Abstract
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.
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This work was supported in part by the National Natural Science Foundation of China under Grant 61673258, Grant 61075115 and in part by the Shanghai Natural Science Foundation under Grant 19ZR1421600.
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The paper and the code of the algorithm were written by Qihuan Wu. Suggestions for revising the manuscript were given by Xiaoming You. The material for the experiment was prepared by Sheng Liu. The final manuscript is approved by all authors.
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Wu, Q., You, X. & Liu, S. Multi-ant colony algorithm based on the Stackelberg game and incremental learning. Soft Comput 29, 2107–2128 (2025). https://doi.org/10.1007/s00500-025-10469-3
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DOI: https://doi.org/10.1007/s00500-025-10469-3