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Many real-world vehicle routing problems involve rich sets of constraints with respect to the capacities of the vehicles, time windows for customers etc. While in recent years first machine learning models have been developed to solve basic…

Machine Learning · Computer Science 2020-06-17 Jonas K. Falkner , Lars Schmidt-Thieme

We consider a vehicle routing problem which seeks to minimize cost subject to service level constraints on several groups of deliveries. This problem captures some essential challenges faced by a logistics provider which operates…

Optimization and Control · Mathematics 2017-06-13 Teobaldo Bulhões , Minh Hoàng Hà , Rafael Martinelli , Thibaut Vidal

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

Recently, several studies have explored the use of neural network to solve different routing problems, which is an auspicious direction. These studies usually design an encoder-decoder based framework that uses encoder embeddings of nodes…

Artificial Intelligence · Computer Science 2021-09-13 Zongtao Liu , Jing Xu , Jintao Su , Tao Xiao , Yang Yang

Recently, machine learning of the branch and bound algorithm has shown promise in approximating competent solutions to NP-hard problems. In this paper, we utilize and comprehensively compare the outcomes of three neural networks--graph…

Machine Learning · Computer Science 2023-10-18 Andrew Naguib , Waleed A. Yousef , Issa Traoré , Mohammad Mamun

The paper presents an approach to solving the Robust Energy Capacitated Vehicle Routing Problem (RECVRP), focusing on electric vehicles and their limited battery capacity. A finite number of customers, each with their own demand, have to be…

Systems and Control · Electrical Eng. & Systems 2024-03-22 Mark Pustilnik , Francesco Borrelli

Unlike traditional homogeneous routing problems, the Heterogeneous Fleet Vehicle Routing Problem (HFVRP) involves heterogeneous fixed costs, variable travel costs, and capacity constraints, rendering solution quality highly sensitive to…

Machine Learning · Computer Science 2026-04-08 Shihong Huang , Shengjie Wang , Lei Gao , Hong Ma , Zhanluo Zhang , Feng Zhang , Weihua Zhou

The capacitated vehicle routing problem (CVRP) involves distributing (identical) items from a depot to a set of demand locations, using a single capacitated vehicle. We study a generalization of this problem to the setting of multiple…

Data Structures and Algorithms · Computer Science 2010-12-09 Inge Li Gortz , Marco Molinaro , Viswanath Nagarajan , R. Ravi

We investigate the capacitated vehicle routing problem (CVRP) under a robotics context, where a vehicle with limited payload must complete delivery (or pickup) tasks to serve a set of geographically distributed customers with varying…

Robotics · Computer Science 2021-07-27 Kai Gao , Jingjin Yu

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 Electric Vehicle Routing Problem (EVRP) extends the classical Vehicle Routing Problem (VRP) to reflect the growing use of electric and hybrid vehicles in logistics. Due to the variety of constraints considered in the literature,…

Artificial Intelligence · Computer Science 2025-11-14 David Woller , Viktor Kozák , Miroslav Kulich , Libor Přeučil

We present a new approach to learning for planning, where knowledge acquired while solving a given set of planning problems is used to plan faster in related, but new problem instances. We show that a deep neural network can be used to…

Artificial Intelligence · Computer Science 2018-07-26 Edward Groshev , Maxwell Goldstein , Aviv Tamar , Siddharth Srivastava , Pieter Abbeel

We propose a feature-based guidance mechanism to enhance metaheuristic algorithms for solving the Capacitated Vehicle Routing Problem (CVRP). This mechanism leverages an Explainable AI (XAI) model to identify features that correlate with…

Artificial Intelligence · Computer Science 2025-12-23 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux

Neural Combinatorial Optimization aims to learn to solve a class of combinatorial problems through data-driven methods and notably through employing neural networks by learning the underlying distribution of problem instances. While, so far…

Machine Learning · Computer Science 2025-08-05 Daniela Thyssens , Tim Dernedde , Wilson Sentanoe , Lars Schmidt-Thieme

This paper introduces a new set of large-scale benchmark instances for the Capacitated Vehicle Routing Problem (CVRP). The proposed XL set extends existing benchmarks by covering instances with 1,000 to 10,000 customers and a wide range of…

Optimization and Control · Mathematics 2026-01-19 Eduardo Queiroga , Rafael Martinelli , Anand Subramanian , Eduardo Uchoa , Thibaut Vidal

Existing neural solvers for vehicle routing problems (VRPs) are typically trained either in a one-off manner on a fixed set of pre-defined tasks or in a lifelong manner with tasks arriving sequentially, assuming sufficient training on each…

Machine Learning · Computer Science 2026-05-08 Jiyuan Pei , Yi Mei , Jialin Liu , Mengjie Zhang , Xin Yao

The Vehicle Routing Problem (VRP) is the combinatorial optimization problem of designing routes for vehicles to visit customers in such a fashion that a cost function, typically the number of vehicles, or the total travelled distance is…

Artificial Intelligence · Computer Science 2021-07-01 Sabino Francesco Roselli , Martin Fabian , Knut Åkesson

We consider a 2-vehicle routing problem (2VRP) which can be viewed as a building block for the variety of vehicle routing problems (VRP). As a simplified version of the 2VRP, we consider a 2-period balanced travelling salesman problem…

Optimization and Control · Mathematics 2018-02-23 Vladimir Deineko , Bettina Klinz

Transportation occupies one-third of the amount in the logistics costs, and accordingly transportation systems largely influence the performance of the logistics system. This work presents an adaptive data-driven innovative modular approach…

Artificial Intelligence · Computer Science 2020-01-08 Emir Zunic , Dzenana Donko , Emir Buza

Recent advances in supervised learning and reinforcement learning have provided new opportunities to apply related methodologies to automated driving. However, there are still challenges to achieve automated driving maneuvers in dynamically…

Machine Learning · Computer Science 2020-08-31 Fei Ye , Pin Wang , Ching-Yao Chan , Jiucai Zhang
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