266 airports of different cities in China. Experimental results show that NST-MOLK outperforms both classical and state-of-the-art algorithms significantly. It has also been verified that neighborhood structure transfer can effectively improve the performance of NST-MOLK.