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An Adaptive Ant Colony Optimization for Solving Large-Scale Traveling Salesman Problem

Author

Listed:
  • Kezong Tang

    (School of Information Engineering, Jingdezhen Ceramic University, Jingdezhen 333403, China)

  • Xiong-Fei Wei

    (School of Information Engineering, Jingdezhen Ceramic University, Jingdezhen 333403, China)

  • Yuan-Hao Jiang

    (School of Computer Science and Technology, East China Normal University, Shanghai 200062, China)

  • Zi-Wei Chen

    (School of Information Engineering, Jingdezhen Ceramic University, Jingdezhen 333403, China)

  • Lihua Yang

    (School of Information Engineering, Jingdezhen Ceramic University, Jingdezhen 333403, China)

Abstract

The ant colony algorithm faces dimensional catastrophe problems when solving the large-scale traveling salesman problem, which leads to unsatisfactory solution quality and convergence speed. To solve this problem, an adaptive ant colony optimization for large-scale traveling salesman problem (AACO-LST) is proposed. First, AACO-LST improves the state transfer rule to make it adaptively adjust with the population evolution, thus accelerating its convergence speed; then, the 2-opt operator is used to locally optimize the part of better ant paths to further optimize the solution quality of the proposed algorithm. Finally, the constructed adaptive pheromone update rules can significantly improve the search efficiency and prevent the algorithm from falling into local optimal solutions or premature stagnation. The simulation based on 45 traveling salesman problem instances shows that AACO-LST improves the solution quality by 79% compared to the ant colony system (ACS), and in comparison with other algorithms, the PE of AACO-LST is not more than 1% and the Err is not more than 2%, which indicates that AACO-LST can find high-quality solutions with high stability. Finally, the convergence speed of the proposed algorithm was tested. The data shows that the average convergence speed of AACO-LST is more than twice that of the comparison algorithm. The relevant code can be found on our project homepage.

Suggested Citation

  • Kezong Tang & Xiong-Fei Wei & Yuan-Hao Jiang & Zi-Wei Chen & Lihua Yang, 2023. "An Adaptive Ant Colony Optimization for Solving Large-Scale Traveling Salesman Problem," Mathematics, MDPI, vol. 11(21), pages 1-26, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4439-:d:1267953
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    References listed on IDEAS

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    2. Sedighizadeh, Davoud & Masehian, Ellips & Sedighizadeh, Mostafa & Akbaripour, Hossein, 2021. "GEPSO: A new generalized particle swarm optimization algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 194-212.
    3. E. L. Lawler & D. E. Wood, 1966. "Branch-and-Bound Methods: A Survey," Operations Research, INFORMS, vol. 14(4), pages 699-719, August.
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