A hybrid genetic algorithm for the min–max Multiple Traveling Salesman Problem

• Published in: Computers & operations research Vol. 162; p. 106455
• Main Authors: Mahmoudinazlou, Sasan, Kwon, Changhyun
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2024
• Subjects: Dynamic programming; Genetic algorithm; Multiple traveling salesman problem; Vehicle routing; Dynamic programming; Vehicle routing; Multiple traveling salesman problem; Genetic algorithm
• ISSN: 0305-0548
• DOI: 10.1016/j.cor.2023.106455

This paper proposes a hybrid genetic algorithm for solving the Multiple Traveling Salesman Problem (mTSP) to minimize the length of the longest tour. The genetic algorithm utilizes a TSP sequence as the representation of each individual, and a dynamic programming algorithm is employed to evaluate the individual and find the optimal mTSP solution for the given sequence of cities. A novel crossover operator is designed to combine similar tours from two parents and offers great diversity for the population. For some of the generated offspring, we detect and remove intersections between tours to obtain a solution with no intersections. This is particularly useful for the min–max mTSP. The generated offspring are also improved by a self-adaptive random local search and a thorough neighborhood search. Our algorithm outperforms all existing algorithms on average, with similar cutoff time thresholds, when tested against multiple benchmark sets found in the literature. Additionally, we improve the best-known solutions for 21 out of 89 instances on four benchmark sets. •We propose a hybrid genetic algorithm for the Multiple Traveling Salesman Problem.•We propose a novel crossover operator that is effective for the min–max problem.•Our algorithm outperforms all existing algorithms on average.•We improve the best-known solutions for 21 out of 89 benchmark instances.