Bioinspired Discrete Two-Stage Surrogate-Assisted Algorithm for Large-Scale Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is a well-known NP-Hard problem, particularly challenging for conventional solving methods due to the curse of dimensionality in high-dimensional instances. This paper proposes a novel Double-stage Surrogate-assisted Pigeon-inspired Optimization algorithm (DOSA-PIO) to address this issue. DOSA-PIO integrates the ordering points to identify the clustering structure method for data clustering and employs a local surrogate model to assist the evolution of the Pigeon-inspired Optimization (PIO) algorithm. This combination enhances the algorithm’s ability to explore the solution space and converge to optimal solutions more effectively. Additionally, two novel approaches are introduced to extend the generalizability of continuous algorithms for solving discrete problems, enabling the adaptation of continuous optimization techniques to the discrete nature of TSP. Extensive experiments using benchmark functions and high-dimensional TSP instances demonstrate that DOSA-PIO significantly outperforms comparative algorithms in various dimensions (10D, 20D, 30D, 50D, and 100D). The proposed algorithm provides superior solutions compared to traditional methods, highlighting its potential for solving high-dimensional TSPs. By leveraging advanced data clustering techniques and surrogate-assisted optimization, DOSA-PIO offers an effective solution for high-dimensional TSP instances, with experimental results confirming its superior performance and potential for practical applications in complex optimization problems.