International Journal of Computer Science & Network Security

International Journal of Computer Science & Network Security (국제컴퓨터통신보호논문지학회)
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The Maximum Scatter Travelling Salesman Problem: A Hybrid Genetic Algorithm

  • Zakir Hussain Ahmed (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU)) ;
  • Asaad Shakir Hameed (Department of Mathematics, General Directorate of Thi-Qar Education, Ministry of education) ;
  • Modhi Lafta Mutar (Department of Mathematics, General Directorate of Thi-Qar Education, Ministry of education) ;
  • Mohammed F. Alrifaie (Department of Information and Communications, Basra University College of science and technology) ;
  • Mundher Mohammed Taresh (College of Information Science and Engineering, Hunan University)
  • Received : 2023.06.05
  • Published : 2023.06.30
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Abstract

In this paper, we consider the maximum scatter traveling salesman problem (MSTSP), a travelling salesman problem (TSP) variant. The problem aims to maximize the minimum length edge in a salesman's tour that travels each city only once in a network. It is a very complicated NP-hard problem, and hence, exact solutions can be found for small sized problems only. For large-sized problems, heuristic algorithms must be applied, and genetic algorithms (GAs) are found to be very successfully to deal with such problems. So, this paper develops a hybrid GA (HGA) for solving the problem. Our proposed HGA uses sequential sampling algorithm along with 2-opt search for initial population generation, sequential constructive crossover, adaptive mutation, randomly selected one of three local search approaches, and the partially mapped crossover along with swap mutation for perturbation procedure to find better quality solution to the MSTSP. Finally, the suggested HGA is compared with a state-of-art algorithm by solving some TSPLIB symmetric instances of many sizes. Our computational experience reveals that the suggested HGA is better. Further, we provide solutions to some asymmetric TSPLIB instances of many sizes.

Keywords

Acknowledgement

This research was supported by Deanery of Academic Research, Imam Muhammad Ibn Saud Islamic University, Saudi Arabia vide Grant No. 18-11-09-010. The first author thanks the Deanery for its financial support.

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