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We present a novel framework that combines machine learning with mixed-integer optimization to solve the Capacitated Location-Routing Problem (CLRP). The CLRP is a classical NP-hard problem that integrates strategic facility location with…

Optimization and Control · Mathematics 2026-02-24 Waquar Kaleem , Doyoung Lee , Changhyun Kwon , Anirudh Subramanyam

The inventory routing problem (IRP) focuses on jointly optimizing inventory and distribution operations from a supplier to retailers over multiple days. Compared to other problems from the vehicle routing family, the interrelations between…

Neural and Evolutionary Computing · Computer Science 2025-11-25 Jingyi Zhao , Claudia Archetti , Tuan Anh Pham , Thibaut Vidal

The Vehicle Routing Problem (VRP) is a complex optimization problem with numerous real-world applications, mostly solved using metaheuristic algorithms due to its $\mathcal{NP}$-Hard nature. Traditionally, these metaheuristics rely on…

Artificial Intelligence · Computer Science 2025-08-11 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux

Numerous Neural Combinatorial Optimization (NCO) solvers have been proposed to address Vehicle Routing Problems (VRPs). However, most of these solvers focus exclusively on single-vehicle VRP variants, overlooking the more realistic min-max…

Machine Learning · Computer Science 2026-03-17 Xuan Wu , Di Wang , Chunguo Wu , Kaifang Qi , Chunyan Miao , Yubin Xiao , Jian Zhang , You Zhou

Learning to solve combinatorial optimization problems, such as the vehicle routing problem, offers great computational advantages over classical operations research solvers and heuristics. The recently developed deep reinforcement learning…

Machine Learning · Computer Science 2022-01-06 Daniela Thyssens , Jonas Falkner , Lars Schmidt-Thieme

Electric Vehicles (EVs) are becoming increasingly prevalent nowadays, with studies highlighting their potential as mobile energy storage systems to provide grid support. Realising this potential requires effective charging coordination,…

Systems and Control · Electrical Eng. & Systems 2025-07-22 Jun Kang Yap , Vishnu Monn Baskaran , Wen Shan Tan , Ze Yang Ding , Hao Wang , David L. Dowe

In this paper, we address two optimisation problems arising in the context of city logistics and two-level transportation systems. The two-echelon vehicle routing problem and the two-echelon location routing problem seek to produce vehicle…

Data Structures and Algorithms · Computer Science 2016-10-05 Ulrich Breunig , Verena Schmid , Richard F. Hartl , Thibaut Vidal

Capacitated vehicle routing problem (CVRP) is being one of the most common optimization problems in our days, considering the wide usage of routing algorithms in multiple fields such as transportation domain, food delivery, network routing,…

Artificial Intelligence · Computer Science 2021-12-28 Hassan Moussa

Multi-depot vehicle routing problems (MDVRPs) are prevalent in a variety of practical applications. However, they are computationally challenging to solve due to their inherent complexity. This paper proposes an effective hybrid algorithm…

Robotics · Computer Science 2026-05-08 Zhenyu Lei , Jin-Kao Hao

Constructive neural combinatorial optimization (NCO) has attracted growing research attention due to its ability to solve complex routing problems without relying on handcrafted rules. However, existing NCO methods face significant…

Artificial Intelligence · Computer Science 2025-05-20 Changliang Zhou , Xi Lin , Zhenkun Wang , Qingfu Zhang

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

This paper introduces a new approach to improve the performance of the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) solvers for a high number of nodes. It proposes to cluster nodes together using Recursive-DBSCAN - an…

Other Computer Science · Computer Science 2019-03-26 Kamil Bujel , Feiko Lai , Michal Szczecinski , Winnie So , Miguel Fernandez

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

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

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

In this paper, we evaluate the use of Reinforcement Learning (RL) to solve a classic combinatorial optimization problem: the Capacitated Vehicle Routing Problem (CVRP). We formalize this problem in the RL framework and compare two of the…

Artificial Intelligence · Computer Science 2022-01-17 Leo Ardon

This work is motivated by solving a problem faced by big agriculture companies implementing precision agriculture operations for spraying practices using two types of operators, namely a tender tanker and a fleet of sprayers. We model this…

Optimization and Control · Mathematics 2023-12-18 Faisal Alkaabneh

Neural Combinatorial Optimization (NCO) has emerged as a promising learning-based paradigm for addressing Vehicle Routing Problems (VRPs) by minimizing the need for extensive manual engineering. While existing NCO methods, trained on…

Machine Learning · Computer Science 2025-11-24 Yuanyao Chen , Rongsheng Chen , Fu Luo , Zhenkun Wang

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

Recent neural combinatorial optimization (NCO) methods have shown promising problem-solving ability without requiring domain-specific expertise. Most existing NCO methods use training and testing data with a fixed constraint value and lack…

Machine Learning · Computer Science 2025-10-31 Fu Luo , Yaoxin Wu , Zhi Zheng , Zhenkun Wang