Bandit based Dynamic Candidate Edge Selection in Solving Traveling Salesman Problems

TL;DR

This paper introduces a bandit-based dynamic candidate edge selection method for the Traveling Salesman Problem, improving solution quality by adaptively choosing edges during local search, outperforming static approaches.

Contribution

It presents a novel multi-armed bandit approach to dynamically select candidate edges in TSP algorithms, enhancing their ability to escape local optima and improve solutions.

Findings

Significant performance improvements on multiple TSP benchmarks.

Enhanced LKH-3 performance across various TSP variants.

Demonstrated effectiveness of bandit-based dynamic selection.

Abstract

Algorithms designed for routing problems typically rely on high-quality candidate edges to guide their search, aiming to reduce the search space and enhance the search efficiency. However, many existing algorithms, like the classical Lin-Kernighan-Helsgaun (LKH) algorithm for the Traveling Salesman Problem (TSP), often use predetermined candidate edges that remain static throughout local searches. This rigidity could cause the algorithm to get trapped in local optima, limiting its potential to find better solutions. To address this issue, we propose expanding the candidate sets to include other promising edges, providing them an opportunity for selection. Specifically, we incorporate multi-armed bandit models to dynamically select the most suitable candidate edges in each iteration, enabling LKH to make smarter choices and lead to improved solutions. Extensive experiments on multiple TSP benchmarks show the excellent performance of our method. Moreover, we employ this bandit-based method to LKH-3, an extension of LKH tailored for solving various TSP variant problems, and our method also significantly enhances LKH-3's performance across typical TSP variants.