Deep Reinforcement Learning for Combinatorial Optimization: Covering Salesman Problems

TL;DR

This paper presents a deep reinforcement learning method using multi-head attention for the Covering Salesman Problem, achieving faster solutions with minimal optimality gap and better performance than existing deep learning approaches.

Contribution

It introduces a novel neural network model with dynamic embedding and attention mechanisms trained via reinforcement learning for CSP, capable of generalizing across different problem sizes and topologies.

Findings

Runs over 20 times faster than traditional heuristics

Outperforms current deep learning methods in training and inference

Maintains a tiny gap to optimal solutions

Abstract

This paper introduces a new deep learning approach to approximately solve the Covering Salesman Problem (CSP). In this approach, given the city locations of a CSP as input, a deep neural network model is designed to directly output the solution. It is trained using the deep reinforcement learning without supervision. Specifically, in the model, we apply the Multi-head Attention to capture the structural patterns, and design a dynamic embedding to handle the dynamic patterns of the problem. Once the model is trained, it can generalize to various types of CSP tasks (different sizes and topologies) with no need of re-training. Through controlled experiments, the proposed approach shows desirable time complexity: it runs more than 20 times faster than the traditional heuristic solvers with a tiny gap of optimality. Moreover, it significantly outperforms the current state-of-the-art deep learning approaches for combinatorial optimization in the aspect of both training and inference. In comparison with traditional solvers, this approach is highly desirable for most of the challenging tasks in practice that are usually large-scale and require quick decisions.