# TOP-Former: A Multi-Agent Transformer Approach for the Team Orienteering Problem

arXiv: https://arxiv.org/abs/2311.18662 · HTML: https://mlsanity.com/paper/2311.18662/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 47 references that are in the map.
- First posted on arXiv 30 Nov 2023.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Combinatorial Optimization by Graph Pointer Networks and Hierarchical Reinforcement Learning](https://mlsanity.com/paper/1911.04936/) (2019)
- [Multi-Agent Routing Value Iteration Network](https://mlsanity.com/paper/2007.05096/) (2020)
- [Robust Multiple-Path Orienteering Problem: Securing Against Adversarial Attacks](https://mlsanity.com/paper/2003.13896/) (2020)
- [A Benchmark for Multi-UAV Task Assignment of an Extended Team Orienteering Problem](https://mlsanity.com/paper/2009.00363/) (2020)
- [A Branch-and-Price Algorithm for a Team Orienteering Problem with Fixed-Wing Drones](https://mlsanity.com/paper/1912.04353/) (2019)
- [A revisited branch-and-cut algorithm for large-scale orienteering problems](https://mlsanity.com/paper/2011.02743/) (2020)

## Built on by (most cited first, 3 of 3)

- [Multi-Agent Environments for Vehicle Routing Problems](https://mlsanity.com/paper/2411.14411/) (2024)
- [Demand Acceptance using Reinforcement Learning for Dynamic Vehicle Routing Problem with Emission Quota](https://mlsanity.com/paper/2603.13279/) (2026)
- [Enhancing Transformer-based Routing by Encoding Distance via Relative Positional Encoding](https://mlsanity.com/paper/2607.18909/) (2026)

## Abstract (arXiv)

Route planning for a fleet of vehicles is an important task in applications such as package delivery, surveillance, or transportation, often integrated within larger Intelligent Transportation Systems (ITS). This problem is commonly formulated as a Vehicle Routing Problem (VRP) known as the Team Orienteering Problem (TOP). Existing solvers for this problem primarily rely on either linear programming, which provides accurate solutions but requires computation times that grow with the size of the problem, or heuristic methods, which typically find suboptimal solutions in a shorter time. In this paper, we introduce TOP-Former, a multi-agent route planning neural network designed to efficiently and accurately solve the Team Orienteering Problem. The proposed algorithm is based on a centralized Transformer neural network capable of learning to encode the scenario (modeled as a graph) and analyze the complete context of all agents to deliver fast, precise, and collaborative solutions. Unlike other neural network-based approaches that adopt a more local perspective, TOP-Former is trained to understand the global situation of the vehicle fleet and generate solutions that maximize long-term expected returns. Extensive experiments demonstrate that the presented system outperforms most state-of-the-art methods in terms of both accuracy and computation speed.