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.

翻译：机器人系统通常需要一组机器人共同访问多个目标点，同时优化相互竞争的目标，如总旅行成本与完工时间。该场景可建模为多目标多旅行商问题（MOMTSP）。尽管基于学习的方法在单智能体TSP和多目标TSP变体上展现出强劲性能，但鲜有方法同时应对多智能体协作与多目标权衡的双重复杂性挑战。为弥补这一空白，我们提出CAMO——一种面向MOMTSP的条件神经求解器，能够泛化至不同数量的目标点、智能体及偏好向量，并生成逼近帕累托前沿（PF）的高质量解。具体而言，CAMO包含条件编码器（将偏好融入实例表征以实现多目标权衡显式控制）和协作解码器（通过交替进行智能体选择与节点选择来自回归构建多智能体路径，协调所有智能体）。为进一步提升泛化能力，我们采用基于REINFORCE的目标函数，在问题规模的混合分布上训练CAMO。大量实验表明，CAMO在逼近帕累托前沿方面优于神经启发式和传统启发式方法。此外，消融实验验证了CAMO关键组件的贡献，移动机器人平台上的实际测试也证明了其实用性。