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<p>To address the difficulties of slow convergence and inadequate accuracy of traditional ant colony algorithms in solving the traveling salesman problem (TSP), we propose a multi-ant colony algorithm based on the Stackelberg game and incremental learning (SGIACO). We incorporate the Stackelberg game strategy across multiple colonies, where the leader guides the follower to optimize population co-evolution, ensuring a balance between convergence and diversity of the algorithm. Furthermore, we propose an incremental learning strategy that enhances efficient paths on the public routes and ignores inefficient ones, thus accelerating the convergence speed of the algorithm. Finally, when the algorithm stagnates, a pheromone balance mechanism is implemented to help the ants escape from local optima. We conducted experiments on 23 TSP instances to validate the algorithm's performance and compare it to ACS, MMAS, as well as other recent algorithms. In addition, non-parametric tests were conducted for comprehensive performance analysis. Moreover, we verified the feasibility of SGIACO through simulations in robot path planning scenarios. The experimental results show that SGIACO has good convergence and accuracy, which is competitive with other algorithms. Future research aims to scale SGIACO for larger real-world applications, enhancing its adaptability and scalability.</p>

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Multi-ant colony algorithm based on the Stackelberg game and incremental learning

  • 期刊论文

  • 发表日期：

    2025年2月25日

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  • Qihuan Wu,
  • Xiaoming You,
  • Sheng Liu

摘要

To address the difficulties of slow convergence and inadequate accuracy of traditional ant colony algorithms in solving the traveling salesman problem (TSP), we propose a multi-ant colony algorithm based on the Stackelberg game and incremental learning (SGIACO). We incorporate the Stackelberg game strategy across multiple colonies, where the leader guides the follower to optimize population co-evolution, ensuring a balance between convergence and diversity of the algorithm. Furthermore, we propose an incremental learning strategy that enhances efficient paths on the public routes and ignores inefficient ones, thus accelerating the convergence speed of the algorithm. Finally, when the algorithm stagnates, a pheromone balance mechanism is implemented to help the ants escape from local optima. We conducted experiments on 23 TSP instances to validate the algorithm's performance and compare it to ACS, MMAS, as well as other recent algorithms. In addition, non-parametric tests were conducted for comprehensive performance analysis. Moreover, we verified the feasibility of SGIACO through simulations in robot path planning scenarios. The experimental results show that SGIACO has good convergence and accuracy, which is competitive with other algorithms. Future research aims to scale SGIACO for larger real-world applications, enhancing its adaptability and scalability.