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The Vehicle Routing Problem (VRP) is a widely studied combinatorial optimization problem and has been applied to various practical problems. While the explainability for VRP is significant for improving the reliability and interactivity in…

Machine Learning · Computer Science 2025-10-10 Daisuke Kikuta , Hiroki Ikeuchi , Kengo Tajiri , Yuusuke Nakano

This paper introduces a new deep learning approach to approximately solve the Covering Salesman Problem (CSP). In this approach, given the city locations of a CSP as input, a deep neural network model is designed to directly output the…

Neural and Evolutionary Computing · Computer Science 2021-09-15 Kaiwen Li , Tao Zhang , Rui Wang Yuheng Wang , Yi Han

The profiled vehicle routing problem (PVRP) is a generalization of the heterogeneous capacitated vehicle routing problem (HCVRP) in which the objective is to optimize the routes of vehicles to serve client demands subject to different…

Multiagent Systems · Computer Science 2025-02-05 Chuanbo Hua , Federico Berto , Jiwoo Son , Seunghyun Kang , Changhyun Kwon , Jinkyoo Park

Transfer learning with large pretrained transformer-based language models like BERT has become a dominating approach for most NLP tasks. Simply fine-tuning those large language models on downstream tasks or combining it with task-specific…

Computation and Language · Computer Science 2021-08-06 Wenjuan Han , Bo Pang , Yingnian Wu

Despite the extensive research efforts and the remarkable results obtained on Vehicle Routing Problems (VRP) by using algorithms proposed by the Machine Learning community that are partially or entirely based on data-driven analysis, most…

Machine Learning · Computer Science 2021-09-30 Luca Accorsi , Andrea Lodi , Daniele Vigo

Deep reinforcement learning (RL) has been shown to be effective in producing approximate solutions to some vehicle routing problems (VRPs), especially when using policies generated by encoder-decoder attention mechanisms. While these…

Machine Learning · Computer Science 2024-12-19 Joshua Levin , Randall Correll , Takanori Ide , Takafumi Suzuki , Takaho Saito , Alan Arai

We investigate a learning decision support system for vehicle routing, where the routing engine learns implicit preferences that human planners have when manually creating route plans (or routings). The goal is to use these learned…

Artificial Intelligence · Computer Science 2021-01-12 Rocsildes Canoy , Víctor Bucarey , Jayanta Mandi , Tias Guns

The Profiled Vehicle Routing Problem (PVRP) extends the classical VRP by incorporating vehicle-client-specific preferences and constraints, reflecting real-world requirements such as zone restrictions and service-level preferences. While…

Machine Learning · Computer Science 2025-08-26 Chuanbo Hua , Federico Berto , Zhikai Zhao , Jiwoo Son , Changhyun Kwon , Jinkyoo Park

In order to deal with the high development time of exact and approximation algorithms for NP-hard combinatorial optimisation problems and the high running time of exact solvers, deep learning techniques have been used in recent years as an…

Machine Learning · Computer Science 2021-04-20 James Fitzpatrick , Deepak Ajwani , Paula Carroll

This paper introduces TuneNSearch, a hybrid transfer learning and local search approach for addressing diverse variants of the vehicle routing problem (VRP). Our method uses reinforcement learning to generate high-quality solutions, which…

Machine Learning · Computer Science 2026-02-19 Arthur Corrêa , Cristóvão Silva , Liming Xu , Alexandra Brintrup , Samuel Moniz

Traveling Salesman Problem (TSP), as a classic routing optimization problem originally arising in the domain of transportation and logistics, has become a critical task in broader domains, such as manufacturing and biology. Recently, Deep…

Artificial Intelligence · Computer Science 2023-04-20 Yan Jin , Yuandong Ding , Xuanhao Pan , Kun He , Li Zhao , Tao Qin , Lei Song , Jiang Bian

The Fleet Size and Mix Vehicle Routing Problem (FSMVRP) is a prominent variant of the Vehicle Routing Problem (VRP), extensively studied in operations research and computational science. FSMVRP requires simultaneous decisions on fleet…

Artificial Intelligence · Computer Science 2026-01-01 Pengfu Wan , Jiawei Chen , Gangyan Xu

In the new wave of artificial intelligence, deep learning is impacting various industries. As a closely related area, optimization algorithms greatly contribute to the development of deep learning. But the reverse applications are still…

Machine Learning · Computer Science 2019-11-06 Zhengxuan Ling , Xinyu Tao , Yu Zhang , Xi Chen

Deep Reinforcement Learning has enabled the learning of policies for complex tasks in partially observable environments, without explicitly learning the underlying model of the tasks. While such model-free methods achieve considerable…

Machine Learning · Computer Science 2017-01-11 Tanmay Shankar , Santosha K. Dwivedy , Prithwijit Guha

Neural routing solvers (NRSs) that leverage deep learning to tackle vehicle routing problems have demonstrated notable potential for practical applications. By learning implicit heuristic rules from data, NRSs replace the handcrafted…

Optimization and Control · Mathematics 2026-03-17 Yunpeng Ba , Xi Lin , Changliang Zhou , Ruihao Zheng , Zhenkun Wang , Xinyan Liang , Zhichao Lu , Jianyong Sun , Yuhua Qian , Qingfu Zhang

The traveling purchaser problem (TPP) is an important combinatorial optimization problem with broad applications. Due to the coupling between routing and purchasing, existing works on TPPs commonly address route construction and purchase…

Optimization and Control · Mathematics 2025-07-03 Haofeng Yuan , Rongping Zhu , Wanlu Yang , Shiji Song , Keyou You , Wei Fan , C. L. Philip Chen

Solving practical multi-depot vehicle routing problems (MDVRP) is a challenging optimization task central to modern logistics, increasingly driven by e-commerce. To address the MDVRP's computational complexity, neural-based combinatorial…

Machine Learning · Computer Science 2026-05-01 Arthur Corrêa , Paulo Nascimento , Samuel Moniz

The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…

Machine Learning · Computer Science 2025-01-09 Yong Liang Goh , Wee Sun Lee , Xavier Bresson , Thomas Laurent , Nicholas Lim

Recent neural heuristics for the Vehicle Routing Problem (VRP) primarily rely on node coordinates as input, which may be less effective in practical scenarios where real cost metrics-such as edge-based distances-are more relevant. To…

Machine Learning · Computer Science 2025-06-23 Dian Meng , Zhiguang Cao , Yaoxin Wu , Yaqing Hou , Hongwei Ge , Qiang Zhang

In this paper a deep reinforcement based multi-agent path planning approach is introduced. The experiments are realized in a simulation environment and in this environment different multi-agent path planning problems are produced. The…

Machine Learning · Computer Science 2021-10-05 Mert Çetinkaya