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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 Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that has been of great interest for decades for both, science and industry. The CVRP is a variant of the vehicle routing problem characterized by capacity…

Visual navigation is a fundamental problem in embodied AI, yet practical deployments demand long-horizon planning capabilities to address multi-objective tasks. A major bottleneck is data scarcity: policies learned from limited data often…

Robotics · Computer Science 2025-10-22 Yiyuan Pan , Yunzhe Xu , Zhe Liu , Hesheng Wang

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…

Machine Learning · Computer Science 2024-12-16 Federico Julian Camerota Verdù , Lorenzo Castelli , Luca Bortolussi

In this paper, we propose a new dataset of Capacitated Vehicle Routing Problem instances which are up to two orders of magnitude larger than those in the currently used benchmarks. Despite these sizes might not have an immediate application…

Discrete Mathematics · Computer Science 2023-06-27 Luca Accorsi , Daniele Vigo

In this research, we propose an iterative learning hybrid optimization solver developed to strengthen the performance of metaheuristic algorithms in solving the Capacitated Vehicle Routing Problem (CVRP). The iterative hybrid mechanism…

Artificial Intelligence · Computer Science 2025-08-13 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux , Daniele Vigo

A key challenge in solving a combinatorial optimization problem is how to guide the agent (i.e., solver) to efficiently explore the enormous search space. Conventional approaches often rely on enumeration (e.g., exhaustive, random, or tabu…

Artificial Intelligence · Computer Science 2020-08-11 Xingwen Zhang , Shuang Yang

Reinforcement Learning (RL) in partially observable environments poses significant challenges due to the complexity of learning under uncertainty. While additional information, such as that available in simulations, can enhance training,…

Machine Learning · Computer Science 2026-03-16 Yueheng Li , Guangming Xie , Zongqing Lu

With the rise of e-commerce and increasing customer requirements, logistics service providers face a new complexity in their daily planning, mainly due to efficiently handling same day deliveries. Existing multi-stage stochastic…

Optimization and Control · Mathematics 2023-04-04 Léo Baty , Kai Jungel , Patrick S. Klein , Axel Parmentier , Maximilian Schiffer

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…

Machine Learning · Computer Science 2021-10-26 Runzhong Wang , Zhigang Hua , Gan Liu , Jiayi Zhang , Junchi Yan , Feng Qi , Shuang Yang , Jun Zhou , Xiaokang Yang

The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of…

Machine Learning · Statistics 2019-02-08 Wouter Kool , Herke van Hoof , Max Welling

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…

Heavy goods vehicles are vital backbones of the supply chain delivery system but also contribute significantly to carbon emissions with only 60% loading efficiency in the United Kingdom. Collaborative vehicle routing has been proposed as a…

Machine Learning · Computer Science 2024-06-12 Stefan Schoepf , Stephen Mak , Julian Senoner , Liming Xu , Netland Torbjörn , Alexandra Brintrup

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

This paper provides a systematic overview of machine learning methods applied to solve NP-hard Vehicle Routing Problems (VRPs). Recently, there has been a great interest from both machine learning and operations research communities to…

Machine Learning · Computer Science 2022-05-06 Aigerim Bogyrbayeva , Meraryslan Meraliyev , Taukekhan Mustakhov , Bissenbay Dauletbayev

This work presents a distributed algorithm for resolving cooperative multi-vehicle conflicts in highly constrained spaces. By formulating the conflict resolution problem as a Multi-Agent Reinforcement Learning (RL) problem, we can train a…

Robotics · Computer Science 2023-02-06 Xu Shen , Francesco Borrelli

Vehicle Routing Problems (VRP) are an extension of the Traveling Salesperson Problem and are a fundamental NP-hard challenge in combinatorial optimization. Solving VRP in real-time at large scale has become critical in numerous…

Machine Learning · Computer Science 2025-09-23 Ido Greenberg , Piotr Sielski , Hugo Linsenmaier , Rajesh Gandham , Shie Mannor , Alex Fender , Gal Chechik , Eli Meirom

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

The ability to plan into the future while utilizing only raw high-dimensional observations, such as images, can provide autonomous agents with broad capabilities. Visual model-based reinforcement learning (RL) methods that plan future…

Machine Learning · Computer Science 2021-08-10 Oleh Rybkin , Chuning Zhu , Anusha Nagabandi , Kostas Daniilidis , Igor Mordatch , Sergey Levine

Large language models~(LLMs) are trained on heterogeneous multilingual corpora, yet existing policy optimization methods often implicitly restrict each training question to a single response language or rely on a fixed dominant language for…

Computation and Language · Computer Science 2026-05-26 Geyang Guo , Hiromi Wakaki , Yuki Mitsufuji , Alan Ritter , Wei Xu
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