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

TL;DR

CAMO is a neural network-based solver designed for the multi-objective multi-agent traveling salesman problem, effectively balancing multiple objectives and coordinating multiple robots to produce high-quality solutions.

Contribution

It introduces a novel conditional neural architecture that generalizes across problem sizes and preferences, explicitly controlling trade-offs and coordinating multiple agents.

Findings

Outperforms existing heuristics and neural methods in approximating Pareto fronts.

Generalizes well across different problem sizes and preference settings.

Validated on real-world robotic platform.

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.