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We introduce a new class of hybrid preconditioners for solving parametric linear systems of equations. The proposed preconditioners are constructed by hybridizing the deep operator network, namely DeepONet, with standard iterative methods.…

Numerical Analysis · Mathematics 2024-01-11 Alena Kopaničáková , George Em Karniadakis

Conflict-Free Vehicle Routing Problems (CF-VRPs) arise in manufacturing, transportation and logistics facilities where Automated Guided Vehicles (AGVs) are utilized to move loads. Unlike \textit{Vehicle Routing Problems} arising in…

Optimization and Control · Mathematics 2024-06-28 Tommaso Adamo , Gianpaolo Ghiani , Emanuela Guerriero

Vehicle routing problems (VRPs) form a class of combinatorial problems with wide practical applications. While previous heuristic or learning-based works achieve decent solutions on small problem instances of up to 100 cities, their…

Machine Learning · Computer Science 2021-10-29 Sirui Li , Zhongxia Yan , Cathy Wu

The vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver goods to a fixed number of customers with…

Quantum Physics · Physics 2025-05-08 Nishikanta Mohanty , Bikash K. Behera , Christopher Ferrie

Existing neural heuristics often train a deep architecture from scratch for each specific vehicle routing problem (VRP), ignoring the transferable knowledge across different VRP variants. This paper proposes the cross-problem learning to…

Artificial Intelligence · Computer Science 2024-06-19 Zhuoyi Lin , Yaoxin Wu , Bangjian Zhou , Zhiguang Cao , Wen Song , Yingqian Zhang , Senthilnath Jayavelu

This study proposes a hybrid deep-learning-metaheuristic framework with a bi-level architecture for road network design problems (NDPs). We train a graph neural network (GNN) to approximate the solution of the user equilibrium (UE) traffic…

Neural and Evolutionary Computing · Computer Science 2023-12-12 Bahman Madadi , Goncalo Homem de Almeida Correia

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…

Artificial Intelligence · Computer Science 2025-12-23 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux

A rich vehicle routing problem is considered, allowing multiple trips of heterogeneous vehicles stationed at geographically distributed vehicle depots having access to different modes of transportation. The problem arises from the…

Optimization and Control · Mathematics 2025-09-18 Santanu Banerjee , Goutam Sen , Siddhartha Mukhopadhyay

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…

Artificial Intelligence · Computer Science 2025-08-11 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux

The dynamic vehicle routing problem with time windows (DVRPTW) is a generalization of the classical VRPTW to an online setting, where customer data arrives in batches and real-time routing solutions are required. In this paper we adapt the…

Neural and Evolutionary Computing · Computer Science 2023-07-27 Mohammed Ghannam , Ambros Gleixner

Generative flow networks (GFlowNets) are a method for learning a stochastic policy for generating compositional objects, such as graphs or strings, from a given unnormalized density by sequences of actions, where many possible action…

Machine Learning · Computer Science 2023-10-05 Nikolay Malkin , Moksh Jain , Emmanuel Bengio , Chen Sun , Yoshua Bengio

The deployment of deep neural networks in real-world applications is mostly restricted by their high inference costs. Extensive efforts have been made to improve the accuracy with expert-designed or algorithm-searched architectures.…

Machine Learning · Computer Science 2020-11-10 Shaofeng Cai , Yao Shu , Wei Wang , Beng Chin Ooi

Dynamic routing occurs when customers are not known in advance, e.g. for real-time routing. Two heuristics are proposed that solve the balanced dynamic multiple travelling salesmen problem (BD-mTSP). These heuristics represent operational…

Optimization and Control · Mathematics 2021-08-24 Wolfgang Garn

Previous geographic routing schemes in Delay/Disruption Tolerant Networks (DTNs) only consider the homogeneous scenario where nodal mobility is identical. Motivated by this gap, we turn to design a DTN based geographic routing scheme in…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-05-05 Yue Cao , Kaimin Wei , Geyong Min , Jian Weng , Xin Yang , Zhili Sun

Quantum computing (QC) is expected to solve incredibly difficult problems, including finding optimal solutions to combinatorial optimization problems. However, to date, QC alone is still far to demonstrate this capability except on…

Emerging Technologies · Computer Science 2025-12-19 James B. Holliday , Eneko Osaba , Khoa Luu

Traditional reinforcement learning often struggles to generate diverse, high-reward solutions, especially in domains like drug design and black-box function optimization. Markov Chain Monte Carlo (MCMC) methods provide an alternative method…

Machine Learning · Computer Science 2024-10-02 Siyi He

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

In response to carbon-neutral policies in developed countries, electric vehicles route optimization has gained importance for logistics companies. With the increasing focus on customer expectations and the shift towards more…

Machine Learning · Computer Science 2024-07-03 Arash Mozhdehi , Mahdi Mohammadizadeh , Xin Wang

Deep learning-based methods are growing prominence for planning purposes. In this paper, we present a hybrid planner that combines a graph machine learning model and an optimal solver based on branch and bound tree search for path-planning…

Artificial Intelligence · Computer Science 2022-04-05 Kevin Osanlou , Andrei Bursuc , Christophe Guettier , Tristan Cazenave , Eric Jacopin

Recent advancements in Neural Combinatorial Optimization (NCO) have shown promise in solving routing problems like the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) without handcrafted designs. Research in…

Machine Learning · Computer Science 2025-02-25 Ke Li , Fei Liu , Zhengkun Wang , Qingfu Zhang
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