Matrix-Based Ant Colony Optimization with Matrix-Based 2-Opt for Traveling Salesman Problem

초록

Matrix-based Ant Colony Optimization (MACO) leverages matrix operations to implement the evolutionary operators in ACO, so that High Performance Computing (HPC) facilities can be used to accelerate the efficiency of ACO in solving Traveling Salesman Problems (TSP). However, existing MACO inherently suffers from low accuracy. To address this limitation, this paper proposes Matrix-based 2-opt (M2-opt) to improve the effectiveness of MACO. Particularly, M2-opt utilizes the matrix operations to implement multiple executions of 2-opt in parallel and then selects the best one to finally execute for the largest improvement. To improve the quality of one route as much as possible, M2-opt is executed continuously until no improvement is obtained. Further, for high efficiency, M2-opt is only executed on a small number of the top best routes constructed by MACO. Subsequently, M2-opt is embedded into MACO to solve TSP with high accuracy. Particularly, beyond Matrix-based Ant System (MAS) and Matrix-based Ant Colony System (MACS), which have been developed by prior studies, this paper further implements the other three classic ACOs, namely Elitist AS (EAS), Rank-based AS (RAS), and Max-Min AS (MMAS), via using matrix operations. As a result, totally five MACOs are developed and cooperate with M2-opt to solve TSP effectively and efficiently. Experiments on 20 TSP instances with the number of cities ranging from nearly 50 to 1300 have demonstrated that M2-opt helps the five MACOs find significantly shorter routes with nearly no serious computational burden under HPC. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2027.

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