# CAMO: A Conditional Neural Solver for the Multi-objective Multiple Traveling Salesman Problem

arXiv: https://arxiv.org/abs/2603.19074 · HTML: https://mlsanity.com/paper/2603.19074/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 14 of 14)

- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Training Very Deep Networks](https://mlsanity.com/paper/1507.06228/) (2015)
- [MogaNet: Multi-order Gated Aggregation Network](https://mlsanity.com/paper/2211.03295/) (2022)
- [Pareto Set Learning for Expensive Multi-Objective Optimization](https://mlsanity.com/paper/2210.08495/) (2022)
- [PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimization](https://mlsanity.com/paper/2409.03811/) (2024)
- [Preference-Driven Multi-Objective Combinatorial Optimization with Conditional Computation](https://mlsanity.com/paper/2506.08898/) (2025)
- [HDPlanner: Advancing Autonomous Deployments in Unknown Environments through Hierarchical Decision Networks](https://mlsanity.com/paper/2408.03768/) (2024)
- [iMTSP: Solving Min-Max Multiple Traveling Salesman Problem with Imperative Learning](https://mlsanity.com/paper/2405.00285/) (2024)
- [Synchronized Dual-arm Rearrangement via Cooperative mTSP](https://mlsanity.com/paper/2403.08191/) (2024)

## Abstract (arXiv)

Robotic systems often require a team of robots to collectively visit multiple targets while optimizing competing objectives, such as total travel cost and makespan. This setting can be formulated as the Multi-Objective Multiple Traveling Salesman Problem (MOMTSP). Although learning-based methods have shown strong performance on the single-agent TSP and multi-objective TSP variants, they rarely address the combined challenges of multi-agent coordination and multi-objective trade-offs, which introduce dual sources of complexity. To bridge this gap, we propose CAMO, a conditional neural solver for MOMTSP that generalizes across varying numbers of targets, agents, and preference vectors, and yields high-quality approximations to the Pareto front (PF). Specifically, CAMO consists of a conditional encoder to fuse preferences into instance representations, enabling explicit control over multi-objective trade-offs, and a collaborative decoder that coordinates all agents by alternating agent selection and node selection to construct multi-agent tours autoregressively. To further improve generalization, we train CAMO with a REINFORCE-based objective over a mixed distribution of problem sizes. Extensive experiments show that CAMO outperforms both neural and conventional heuristics, achieving a closer approximation of PFs. In addition, ablation results validate the contributions of CAMO's key components, and real-world tests on a mobile robot platform demonstrate its practical applicability.