# Bandit based Dynamic Candidate Edge Selection in Solving Traveling Salesman Problems

arXiv: https://arxiv.org/abs/2505.15862 · HTML: https://mlsanity.com/paper/2505.15862/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 21 May 2025.

## Builds on (most cited first, 15 of 15)

- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [Reinforcement Learning for Combinatorial Optimization: A Survey](https://mlsanity.com/paper/2003.03600/) (2020)
- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problem](https://mlsanity.com/paper/2110.07983/) (2021)
- [Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learning](https://mlsanity.com/paper/2004.01608/) (2020)
- [GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-time](https://mlsanity.com/paper/2312.08224/) (2023)
- [Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt](https://mlsanity.com/paper/2310.18264/) (2023)
- [The Transformer Network for the Traveling Salesman Problem](https://mlsanity.com/paper/2103.03012/) (2021)
- [Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problem](https://mlsanity.com/paper/2304.09407/) (2023)
- [Combining Reinforcement Learning with Lin-Kernighan-Helsgaun Algorithm for the Traveling Salesman Problem](https://mlsanity.com/paper/2012.04461/) (2020)
- [Learning to Solve Routing Problems via Distributionally Robust Optimization](https://mlsanity.com/paper/2202.07241/) (2022)
- [A Deep Reinforcement Learning Approach for Solving the Traveling Salesman Problem with Drone](https://mlsanity.com/paper/2112.12545/) (2021)
- [A reinforcement learning guided hybrid evolutionary algorithm for the latency location routing problem](https://mlsanity.com/paper/2403.14405/) (2024)

## Built on by (most cited first, 1 of 1)

- [Machine Learning-based Two-Stage Graph Sparsification for the Travelling Salesman Problem](https://mlsanity.com/paper/2604.20236/) (2026)

## Abstract (arXiv)

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.