Memetic search for the minmax multiple traveling salesman problem with single and multiple depots

• Published in: European journal of operational research Vol. 307; no. 3; pp. 1055 - 1070
• Main Authors: He, Pengfei, Hao, Jin-Kao
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16.06.2023; Elsevier
• Subjects: Artificial Intelligence; Combinatorial optimization; Computer Science; Heuristics; Minmax; Multidepot; Operations Research; Travelling salesman; Minmax; Combinatorial optimization; Heuristics; Multidepot; Travelling salesman
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2022.11.010

•The minmax multiple traveling salesman problem is a relevant model for many applications.•We present an effective memetic algorithm for the problem with single and multiple depots.•We show computational results on 120 benchmark instances in the literature.•We report 83 new upper bounds.•The algorithm can help to better solve various related practical applications. The minmax multiple traveling salesman problem with single depot (the minmax mTSP) or multiple depots (the minmax multidepot mTSP) aims to minimize the longest tour among a set of tours. These two minmax problems are useful for a variety of real-life applications and typically studied separately in the literature. We propose a unified memetic approach to solving both cases of the minmax mTSP and the minmax multidepot mTSP. The proposed algorithm features a generalized edge assembly crossover to generate offspring solutions, an efficient variable neighborhood descent to ensure local optimization as well as an aggressive post-optimization for additional solution improvement. Extensive experimental results on 77 minmax mTSP benchmark instances and 43 minmax multidepot mTSP instances commonly used in the literature indicate a high performance of the algorithm compared to the leading algorithms. Additional experimental investigations are conducted to shed light on the rationality of the key algorithmic ingredients.