Diversity Optimization for Travelling Salesman Problem via Deep Reinforcement Learning

TL;DR

This paper introduces a deep reinforcement learning approach for the TSP that generates diverse, high-quality solutions efficiently, outperforming recent neural methods and competing with traditional heuristics.

Contribution

A novel neural solver with an encoder-decoder policy, featuring a Relativization Filter and Multi-Attentive Adaptive Active Search for diverse solution generation.

Findings

Outperforms recent neural baselines on benchmark TSP instances.

Achieves 1.3 to 15 times faster performance than traditional heuristics.

Successfully extends to the Capacitated Vehicle Routing Problem.

Abstract

Existing neural methods for the Travelling Salesman Problem (TSP) mostly aim at finding a single optimal solution. To discover diverse yet high-quality solutions for Multi-Solution TSP (MSTSP), we propose a novel deep reinforcement learning based neural solver, which is primarily featured by an encoder-decoder structured policy. Concretely, on the one hand, a Relativization Filter (RF) is designed to enhance the robustness of the encoder to affine transformations of the instances, so as to potentially improve the quality of the found solutions. On the other hand, a Multi-Attentive Adaptive Active Search (MA3S) is tailored to allow the decoders to strike a balance between the optimality and diversity. Experimental evaluations on benchmark instances demonstrate the superiority of our method over recent neural baselines across different metrics, and its competitive performance against state-of-the-art traditional heuristics with significantly reduced computational time, ranging from $1.3\times$ to $15\times$ faster. Furthermore, we demonstrate that our method can also be applied to the Capacitated Vehicle Routing Problem (CVRP).