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Combinatorial optimization serves as an essential part in many modern industrial applications. A great number of the problems are offline setting due to safety and/or cost issues. While simulation-based approaches appear difficult to…

机器学习 · 计算机科学 2020-07-21 Wenpeng Wei , Toshiko Aizono

Self-improvement has emerged as a state-of-the-art paradigm in Neural Combinatorial Optimization (NCO), where models iteratively refine their policies by generating and imitating high-quality solutions. Despite strong empirical performance,…

机器学习 · 计算机科学 2025-10-15 Laurin Luttmann , Lin Xie

Many relevant problems in industrial settings result in NP-hard optimization problems, such as the Capacitated Vehicle Routing Problem (CVRP) or its reduced variant, the Travelling Salesperson Problem (TSP). Even with today's most powerful…

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

We introduce Limited Rollout Beam Search (LRBS), a beam search strategy for deep reinforcement learning (DRL) based combinatorial optimization improvement heuristics. Utilizing pre-trained models on the Euclidean Traveling Salesperson…

机器学习 · 计算机科学 2024-12-16 Federico Julian Camerota Verdù , Lorenzo Castelli , Luca Bortolussi

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…

机器学习 · 计算机科学 2024-05-07 Chengrui Gao , Haopu Shang , Ke Xue , Dong Li , Chao Qian

This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the…

分布式、并行与集群计算 · 计算机科学 2018-01-16 Keyou You , Roberto Tempo , Pei Xie

Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require…

机器学习 · 计算机科学 2025-05-27 Arman Mielke , Uwe Bauknecht , Thilo Strauss , Mathias Niepert

Neural combinatorial optimization (NCO) has achieved remarkable performance, yet its learned model representations and decision rationale remain a black box. This impedes both academic research and practical deployment, since researchers…

机器学习 · 计算机科学 2025-10-28 Zhiqin Zhang , Yining Ma , Zhiguang Cao , Hoong Chuin Lau

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…

人工智能 · 计算机科学 2025-08-11 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux

We propose a feature-based guidance mechanism to enhance metaheuristic algorithms for solving the Capacitated Vehicle Routing Problem (CVRP). This mechanism leverages an Explainable AI (XAI) model to identify features that correlate with…

人工智能 · 计算机科学 2025-12-23 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux

In recent years new deep learning approaches to solve combinatorial optimization problems, in particular NP-hard Vehicle Routing Problems (VRP), have been proposed. The most impactful of these methods are sequential neural construction…

机器学习 · 计算机科学 2023-10-02 Jonas K. Falkner , Lars Schmidt-Thieme

Combinatorial optimization problem (COP) over graphs is a fundamental challenge in optimization. Reinforcement learning (RL) has recently emerged as a new framework to tackle these problems and has demonstrated promising results. However,…

机器学习 · 计算机科学 2022-09-05 Fan Yao , Renqin Cai , Hongning Wang

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…

机器学习 · 计算机科学 2025-03-14 Zhenwei Wang , Ruibin Bai , Tiehua Zhang

Many problems in real life can be converted to combinatorial optimization problems (COPs) on graphs, that is to find a best node state configuration or a network structure such that the designed objective function is optimized under some…

机器学习 · 计算机科学 2019-09-17 Jing Liu , Fei Gao , Jiang Zhang

The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in…

Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the…

机器学习 · 计算机科学 2021-10-26 Runzhong Wang , Zhigang Hua , Gan Liu , Jiayi Zhang , Junchi Yan , Feng Qi , Shuang Yang , Jun Zhou , Xiaokang Yang

Solving NP-hard/complete combinatorial problems with neural networks is a challenging research area that aims to surpass classical approximate algorithms. The long-term objective is to outperform hand-designed heuristics for…

神经与进化计算 · 计算机科学 2024-02-14 Dobrik Georgiev , Danilo Numeroso , Davide Bacciu , Pietro Liò

Recent advances in Neural Combinatorial Optimization (NCO) methods have significantly improved the capability of neural solvers to handle synthetic routing instances. Nonetheless, existing neural solvers typically struggle to generalize…

人工智能 · 计算机科学 2026-01-30 Jianghan Zhu , Yaoxin Wu , Zhuoyi Lin , Zhengyuan Zhang , Haiyan Yin , Zhiguang Cao , Senthilnath Jayavelu , Xiaoli Li

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…

机器学习 · 计算机科学 2022-10-04 Sahil Manchanda , Sofia Michel , Darko Drakulic , Jean-Marc Andreoli