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A Comparison of GA Crossover and Mutation Methods for the Traveling Salesman Problem

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Innovations in Computational Intelligence and Computer Vision

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1189))

Abstract

The traveling salesman problem is a very popular combinatorial optimization problem in fields such as computer science, operations research, mathematics and optimization theory. Given a list of cities and the distances between any city to another, the objective of the problem is to find the optimal permutation (tour) in the sense of minimum traveled distance when visiting each city only once before returning to the starting city. Because many real-world problems can be modeled to fit this formulation, the traveling salesman problem has applications in challenges related to planning, routing, scheduling, manufacturing, logistics, and other domains. Moreover, the traveling salesman problem serves as a benchmark problem for optimization methods and algorithms, including the genetic algorithm. In this paper, we examine various implementations of the genetic algorithm for solving two examples of the traveling salesman problem. Specifically, we compare commonly employed methods of partially mapped crossover and order crossover with an alternative encoding scheme that allows for single-point, multipoint, and uniform crossovers. In addition, we examine several mutation methods, including Twors mutation, center inverse mutation, reverse sequence mutation, and partial shuffle mutation. We empirically compare the implementations in terms of the chosen crossover and mutation methods to solve two benchmark variations of the traveling salesperson problem. The experimental results show that the genetic algorithm with order crossover and the center inverse mutation method provides the best solution for the two test cases.

This research was supported by the European Research Consortium for Informatics and Mathematics (ERCIM).

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Notes

  1. 1.

    Wikipedia: https://en.wikipedia.org/wiki/Travelling_salesman_problem.

  2. 2.

    https://www.ntnu.no/blogger/cpslab/.

  3. 3.

    http://www.math.uwaterloo.ca/tsp.

  4. 4.

    E.g., see Wikipedia: https://en.wikipedia.org/wiki/Inversion_(discrete_mathematics).

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Acknowledgements

This research was supported by the European Research Consortium for Informatics and Mathematics (ERCIM), which provided funding to Ramesh Chandra for his postdoctoral fellowship at the CPS Lab at NTNU, Ålesund, Norway.

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Authors and Affiliations

  1. Cyber-Physical Systems Laboratory, Department of ICT and Natural Sciences, NTNU—Norwegian University of Science and Technology, Postboks 1517, NO-6025 Ålesund, Norway

    Robin T. Bye, Magnus Gribbestad, Ramesh Chandra & Ottar L. Osen

Authors
  1. Robin T. Bye
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  2. Magnus Gribbestad
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  3. Ramesh Chandra
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  4. Ottar L. Osen
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Corresponding author

Correspondence to Robin T. Bye .

Editor information

Editors and Affiliations

  1. Department of Computer and Communication Engineering, Manipal University Jaipur, Jaipur, Rajasthan, India

    Manoj Kumar Sharma

  2. Department of Computer and Communication Engineering, Manipal University Jaipur, Jaipur, Rajasthan, India

    Vijaypal Singh Dhaka

  3. Department of Computer Science, Faculty of Computer Science and Information Technology, Universiti Putra Malaysia, Serdang, Selangor, Malaysia

    Thinagaran Perumal

  4. Department of Information Technology, Techno India College of Technology, Kolkata, West Bengal, India

    Nilanjan Dey

  5. Faculdade de Engenharia da, Universidade do Porto, Porto, Portugal

    João Manuel R. S. Tavares

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Bye, R.T., Gribbestad, M., Chandra, R., Osen, O.L. (2021). A Comparison of GA Crossover and Mutation Methods for the Traveling Salesman Problem. In: Sharma, M.K., Dhaka, V.S., Perumal, T., Dey, N., Tavares, J.M.R.S. (eds) Innovations in Computational Intelligence and Computer Vision. Advances in Intelligent Systems and Computing, vol 1189. Springer, Singapore. https://doi.org/10.1007/978-981-15-6067-5_60

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