A discrete bat algorithm based on Lévy flights for Euclidean traveling salesman problem

• Published in: Expert systems with applications Vol. 172; p. 114639
• Main Authors: Saji, Yassine, Barkatou, Mohammed
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 15.06.2021; Elsevier BV
• Subjects: Algorithms; Bat algorithm; Combinatorial analysis; Comparative studies; Heuristic methods; Lévy flights; NP-hard combinatorial optimization problem; Optimization; Population-based metaheuristics; Random walk; Search methods; Traveling salesman problem; Lévy flights; Traveling salesman problem; Population-based metaheuristics; Bat algorithm; NP-hard combinatorial optimization problem
• ISSN: 0957-4174; 1873-6793
• DOI: 10.1016/j.eswa.2021.114639

•A new discrete bat algorithm based on Lévy flights is proposed.•2-opt, 2.5-opt and 3-opt define the movement of bats in the search space.•A modified uniform crossover is designed for diversification and intensification.•Bat algorithm is tested on set of symmetric instances from TSPLIB.•Statistical tests prove the superiority of the discrete bat algorithm. Bat algorithm is a swarm-intelligence-based metaheuristic proposed in 2010. This algorithm was inspired by echolocation behavior of bats when searching their prey in nature. Since it first introduction, it continues to be used extensively until today, owing to its simplicity, easy handling and applicability to a wide range of problems. However, sometimes the major challenge faced by this technique is can be trapped in a local optimum when facing large complex problems. In this research work, a new discrete bat algorithm is proposed to solve the famous traveling salesman problem as NP-hard combinatorial optimization problem. To enhance the searching strategy and to avoid getting stuck in local minima, random walks based on Lévy's flights are combined with bat’s movement. In addition, to improve the diversity and convergence of the swarm, a neutral crossover operator is embedded to the proposed algorithm. To evaluate the performance of our proposal, two experiments are conducted on 38 benchmark datasets and the obtained results are compared with eight different approaches. Furthermore, the student’s t-test, the Friedman’s test and the post hoc Wilcoxon's test are performed to check whether there are significant differences between the proposed optimizer and the alternative techniques. The experimental results under comparative studies have shown that, in most cases, the proposed discrete bat algorithm yields significantly better results compared with its competitors.