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Combinatorial optimization problems (COPs) are an important research topic in various fields. In recent times, there have been many attempts to solve COPs using deep learning-based approaches. We propose a novel neural network model that…

Computational Geometry · Computer Science 2023-04-17 Jaeseung Lee , Woojin Choi , Jibum Kim

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

Neural Combinatorial Optimization approaches have recently leveraged the expressiveness and flexibility of deep neural networks to learn efficient heuristics for hard Combinatorial Optimization (CO) problems. However, most of the current…

Machine Learning · Computer Science 2022-10-04 Sahil Manchanda , Sofia Michel , Darko Drakulic , Jean-Marc Andreoli

This paper tackles the multi-vehicle Coverage Path Planning (CPP) problem, crucial for applications like search and rescue or environmental monitoring. Due to its NP-hard nature, finding optimal solutions becomes infeasible with larger…

Quantum Physics · Physics 2024-07-15 Poojith U Rao , Florian Speelman , Balwinder Sodhi , Sachin Kinge

Connected vehicles will change the modes of future transportation management and organization, especially at an intersection without traffic light. Centralized coordination methods globally coordinate vehicles approaching the intersection…

Robotics · Computer Science 2021-03-12 Yang Guan , Yangang Ren , Shengbo Eben Li , Qi Sun , Laiquan Luo , Keqiang Li

The Pickup and Delivery Problem (PDP) is a fundamental and challenging variant of the Vehicle Routing Problem, characterized by tightly coupled pickup--delivery pairs, precedence constraints, and spatial layouts that often exhibit…

Machine Learning · Computer Science 2026-03-12 Wentao Wang , Lifeng Han , Guangyu Zou

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

Since the 1990s, considerable empirical work has been carried out to train statistical models, such as neural networks (NNs), as learned heuristics for combinatorial optimization (CO) problems. When successful, such an approach eliminates…

Machine Learning · Statistics 2026-01-21 Orit Davidovich , Shimrit Shtern , Segev Wasserkrug , Nimrod Megiddo

Neural solvers have achieved impressive progress in addressing simple routing problems, particularly excelling in computational efficiency. However, their advantages under complex constraints remain nascent, for which current…

Artificial Intelligence · Computer Science 2026-02-19 Jieyi Bi , Zhiguang Cao , Jianan Zhou , Wen Song , Yaoxin Wu , Jie Zhang , Yining Ma , Cathy Wu

Recent advancements in Connected Vehicle (CV) technology have prompted research on leveraging CV data for more effective traffic management. Despite the low penetration rate, such detailed CV data has demonstrated great potential in…

Optimization and Control · Mathematics 2024-06-21 Chaopeng Tan , Yue Ding , Kaidi Yang , Hong Zhu , Keshuang Tang

The Quantum Approximate Optimization Algorithm (QAOA) is a leading framework for quantum combinatorial optimization. The Vehicle Routing Problem (VRP), a core problem in logistics and transportation, is a natural application target, but it…

Emerging Technologies · Computer Science 2026-04-09 Yuan-Zheng Lei , Yaobang Gong , Xianfeng Terry Yang , Nii Attoh-Okine

Over the past decade, neural network solvers powered by generative artificial intelligence have garnered significant attention in the domain of vehicle routing problems (VRPs), owing to their exceptional computational efficiency and…

Machine Learning · Computer Science 2026-03-10 Zhenwei Wang , Tiehua Zhang , Ning Xue , Ender Ozcan , Ling Wang , Ruibin Bai

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

Transformers have advanced the field of natural language processing (NLP) on a variety of important tasks. At the cornerstone of the Transformer architecture is the multi-head attention (MHA) mechanism which models pairwise interactions…

Computation and Language · Computer Science 2021-06-01 Lin Zheng , Zhiyong Wu , Lingpeng Kong

This study proposes a hybrid quantum-classical approach to solving the Capacitated Vehicle Routing Problem (CVRP) by integrating the Column Generation (CG) method with the Quantum Alternating Operator Ansatz (QAOAnsatz). The CG method…

Quantum Physics · Physics 2025-03-24 Wei-hao Huang , Hiromichi Matsuyama , Yu Yamashiro

Vehicle routing problems (VRPs) are central to combinatorial optimization with significant practical implications. Recent advancements in neural combinatorial optimization (NCO) have demonstrated promising results by leveraging neural…

Machine Learning · Computer Science 2025-07-08 Han Li , Fei Liu , Zhenkun Wang , Qingfu Zhang

Routing controllability of connected and autonomous vehicles (CAVs) has been shown to reduce the adverse effects of selfish routing on the network efficiency. However, the assumption that CAV owners would readily allow themselves to be…

Systems and Control · Electrical Eng. & Systems 2021-08-10 Mohammadhadi Mansourianfar , Ziyuan Gu , S. Travis Waller , Meead Saberi

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-task Vehicle Routing Problems (VRPs) aim to minimize routing costs while satisfying diverse constraints. Existing solvers typically adopt a unified reinforcement learning (RL) framework to learn generalizable patterns across tasks.…

Artificial Intelligence · Computer Science 2026-03-03 Shuangchun Gui , Suyu Liu , Xuehe Wang , Zhiguang Cao

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
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