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Firstly, taking into account the actual multiple constraints such as customer distribution, vehicle load constraints, and time windows in urban logistics distribution regions, a multi constraint and multi-objective urban logistics distribution mathematical model was established with the goal of minimizing the total length, cost, and maximum makespan of urban logistics distribution paths. Secondly, based on the decomposition strategy, a DRL framework for optimizing urban logistics delivery paths based on Graph Capsule Network (G-Caps Net) was designed. This framework takes the node information of VRP as input in the form of a 2D graph, modifies the graph attention capsule network by considering multi-layer features, edge information, and residual connections between layers in the graph structure, and replaces probability calculation with the module length of the capsule vector as output. Then, the baseline REINFORCE algorithm with rollout is used for network training, and a 2-opt local search strategy and sampling search strategy are used to improve the quality of the solution. Finally, the performance of the proposed method was evaluated on standard examples of problems of different scales. The experimental results showed that the constructed model and solution framework can improve logistics delivery efficiency. This method achieved the best comprehensive performance, surpassing the most advanced distress methods, and has great potential in practical engineering.<\/jats:p>","DOI":"10.3233\/ida-230480","type":"journal-article","created":{"date-parts":[[2024,6,7]],"date-time":"2024-06-07T11:24:33Z","timestamp":1717759473000},"page":"116-140","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Combining decomposition and graph capsule network for multi-objective vehicle routing optimization"],"prefix":"10.1177","volume":"29","author":[{"given":"Haifei","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence and Computer Science, Jiangnan University, Wuxi, Jiangsu, China"},{"name":"Key Laboratory of Advanced Process Control for Light Industry (Jiangnan University), Ministry of Education, Wuxi, Jiangsu, 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