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The Electric Vehicle Routing Problem (EVRP) extends the capacitated vehicle routing problem by incorporating battery constraints and charging stations, posing significant optimization challenges. This paper introduces a Trilevel Memetic…

Neural and Evolutionary Computing · Computer Science 2025-06-03 Ivan Milinović , Leon Stjepan Uroić , Marko Đurasević

The vehicle routing problem with two-dimensional loading constraints (2L-CVRP) and the last-in-first-out (LIFO) rule presents significant practical and algorithmic challenges. While numerous heuristic approaches have been proposed to…

Artificial Intelligence · Computer Science 2024-06-19 Yifan Xia , Xiangyi Zhang

In this paper, we are concerned with the automated exchange of orders between logistics companies in a marketplace platform to optimize total revenues. We introduce a novel multi-agent approach to this problem, focusing on the Collaborative…

Multiagent Systems · Computer Science 2023-09-01 Paul Mingzheng Tang , Ba Phong Tran , Hoong Chuin Lau

Managing disruptions in railway traffic management is a major challenge. Rising traffic density and infrastructure limits increase complexity, making the Vehicle Routing and Scheduling Problem (VRSP) difficult to solve reliably and in real…

Artificial Intelligence · Computer Science 2026-05-12 Alberto Castagna , Stefan Zahlner , Adrian Egli , Christian Eichenberger , Daniel Boos , Manuel Meyer , Anton Fuxjager

Vehicle routing problems (VRPs), which can be found in numerous real-world applications, have been an important research topic for several decades. Recently, the neural combinatorial optimization (NCO) approach that leverages a…

Machine Learning · Computer Science 2024-04-15 Fei Liu , Xi Lin , Zhenkun Wang , Qingfu Zhang , Xialiang Tong , Mingxuan Yuan

A key challenge in solving a combinatorial optimization problem is how to guide the agent (i.e., solver) to efficiently explore the enormous search space. Conventional approaches often rely on enumeration (e.g., exhaustive, random, or tabu…

Artificial Intelligence · Computer Science 2020-08-11 Xingwen Zhang , Shuang Yang

Manually designing (meta-)heuristics for the Vehicle Routing Problem (VRP) is a challenging task that requires significant domain expertise. Recently, data-driven approaches have emerged as a promising solution, automatically learning…

Neural and Evolutionary Computing · Computer Science 2025-05-23 Saining Liu , Yi Mei , Mengjie Zhang

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

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

We consider several Vehicle Routing Problems (VRP) with profits, which seek to select a subset of customers, each one being associated with a profit, and to design service itineraries. When the sum of profits is maximized under distance…

Data Structures and Algorithms · Computer Science 2014-07-29 Thibaut Vidal , Nelson Maculan , Puca Huachi Vaz Penna , Luis Satoru Ochi

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

We investigate a structural decomposition for the capacitated vehicle routing problem (CVRP) based on vehicle-to-customer "assignment" and visits "sequencing" decision variables. We show that an heuristic search focused on assignment…

Optimization and Control · Mathematics 2018-03-19 Túlio A. M. Toffolo , Thibaut Vidal , Tony Wauters

Model-free deep-reinforcement-based learning algorithms have been applied to a range of COPs~\cite{bello2016neural}~\cite{kool2018attention}~\cite{nazari2018reinforcement}. However, these approaches suffer from two key challenges when…

Machine Learning · Computer Science 2022-06-01 Nasrin Sultana , Jeffrey Chan , Tabinda Sarwar , A. K. Qin

Designing high-performing heuristics for vehicle routing problems (VRPs) is a complex task that requires both intuition and deep domain knowledge. Large language model (LLM)-based code generation has recently shown promise across many…

Complex real-life routing challenges can be modeled as variations of well-known combinatorial optimization problems. These routing problems have long been studied and are difficult to solve at scale. The particular setting may also make…

Neural and Evolutionary Computing · Computer Science 2020-09-23 Marijn van Knippenberg , Mike Holenderski , Vlado Menkovski

We are in the midst of a semi-autonomous era in urban transportation in which varying forms of vehicle autonomy are gradually being introduced. This phase of partial autonomy is anticipated by some to span a few decades due to various…

Optimization and Control · Mathematics 2025-02-07 Hins Hu , Samitha Samaranayake

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

The vehicle routing problem (VRP) is a fundamental NP-hard task in intelligent transportation systems with broad applications in logistics and distribution. Deep reinforcement learning (DRL) with Graph Neural Networks (GNNs) has shown…

Machine Learning · Computer Science 2025-11-20 Le Tung Giang , Vu Hoang Viet , Nguyen Xuan Tung , Trinh Van Chien , Won-Joo Hwang

There has been a paradigm-shift in urban logistic services in the last years; demand for real-time, instant mobility and delivery services grows. This poses new challenges to logistic service providers as the underlying stochastic dynamic…

Artificial Intelligence · Computer Science 2021-03-02 Florentin D Hildebrandt , Barrett Thomas , Marlin W Ulmer

Existing deep reinforcement learning (DRL) based methods for solving the capacitated vehicle routing problem (CVRP) intrinsically cope with homogeneous vehicle fleet, in which the fleet is assumed as repetitions of a single vehicle. Hence,…

Machine Learning · Computer Science 2022-03-08 Jingwen Li , Yining Ma , Ruize Gao , Zhiguang Cao , Andrew Lim , Wen Song , Jie Zhang