mlsanityData to 7 Oct 2026

Learning the Multiple Traveling Salesmen Problem with Permutation Invariant Pooling Networks

arXiv 1803.09621 ↗First posted 26 Mar 2018cs.LG stat.MLcited by 22

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Abstract (arXiv)

While there are optimal TSP solvers, as well as recent learning-based approaches, the generalization of the TSP to the Multiple Traveling Salesmen Problem is much less studied. Here, we design a neural network solution that treats the salesmen, cities and depot as three different sets of varying cardinalities. We apply a novel technique that combines elements from recent architectures that were developed for sets, as well as elements from graph networks. Coupled with new constraint enforcing output layers, a dedicated loss, and a search method, our solution is shown to outperform all the meta-heuristics of the leading solver in the field.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Mar 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 7; 2022: 5; 2023: 1; 2024: 5; 2025: 2; 2026: 2.

22 papers.

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  1. 2021The Transformer Network for the Traveling Salesman Problemcited by 59
  2. 2021Learning to schedule job-shop problems: Representation and policy learning using graph neural network and reinforcement learningcited by 52
  3. 2021ScheduleNet: Learn to solve multi-agent scheduling problems with reinforcement learningcited by 31
  4. 2021Analytics and Machine Learning in Vehicle Routing Researchcited by 22
  5. 2021An Overview and Experimental Study of Learning-based Optimization Algorithms for Vehicle Routing Problemcited by 22
  6. 2024DPN: Decoupling Partition and Navigation for Neural Solvers of Min-max Vehicle Routing Problemscited by 18
  7. 2022Learning to Solve Multiple-TSP with Time Window and Rejections via Deep Reinforcement Learningcited by 8
  8. 2023Neural Airport Ground Handlingcited by 7
  9. 2021DAN: Decentralized Attention-based Neural Network for the MinMax Multiple Traveling Salesman Problemcited by 5
  10. 2022Learning to Solve Soft-Constrained Vehicle Routing Problems with Lagrangian Relaxationcited by 5
  11. 2021Boosting Graph Search with Attention Network for Solving the General Orienteering Problemcited by 2
  12. 2022Supervised Permutation Invariant Networks for Solving the CVRP with Bounded Fleet Sizecited by 2
10 more
  1. 2022Solving the Traveling Salesperson Problem with Precedence Constraints by Deep Reinforcement Learningcited by 1
  2. 2024Graph Learning-based Fleet Scheduling for Urban Air Mobility under Operational Constraints, Varying Demand & Uncertaintiescited by 1
  3. 2024Bigraph Matching Weighted with Learnt Incentive Function for Multi-Robot Task Allocationcited by 1
  4. 2024A Graph-based Adversarial Imitation Learning Framework for Reliable & Realtime Fleet Scheduling in Urban Air Mobilitycited by 1
  5. 2022Hierarchically Structured Scheduling and Execution of Tasks in a Multi-Agent Environmentcited by 0
  6. 2024Test-Time Augmentation for Traveling Salesperson Problemcited by 0
  7. 2025Learning-aided Bigraph Matching Approach to Multi-Crew Restoration of Damaged Power Networks Coupled with Road Transportation Networkscited by 0
  8. 2025Understanding the Nature of Depth-1 Equivariant Quantum Circuitcited by 0
  9. 2026Imitation Learning for Combinatorial Optimisation under Uncertaintycited by 0
  10. 2026EGAM: Extended Graph Attention Model for Solving Routing Problemscited by 0