A Combined Diffusion Model and Reinforcement Learning Approach for Solving the Vehicle Routing Problem With Multiple Soft Time Windows

The Vehicle Routing Problem with Multiple Soft Time Windows (VRPMSTW) is a challenging combinatorial optimization problem where a fleet of vehicles must deliver goods to a set of customers, adhering to time windows while minimizing costs. In this paper, we propose a novel solution approach that comb...

Full description

Saved in:
Bibliographic Details
Main Authors: Yu Qiao, Jianjun Miao, Xiaoying Huang
Format: Article
Language:English
Published: IEEE 2025-01-01
Series:IEEE Access
Subjects:
Online Access:https://ieeexplore.ieee.org/document/11053837/
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849424091503656960
author Yu Qiao
Jianjun Miao
Xiaoying Huang
author_facet Yu Qiao
Jianjun Miao
Xiaoying Huang
author_sort Yu Qiao
collection DOAJ
description The Vehicle Routing Problem with Multiple Soft Time Windows (VRPMSTW) is a challenging combinatorial optimization problem where a fleet of vehicles must deliver goods to a set of customers, adhering to time windows while minimizing costs. In this paper, we propose a novel solution approach that combines a Diffusion Model with Reinforcement Learning (RL) to efficiently solve the VRPMSTW. The Diffusion Model generates feasible vehicle routes by denoising a noise distribution, ensuring that constraints such as vehicle capacity, travel distance, and time windows are respected. Subsequently, the RL module fine-tunes these paths by optimizing the objective function, which minimizes the number of vehicles, travel distance, and time window penalties. We evaluate our approach on benchmark datasets and compare it with other state-of-the-art methods. The results demonstrate that our combined model outperforms traditional heuristics, achieving better optimization in terms of the number of vehicles, travel cost, and time window violations. The proposed method provides a promising solution for solving complex real-world vehicle routing problems with soft time window constraints.
format Article
id doaj-art-2ec4e693cb5a4568a2d26cbb038bbe02
institution Kabale University
issn 2169-3536
language English
publishDate 2025-01-01
publisher IEEE
record_format Article
series IEEE Access
spelling doaj-art-2ec4e693cb5a4568a2d26cbb038bbe022025-08-20T03:30:20ZengIEEEIEEE Access2169-35362025-01-011311352911354310.1109/ACCESS.2025.358398411053837A Combined Diffusion Model and Reinforcement Learning Approach for Solving the Vehicle Routing Problem With Multiple Soft Time WindowsYu Qiao0https://orcid.org/0009-0006-7874-639XJianjun Miao1Xiaoying Huang2School of Management, Guangzhou Huali College, Guangzhou, ChinaSchool of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, ChinaInstitute of Foreign Languages and Trade, Guangzhou Vocational and Technical University of Science and Technology, Guangzhou, ChinaThe Vehicle Routing Problem with Multiple Soft Time Windows (VRPMSTW) is a challenging combinatorial optimization problem where a fleet of vehicles must deliver goods to a set of customers, adhering to time windows while minimizing costs. In this paper, we propose a novel solution approach that combines a Diffusion Model with Reinforcement Learning (RL) to efficiently solve the VRPMSTW. The Diffusion Model generates feasible vehicle routes by denoising a noise distribution, ensuring that constraints such as vehicle capacity, travel distance, and time windows are respected. Subsequently, the RL module fine-tunes these paths by optimizing the objective function, which minimizes the number of vehicles, travel distance, and time window penalties. We evaluate our approach on benchmark datasets and compare it with other state-of-the-art methods. The results demonstrate that our combined model outperforms traditional heuristics, achieving better optimization in terms of the number of vehicles, travel cost, and time window violations. The proposed method provides a promising solution for solving complex real-world vehicle routing problems with soft time window constraints.https://ieeexplore.ieee.org/document/11053837/Vehicle routing problem (VRP)multiple soft time windows (VRPMSTW)diffusion modelreinforcement learning (RL)combinatorial optimizationpath generation
spellingShingle Yu Qiao
Jianjun Miao
Xiaoying Huang
A Combined Diffusion Model and Reinforcement Learning Approach for Solving the Vehicle Routing Problem With Multiple Soft Time Windows
IEEE Access
Vehicle routing problem (VRP)
multiple soft time windows (VRPMSTW)
diffusion model
reinforcement learning (RL)
combinatorial optimization
path generation
title A Combined Diffusion Model and Reinforcement Learning Approach for Solving the Vehicle Routing Problem With Multiple Soft Time Windows
title_full A Combined Diffusion Model and Reinforcement Learning Approach for Solving the Vehicle Routing Problem With Multiple Soft Time Windows
title_fullStr A Combined Diffusion Model and Reinforcement Learning Approach for Solving the Vehicle Routing Problem With Multiple Soft Time Windows
title_full_unstemmed A Combined Diffusion Model and Reinforcement Learning Approach for Solving the Vehicle Routing Problem With Multiple Soft Time Windows
title_short A Combined Diffusion Model and Reinforcement Learning Approach for Solving the Vehicle Routing Problem With Multiple Soft Time Windows
title_sort combined diffusion model and reinforcement learning approach for solving the vehicle routing problem with multiple soft time windows
topic Vehicle routing problem (VRP)
multiple soft time windows (VRPMSTW)
diffusion model
reinforcement learning (RL)
combinatorial optimization
path generation
url https://ieeexplore.ieee.org/document/11053837/
work_keys_str_mv AT yuqiao acombineddiffusionmodelandreinforcementlearningapproachforsolvingthevehicleroutingproblemwithmultiplesofttimewindows
AT jianjunmiao acombineddiffusionmodelandreinforcementlearningapproachforsolvingthevehicleroutingproblemwithmultiplesofttimewindows
AT xiaoyinghuang acombineddiffusionmodelandreinforcementlearningapproachforsolvingthevehicleroutingproblemwithmultiplesofttimewindows
AT yuqiao combineddiffusionmodelandreinforcementlearningapproachforsolvingthevehicleroutingproblemwithmultiplesofttimewindows
AT jianjunmiao combineddiffusionmodelandreinforcementlearningapproachforsolvingthevehicleroutingproblemwithmultiplesofttimewindows
AT xiaoyinghuang combineddiffusionmodelandreinforcementlearningapproachforsolvingthevehicleroutingproblemwithmultiplesofttimewindows