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Recently, neural networks (NN) have made great strides in combinatorial optimization. However, they face challenges when solving the capacitated arc routing problem (CARP) which is to find the minimum-cost tour covering all required edges…

机器学习 · 计算机科学 2024-03-13 Runze Guo , Feng Xue , Anlong Ming , Nicu Sebe

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…

机器学习 · 计算机科学 2025-08-05 Daniela Thyssens , Tim Dernedde , Wilson Sentanoe , Lars Schmidt-Thieme

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…

机器学习 · 计算机科学 2025-10-31 Fu Luo , Xi Lin , Mengyuan Zhong , Fei Liu , Zhenkun Wang , Jianyong Sun , Qingfu Zhang

Heavy-Encoder-Light-Decoder (HELD) neural routing solvers have emerged as a promising paradigm due to their broad applicability across multiple vehicle routing problems (VRPs). However, they typically struggle with VRP variants with complex…

人工智能 · 计算机科学 2026-05-12 Canhong Yu , Changliang Zhou , Rongsheng Chen , Zhenkun Wang , Yu Zhou

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…

机器学习 · 计算机科学 2021-05-07 Kun Lei , Peng Guo , Yi Wang , Xiao Wu , Wenchao Zhao

This paper presents a novel graph reinforcement learning (RL) architecture to solve multi-robot task allocation (MRTA) problems that involve tasks with deadlines and workload, and robot constraints such as work capacity. While drawing…

多智能体系统 · 计算机科学 2022-05-09 Steve Paul , Payam Ghassemi , Souma Chowdhury

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…

人工智能 · 计算机科学 2026-05-26 Changliang Zhou , Xi Lin , Zhenkun Wang , Xialiang Tong , Mingxuan Yuan , Qingfu Zhang

Combinatorial optimization problems involving multiple agents are notoriously challenging due to their NP-hard nature and the necessity for effective agent coordination. Despite advancements in learning-based methods, existing approaches…

多智能体系统 · 计算机科学 2025-10-23 Federico Berto , Chuanbo Hua , Laurin Luttmann , Jiwoo Son , Junyoung Park , Kyuree Ahn , Changhyun Kwon , Lin Xie , Jinkyoo Park

Vehicle Routing Problem (VRP) is one of the most complex NP-hard combinatorial optimization problem in transportation and logistics that requires a dynamic solution approach. In this paper we present a new hybrid approach that combines the…

Recent researches show that machine learning has the potential to learn better heuristics than the one designed by human for solving combinatorial optimization problems. The deep neural network is used to characterize the input instance for…

机器学习 · 计算机科学 2020-02-11 Bo Peng , Jiahai Wang , Zizhen Zhang

Deep reinforcement learning (DRL)-based combinatorial optimization (CO) methods (i.e., DRL-NCO) have shown significant merit over the conventional CO solvers as DRL-NCO is capable of learning CO solvers less relying on problem-specific…

机器学习 · 计算机科学 2023-01-06 Minsu Kim , Junyoung Park , Jinkyoo Park

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…

数据结构与算法 · 计算机科学 2026-04-07 Yongyu Chen

The Capacitated Vehicle Routing Problem (CVRP) underpins modern last-mile logistics. Current Neural Combinatorial Optimization (NCO) methods construct CVRP solutions autoregressively, inheriting sequential decoding bottlenecks, sensitivity…

机器学习 · 计算机科学 2026-05-12 Samuel J. K. Chin , Maximilian Schiffer

This paper presents a framework to tackle constrained combinatorial optimization problems using deep Reinforcement Learning (RL). To this end, we extend the Neural Combinatorial Optimization (NCO) theory in order to deal with constraints in…

机器学习 · 计算机科学 2020-06-23 Ruben Solozabal , Josu Ceberio , Martin Takáč

Learning-based methods have become increasingly popular for solving vehicle routing problems due to their near-optimal performance and fast inference speed. Among them, the combination of deep reinforcement learning and graph representation…

机器学习 · 计算机科学 2024-05-22 Zhenwei Wang , Ruibin Bai , Fazlullah Khan , Ender Ozcan , Tiehua Zhang

Reinforcement learning has recently shown promise in learning quality solutions in many combinatorial optimization problems. In particular, the attention-based encoder-decoder models show high effectiveness on various routing problems,…

最优化与控制 · 数学 2022-12-06 Aigerim Bogyrbayeva , Taehyun Yoon , Hanbum Ko , Sungbin Lim , Hyokun Yun , Changhyun Kwon

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,…

机器学习 · 计算机科学 2022-03-08 Jingwen Li , Yining Ma , Ruize Gao , Zhiguang Cao , Andrew Lim , Wen Song , Jie Zhang

Recently, Transformer has become a prevailing deep architecture for solving vehicle routing problems (VRPs). However, it is less effective in learning improvement models for VRP because its positional encoding (PE) method is not suitable in…

机器学习 · 计算机科学 2022-12-02 Yining Ma , Jingwen Li , Zhiguang Cao , Wen Song , Le Zhang , Zhenghua Chen , Jing Tang

Traditional solvers for tackling combinatorial optimization (CO) problems are usually designed by human experts. Recently, there has been a surge of interest in utilizing deep learning, especially deep reinforcement learning, to…

神经与进化计算 · 计算机科学 2023-04-13 Shengcai Liu , Yu Zhang , Ke Tang , Xin Yao

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…

机器学习 · 计算机科学 2025-11-20 Le Tung Giang , Vu Hoang Viet , Nguyen Xuan Tung , Trinh Van Chien , Won-Joo Hwang