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This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city…

Artificial Intelligence · Computer Science 2017-01-16 Irwan Bello , Hieu Pham , Quoc V. Le , Mohammad Norouzi , Samy Bengio

The application of learning based methods to vehicle routing problems has emerged as a pivotal area of research in combinatorial optimization. These problems are characterized by vast solution spaces and intricate constraints, making…

Machine Learning · Computer Science 2025-03-14 Zhenwei Wang , Ruibin Bai , Tiehua Zhang

The recent end-to-end neural solvers have shown promise for small-scale routing problems but suffered from limited real-time scaling-up performance. This paper proposes GLOP (Global and Local Optimization Policies), a unified hierarchical…

Artificial Intelligence · Computer Science 2024-07-23 Haoran Ye , Jiarui Wang , Helan Liang , Zhiguang Cao , Yong Li , Fanzhang Li

Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational…

Machine Learning · Computer Science 2026-03-25 Fateme Memar , Tao Zhe , Dongjie Wang

Exploring machine learning techniques for addressing vehicle routing problems has attracted considerable research attention. To achieve decent and efficient solutions, existing deep models for vehicle routing problems are typically trained…

Machine Learning · Computer Science 2025-10-21 Jingwen Li , Zhiguang Cao , Yaoxin Wu , Tang Liu

Neural routing solvers (NRSs) that leverage deep learning to tackle vehicle routing problems have demonstrated notable potential for practical applications. By learning implicit heuristic rules from data, NRSs replace the handcrafted…

Optimization and Control · Mathematics 2026-03-17 Yunpeng Ba , Xi Lin , Changliang Zhou , Ruihao Zheng , Zhenkun Wang , Xinyan Liang , Zhichao Lu , Jianyong Sun , Yuhua Qian , Qingfu Zhang

In recent years, there has been notable interest in investigating combinatorial optimization (CO) problems by neural-based framework. An emerging strategy to tackle these challenging problems involves the adoption of graph neural networks…

Machine Learning · Computer Science 2024-06-11 Yang Liu , Chuan Zhou , Peng Zhang , Shirui Pan , Zhao Li , Hongyang Chen

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

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

The Vehicle Routing Problem is about optimizing the routes of vehicles to meet the needs of customers at specific locations. The route graph consists of depots on several levels and customer positions. Several optimization methods have been…

Artificial Intelligence · Computer Science 2024-09-18 László Kovács , Ali Jlidi

We introduce a combinatorial optimization-enriched machine learning pipeline and a novel learning paradigm to solve inventory routing problems with stochastic demand and dynamic inventory updates. After each inventory update, our approach…

Optimization and Control · Mathematics 2024-02-08 Toni Greif , Louis Bouvier , Christoph M. Flath , Axel Parmentier , Sonja U. K. Rohmer , Thibaut Vidal

Recent advances in learnable evolutionary algorithms have demonstrated the importance of leveraging population distribution information and historical evolutionary trajectories. While significant progress has been made in continuous…

Neural and Evolutionary Computing · Computer Science 2024-12-10 Jiaxiang Huang , Licheng Jiao

Existing neural constructive solvers for routing problems have predominantly employed transformer architectures, conceptualizing the route construction as a set-to-sequence learning task. However, their efficacy has primarily been…

Machine Learning · Computer Science 2024-08-08 Yong Liang Goh , Zhiguang Cao , Yining Ma , Yanfei Dong , Mohammed Haroon Dupty , Wee Sun Lee

In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…

Neural and Evolutionary Computing · Computer Science 2017-03-23 Shumeet Baluja

Long-horizon combinatorial optimization problems (COPs), such as the Flexible Job-Shop Scheduling Problem (FJSP), often involve complex, interdependent decisions over extended time frames, posing significant challenges for existing solvers.…

Optimization and Control · Mathematics 2025-02-25 Sirui Li , Wenbin Ouyang , Yining Ma , Cathy Wu

Column Generation (CG) is a popular method dedicated to enhancing computational efficiency in large scale Combinatorial Optimization (CO) problems. It reduces the number of decision variables in a problem by solving a pricing problem. For…

Machine Learning · Computer Science 2025-04-18 Abdo Abouelrous , Laurens Bliek , Adriana F. Gabor , Yaoxin Wu , Yingqian Zhang

Recurrent neural networks (RNNs) are a powerful approach for time series prediction. However, their performance is strongly affected by their architecture and hyperparameter settings. The architecture optimization of RNNs is a…

Machine Learning · Computer Science 2021-04-26 Andrés Camero , Hao Wang , Enrique Alba , Thomas Bäck

Recurrent neural networks (RNNs) have recently achieved remarkable successes in a number of applications. However, the huge sizes and computational burden of these models make it difficult for their deployment on edge devices. A practically…

Machine Learning · Computer Science 2019-12-10 Liangjian Wen , Xuanyang Zhang , Haoli Bai , Zenglin Xu

Many real-world problems can be reduced to combinatorial optimization on a graph, where the subset or ordering of vertices that maximize some objective function must be found. With such tasks often NP-hard and analytically intractable,…

Machine Learning · Computer Science 2021-03-22 Thomas D. Barrett , William R. Clements , Jakob N. Foerster , A. I. Lvovsky

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
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