Learning to Solve Multiple-TSP With Time Window and Rejections via Deep Reinforcement Learning

• Published in: IEEE transactions on intelligent transportation systems Vol. 24; no. 1; pp. 1325 - 1336
• Main Authors: Zhang, Rongkai, Zhang, Cong, Cao, Zhiguang, Song, Wen, Tan, Puay Siew, Zhang, Jie, Wen, Bihan, Dauwels, Justin
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Costs; Customers; Deep learning; deep reinforcement learning; graph neural network; Isomorphism; Machine learning; Reinforcement learning; Rejection rate; Routing; Task analysis; Time factors; Training data; Traveling salesman problem; Travelling salesman problem; Windows (intervals)
• ISSN: 1524-9050; 1558-0016
• DOI: 10.1109/TITS.2022.3207011

We propose a manager-worker framework (the implementation of our model is publically available at: https://github.com/zcaicaros/manager-worker-mtsptwr ) based on deep reinforcement learning to tackle a hard yet nontrivial variant of Travelling Salesman Problem (TSP), i.e., multiple-vehicle TSP with time window and rejections (mTSPTWR), where customers who cannot be served before the deadline are subject to rejections. Particularly, in the proposed framework, a manager agent learns to divide mTSPTWR into sub-routing tasks by assigning customers to each vehicle via a Graph Isomorphism Network (GIN) based policy network. A worker agent learns to solve sub-routing tasks by minimizing the cost in terms of both tour length and rejection rate for each vehicle, the maximum of which is then fed back to the manager agent to learn better assignments. Experimental results demonstrate that the proposed framework outperforms strong baselines in terms of higher solution quality and shorter computation time. More importantly, the trained agents also achieve competitive performance for solving unseen larger instances.