Flexible Capacitated Vehicle Routing Problem Solution Method Based on Memory Pointer Network

Enliang Wang, Yue Cai and Zhixin Sun ()
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Enliang Wang: Big Data Technology and Application Engineering Research Center of Jiangsu Province, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
Yue Cai: College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
Zhixin Sun: Big Data Technology and Application Engineering Research Center of Jiangsu Province, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

Mathematics, 2025, vol. 13, issue 7, 1-21

Abstract: In real-world logistics scenarios, the complexities often surpass what traditional Capacitated Vehicle Routing Problem (CVRP) models can effectively address. For instance, when there is an excess of goods and limited vehicles, traditional CVRP models frequently fail to yield feasible solutions. Additionally, the time sensitivity of goods and the large scale of vehicles and goods in practical logistics scenarios present significant challenges for efficient problem-solving. This underscores the urgent need to develop a novel CVRP model that is better suited for logistics scenarios and enhances the scalability of CVRP. To address these limitations, we propose a flexible CVRP model, referred to as Flexible CVRP, which modifies the optimization objectives and constraints. This allows CVRP to provide a sensible solution even when no feasible solution exists in the traditional sense. To tackle the challenges posed by large-scale problems, we leverage the Memory Pointer Network (MemPtrN). This approach enables the modeling of solution strategies, offering strong generalization capabilities and mitigating the explosive growth in complexity to some extent. Compared to commonly used heuristic algorithms, our method achieves superior solution quality for large-scale problems. Specifically, when addressing large-scale scenarios, the MemPtrN outperforms Google’s OR-Tools solver, heuristic algorithms, enhanced evolutionary algorithms, and other reinforcement learning methods in terms of both solution speed and quality.

Keywords: memory pointer network; deep reinforcement learning; flexible CVRP; combinatorial optimization problem; actor–critic algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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