# Construct, Merge, Solve & Adapt with Reinforcement Learning for the min-max Multiple Traveling Salesman Problem

arXiv: https://arxiv.org/abs/2602.23579 · HTML: https://mlsanity.com/paper/2602.23579/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 3 of its 16 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 3 of 3)

- [ScheduleNet: Learn to solve multi-agent scheduling problems with reinforcement learning](https://mlsanity.com/paper/2106.03051/) (2021)
- [A Hybrid Genetic Algorithm for the min-max Multiple Traveling Salesman Problem](https://mlsanity.com/paper/2307.07120/) (2023)
- [An Effective Iterated Two-stage Heuristic Algorithm for the Multiple Traveling Salesmen Problem](https://mlsanity.com/paper/2201.09424/) (2022)

## Abstract (arXiv)

The Multiple Traveling Salesman Problem (mTSP) extends the Traveling Salesman Problem to m tours that start and end at a common depot and jointly visit all customers exactly once. In the min-max variant, the objective is to minimize the longest tour, reflecting workload balance. We propose a hybrid approach, Construct, Merge, Solve & Adapt with Reinforcement Learning (RL-CMSA), for the symmetric single-depot min-max mTSP. The method iteratively constructs diverse solutions using probabilistic clustering guided by learned pairwise q-values, merges routes into a compact pool, solves a restricted set-covering MILP, and refines solutions via inter-route remove, shift, and swap moves. The q-values are updated by reinforcing city-pair co-occurrences in high-quality solutions, while the pool is adapted through ageing and pruning. This combination of exact optimization and reinforcement-guided construction balances exploration and exploitation. Computational results on random and TSPLIB instances show that RL-CMSA consistently finds (near-)best solutions and outperforms a state-of-the-art hybrid genetic algorithm under comparable time limits, especially as instance size and the number of salesmen increase.