From Graph Embedding to LKH: Bridging Learning and Heuristics for a Streamlined General TSP Solver
Keywords: Traveling salesman problem, graph embedding
Abstract: The Traveling Salesman Problem (TSP) is known as one of the most notorious NP-hard combinatorial optimization problems.
In recent decades, researchers from fields such as computer science, operations research, and artificial intelligence including deep learning (DL) have made numerous attempts on the problem.
Among the works, the Lin-Kernighan-Helsgaun (LKH) heuristic algorithm is one of the most competent methods for obtaining optimal or near-optimal solutions.
Despite the rapid development in DL-based solvers, few of them can defeat LKH in terms of both running efficiency and solution quality across different distributions.
In this paper, we would introduce a very novel approach that enhances LKH with graph embedding (GE) techniques in solving general TSP (distances can be non-metric and asymmetric), named as Embed-LKH.
It is presented as two stages: i) in the GE stage, it transforms the distances to transition probabilities, then conduct GE given the transition probabilities, and finally it uses the learned embeddings to construct the so-called `ghost distances'; ii) in the LKH stage, LKH generates candidates based on the ghost distances but searches tours according to the original distances. As the experiments show, compared with the original LKH counterpart, in most cases, our approach can obtain better solutions within the same amount of trials across six distance distributions (non-metric and asymmetric: normal, uniform, exponential, metric and symmetric: Euclidean 2D/10D/50D) and two problem scales (TSP-100/1000). The source files, running scripts, and data will be made publicly available after the review.
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 1625
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