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

2026-03-19

AI Summary

This work proposes CAMO, a conditional neural solver for the multi-objective multiple traveling salesman problem (MOMTSP), which jointly addresses the dual challenges of multi-agent coordination and multi-objective trade-offs. CAMO integrates a preference vector into an instance representation via a conditional encoder and employs a collaborative autoregressive decoder that alternately selects agents and target nodes to construct feasible multi-agent tours satisfying the specified preference constraints. To our knowledge, this is the first approach to unify preference-conditioned modeling with cooperative path construction in MOMTSP, enabling generalization across varying numbers of objectives, agents, and preference vectors. Combined with a REINFORCE-based hybrid-scale training strategy, CAMO outperforms existing neural and heuristic methods in approximating the Pareto front and demonstrates practical efficacy on a real-world mobile robot platform.

Technology Category

• Multiagent Systems: Multiagent Planning
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Multi-Objective Multiple Traveling Salesman Problem
• multi-agent coordination
• multi-objective trade-offs
• Pareto front approximation

Innovation

• conditional neural solver
• multi-objective optimization
• multi-agent coordination
• Pareto front approximation
• autoregressive tour construction