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For NP-hard combinatorial optimization problems, it is usually difficult to find high-quality solutions in polynomial time. The design of either an exact algorithm or an approximate algorithm for these problems often requires significantly…

Machine Learning · Computer Science 2021-05-07 Kun Lei , Peng Guo , Yi Wang , Xiao Wu , Wenchao Zhao

Efficiently solving a vehicle routing problem (VRP) in a practical runtime is a critical challenge for delivery management companies. This paper explores both a theoretical and experimental connection between the Capacitated Vehicle Routing…

Optimization and Control · Mathematics 2024-03-22 Abdelhakim Abdellaoui , Loubna Benabbou , Issmail El Hallaoui

This paper presents a model for a vehicle routing problem in which customer demands are stochastic and vehicles are divided into compartments. The problem is motivated by the needs of certain agricultural cooperatives that produce various…

Optimization and Control · Mathematics 2024-10-24 Juan Carlos Gonçalves-Dosantos , Laura Davila-Pena , Balbina Casas-Méndez

In this paper we study the routing and rebalancing problem for a fleet of autonomous vehicles providing on-demand transportation within a congested urban road network (that is, a road network where traffic speed depends on vehicle density).…

Systems and Control · Computer Science 2016-09-16 Federico Rossi , Rick Zhang , Marco Pavone

The Capacitated Vehicle Routing Problem (CVRP) is a core NP-hard problem in the field of combinatorial optimization. It aims to plan optimal routes for a fleet of vehicles with uniform capacity, serving a set of customers with specific…

Data Structures and Algorithms · Computer Science 2026-04-07 Yongyu Chen

This paper provides a systematic overview of machine learning methods applied to solve NP-hard Vehicle Routing Problems (VRPs). Recently, there has been a great interest from both machine learning and operations research communities to…

Machine Learning · Computer Science 2022-05-06 Aigerim Bogyrbayeva , Meraryslan Meraliyev , Taukekhan Mustakhov , Bissenbay Dauletbayev

The capacitated vehicle routing problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. In this problem, we are given a depot and a set of customers, each with a demand, embedded in a metric space. The…

Data Structures and Algorithms · Computer Science 2026-01-30 Jingyang Zhao , Mingyu Xiao

This study presents an in-depth computational analysis of four well-known Capacitated Vehicle Routing Problem (CVRP) formulations with polynomial number of subtour elimination constraints: a node-based formulation and three arc-based…

Optimization and Control · Mathematics 2018-10-02 Deniz Aksen , Temel Oncan , Mir Ehsan Hesam Sadati

The rapid growth of e-commerce and the increasing demand for timely, cost-effective last-mile delivery have increased interest in collaborative logistics. This research introduces a novel collaborative synchronized multi-platform vehicle…

Multiagent Systems · Computer Science 2025-05-30 Sumbal Malik , Majid Khonji , Khaled Elbassioni , Jorge Dias

Recently, there is an emerging trend to apply deep reinforcement learning to solve the vehicle routing problem (VRP), where a learnt policy governs the selection of next node for visiting. However, existing methods could not handle well the…

Machine Learning · Computer Science 2021-10-07 Jingwen Li , Liang Xin , Zhiguang Cao , Andrew Lim , Wen Song , Jie Zhang

Vehicle Routing Problems (VRPs) can model many real-world scenarios and often involve complex constraints. While recent neural methods excel in constructing solutions based on feasibility masking, they struggle with handling complex…

Artificial Intelligence · Computer Science 2024-10-29 Jieyi Bi , Yining Ma , Jianan Zhou , Wen Song , Zhiguang Cao , Yaoxin Wu , Jie Zhang

This paper considers the vehicle routing problem with stochastic demands (VRPSD) under optimal restocking. We develop an exact algorithm that is effective for solving instances with many vehicles and few customers per route. In our…

Optimization and Control · Mathematics 2018-06-25 Alexandre Florio , Richard Hartl , Stefan Minner

In this paper we deal with a complex real world scheduling problem closely related to the well-known Resource-Constrained Project Scheduling Problem (RCPSP). The problem concerns industrial test laboratories in which a large number of tests…

Artificial Intelligence · Computer Science 2024-11-01 Tobias Geibinger , Florian Mischek , Nysret Musliu

We propose a Large Neighborhood Search (LNS) approach utilizing a learned construction heuristic based on neural networks as repair operator to solve the vehicle routing problem with time windows (VRPTW). Our method uses graph neural…

Machine Learning · Computer Science 2022-05-11 Jonas K. Falkner , Daniela Thyssens , Lars Schmidt-Thieme

The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in…

In this work, a study on Variable Neighborhood Search algorithms for multi-depot dial-a-ride problems is presented. In dial-a-ride problems patients need to be transported from pre-specified pickup locations to pre-specified delivery…

Discrete Mathematics · Computer Science 2016-11-17 Paolo Detti , Garazi Zabalo Manrique de Lara

Autonomous robots are widely utilized for mapping and exploration tasks due to their cost-effectiveness. Multi-robot systems offer scalability and efficiency, especially in terms of the number of robots deployed in more complex…

Robotics · Computer Science 2025-06-04 Apoorva Vashisth , Manav Kulshrestha , Damon Conover , Aniket Bera

The Ride-Pool Matching Problem (RMP) is central to on-demand ride-pooling services, where vehicles must be matched with multiple requests while adhering to service constraints such as pickup delays, detour limits, and vehicle capacity. Most…

Robotics · Computer Science 2025-03-12 Hao Jiang , Yixing Xu , Pradeep Varakantham

In this work, we investigate the problem of order batching and picker routing in warehouse storage areas. These problems are known to be capital and labour intensive, and often contribute to a sizable fraction of warehouse operating costs.…

Data Structures and Algorithms · Computer Science 2020-02-04 Wei Hao Khoong

We consider two-machine routing open shop problem on a tree. In this problem a transportation network with a tree-like structure is given, and each node contains some jobs to be processed by two mobile machines. Machines are initially…

Computational Complexity · Computer Science 2020-04-09 Ilya Chernykh , Ekaterina Lgotina