DualOpt: A Dual Divide-and-Optimize Algorithm for the Large-scale Traveling Salesman Problem
This work addresses the computational efficiency and solution quality challenges in solving large-scale TSPs, which is important for logistics and optimization applications, but it is incremental as it builds on existing divide-and-conquer and neural solver techniques.
The paper tackles the large-scale traveling salesman problem (TSP) by proposing DualOpt, a dual divide-and-optimize algorithm that combines grid-based and path-based strategies, achieving up to 1.40% improvement and 104x speed-up on instances with up to 100,000 nodes compared to state-of-the-art methods.
This paper proposes a dual divide-and-optimize algorithm (DualOpt) for solving the large-scale traveling salesman problem (TSP). DualOpt combines two complementary strategies to improve both solution quality and computational efficiency. The first strategy is a grid-based divide-and-conquer procedure that partitions the TSP into smaller sub-problems, solving them in parallel and iteratively refining the solution by merging nodes and partial routes. The process continues until only one grid remains, yielding a high-quality initial solution. The second strategy involves a path-based divide-and-optimize procedure that further optimizes the solution by dividing it into sub-paths, optimizing each using a neural solver, and merging them back to progressively improve the overall solution. Extensive experiments conducted on two groups of TSP benchmark instances, including randomly generated instances with up to 100,000 nodes and real-world datasets from TSPLIB, demonstrate the effectiveness of DualOpt. The proposed DualOpt achieves highly competitive results compared to 10 state-of-the-art algorithms in the literature. In particular, DualOpt achieves an improvement gap up to 1.40% for the largest instance TSP100K with a remarkable 104x speed-up over the leading heuristic solver LKH3. Additionally, DualOpt demonstrates strong generalization on TSPLIB benchmarks, confirming its capability to tackle diverse real-world TSP applications.