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We study the problem of routing vehicles with energy constraints through a network where there are at least some charging nodes. We seek to minimize the total elapsed time for vehicles to reach their destinations by determining routes as…

Optimization and Control · Mathematics 2014-01-28 Tao Wang , Christos G. Cassandras , Sepideh Pourazarm

Learning how to automatically solve optimization problems has the potential to provide the next big leap in optimization technology. The performance of automatically learned heuristics on routing problems has been steadily improving in…

Artificial Intelligence · Computer Science 2020-12-01 André Hottung , Kevin Tierney

Combinatorial Optimization (CO) encompasses a wide range of problems that arise in many real-world scenarios. While significant progress has been made in developing learning-based methods for specialized CO problems, a unified model with a…

Machine Learning · Computer Science 2025-05-13 Zefang Zong , Xiaochen Wei , Guozhen Zhang , Chen Gao , Huandong Wang , Yong Li

Mixture-of-Experts (MoE) has emerged as an effective approach to reduce the computational overhead of Transformer architectures by sparsely activating a subset of parameters for each token while preserving high model capacity. This paradigm…

Computer Vision and Pattern Recognition · Computer Science 2026-03-31 Dohwan Ko , Jinyoung Park , Seoung Choi , Sanghyeok Lee , Seohyun Lee , Hyunwoo J. Kim

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

Learning to optimize (L2O) has recently emerged as a promising approach to solving optimization problems by exploiting the strong prediction power of neural networks and offering lower runtime complexity than conventional solvers. While L2O…

Machine Learning · Computer Science 2021-12-21 Zhihui Shao , Jianyi Yang , Cong Shen , Shaolei Ren

The vehicle routing problem is a well known class of NP-hard combinatorial optimisation problems in literature. Traditional solution methods involve either carefully designed heuristics, or time-consuming metaheuristics. Recent work in…

Artificial Intelligence · Computer Science 2022-06-15 Harshad Khadilkar

Unsupervised neural combinatorial optimization (NCO) offers an appealing alternative to supervised approaches by training learning-based solvers without ground-truth solutions, directly minimizing instance objectives and constraint…

Machine Learning · Computer Science 2026-03-13 Kien X. Nguyen , Ilya Safro

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

Connected and autonomous vehicles have the potential to minimize energy consumption by optimizing the vehicle velocity and powertrain dynamics with Vehicle-to-Everything info en route. Existing deterministic and stochastic methods created…

Machine Learning · Computer Science 2023-10-18 Jacob Paugh , Zhaoxuan Zhu , Shobhit Gupta , Marcello Canova , Stephanie Stockar

Neural models produce promising results when solving Vehicle Routing Problems (VRPs), but often fall short in generalization. Recent attempts to enhance model generalization often incur unnecessarily large training cost or cannot be…

Machine Learning · Computer Science 2025-03-19 Yubin Xiao , Di Wang , Xuan Wu , Yuesong Wu , Boyang Li , Wei Du , Liupu Wang , You Zhou

The Capacitated Vehicle Routing Problem is a well-known NP-hard problem that poses the challenge of finding the optimal route of a vehicle delivering products to multiple locations. Recently, new efforts have emerged to create constructive…

The Maximum Minimal Cut Problem (MMCP), a NP-hard combinatorial optimization (CO) problem, has not received much attention due to the demanding and challenging bi-connectivity constraint. Moreover, as a CO problem, it is also a daunting…

Artificial Intelligence · Computer Science 2024-08-19 Huaiyuan Liu , Xianzhang Liu , Donghua Yang , Hongzhi Wang , Yingchi Long , Mengtong Ji , Dongjing Miao , Zhiyu Liang

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

Neural Combinatorial Optimisation (NCO) is a promising learning-based approach for solving Vehicle Routing Problems (VRPs) without extensive manual design. While existing constructive NCO methods typically follow an appending-based paradigm…

Machine Learning · Computer Science 2025-10-31 Fu Luo , Xi Lin , Mengyuan Zhong , Fei Liu , Zhenkun Wang , Jianyong Sun , Qingfu Zhang

Logistics has gained great attentions with the prosperous development of commerce, which is often seen as the classic optimal vehicle routing problem. Meanwhile, electric vehicle (EV) has been widely used in logistic fleet to curb the…

Optimization and Control · Mathematics 2021-09-14 Canqi Yao , Shibo Chen , Zaiyue Yang

Machine learning has been adapted to help solve NP-hard combinatorial optimization problems. One prevalent way is learning to construct solutions by deep neural networks, which has been receiving more and more attention due to the high…

Machine Learning · Computer Science 2024-05-07 Chengrui Gao , Haopu Shang , Ke Xue , Dong Li , Chao Qian

The Moving Target Vehicle Routing Problem (MT-VRP) seeks trajectories for several agents that intercept a set of moving targets, subject to speed, time window, and capacity constraints. We introduce an exact algorithm, Branch-and-Price with…

Robotics · Computer Science 2026-04-20 Anoop Bhat , Geordan Gutow , Zhongqiang Ren , Sivakumar Rathinam , Howie Choset

The neural combinatorial optimization (NCO) method has shown great potential for solving routing problems of intelligent transportation systems without requiring expert knowledge. However, existing constructive NCO methods still struggle to…

Artificial Intelligence · Computer Science 2026-05-26 Changliang Zhou , Xi Lin , Zhenkun Wang , Xialiang Tong , Mingxuan Yuan , Qingfu Zhang

This study aims to develop a real-time intersection optimization (RIO) control algorithm to efficiently serve traffic of Connected and Automated Vehicles (CAVs) and conventional vehicles (CNVs). This paper extends previous work to consider…

Signal Processing · Electrical Eng. & Systems 2020-07-09 Mahmoud Pourmehrab , Lily Elefteriadou , Sanjay Ranka