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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 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…

Machine Learning · Computer Science 2025-11-20 Le Tung Giang , Vu Hoang Viet , Nguyen Xuan Tung , Trinh Van Chien , Won-Joo Hwang

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…

We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral…

Optimization and Control · Mathematics 2021-08-16 Martin Neuenhofen , Eric Kerrigan

Many traditional algorithms for solving combinatorial optimization problems involve using hand-crafted heuristics that sequentially construct a solution. Such heuristics are designed by domain experts and may often be suboptimal due to the…

Machine Learning · Computer Science 2020-12-25 Nina Mazyavkina , Sergey Sviridov , Sergei Ivanov , Evgeny Burnaev

We present a numerical method for the minimization of objectives that are augmented with large quadratic penalties of overdetermined inconsistent equality constraints. Such objectives arise from quadratic integral penalty methods for the…

Optimization and Control · Mathematics 2020-09-15 Martin P. Neuenhofen , Eric C. Kerrigan

This paper presents a Quantum Reinforcement Learning (QRL) solution to the dynamic portfolio optimization problem based on Variational Quantum Circuits. The implemented QRL approaches are quantum analogues of the classical…

Machine Learning · Computer Science 2026-01-29 Vincent Gurgul , Ying Chen , Stefan Lessmann

We present an end-to-end framework for solving the Vehicle Routing Problem (VRP) using reinforcement learning. In this approach, we train a single model that finds near-optimal solutions for problem instances sampled from a given…

Artificial Intelligence · Computer Science 2018-05-23 Mohammadreza Nazari , Afshin Oroojlooy , Lawrence V. Snyder , Martin Takáč

We address the problem of coordination and control of Connected and Automated Vehicles (CAVs) in the presence of imperfect observations in mixed traffic environment. A commonly used approach is learning-based decision-making, such as…

Robotics · Computer Science 2024-09-25 Zhili Zhang , H M Sabbir Ahmad , Ehsan Sabouni , Yanchao Sun , Furong Huang , Wenchao Li , Fei Miao

Deep reinforcement learning (DRL) has been used to learn effective heuristics for solving complex combinatorial optimisation problem via policy networks and have demonstrated promising performance. Existing works have focused on solving…

Machine Learning · Computer Science 2020-12-25 Nasrin Sultana , Jeffrey Chan , A. K. Qin , Tabinda Sarwar

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

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

Neural Combinatorial Optimization (NCO) has emerged as a promising learning-based paradigm for addressing Vehicle Routing Problems (VRPs) by minimizing the need for extensive manual engineering. While existing NCO methods, trained on…

Machine Learning · Computer Science 2025-11-24 Yuanyao Chen , Rongsheng Chen , Fu Luo , Zhenkun Wang

Complex real-life routing challenges can be modeled as variations of well-known combinatorial optimization problems. These routing problems have long been studied and are difficult to solve at scale. The particular setting may also make…

Neural and Evolutionary Computing · Computer Science 2020-09-23 Marijn van Knippenberg , Mike Holenderski , Vlado Menkovski

We present a novel framework that combines machine learning with mixed-integer optimization to solve the Capacitated Location-Routing Problem (CLRP). The CLRP is a classical NP-hard problem that integrates strategic facility location with…

Optimization and Control · Mathematics 2026-02-24 Waquar Kaleem , Doyoung Lee , Changhyun Kwon , Anirudh Subramanyam

Metaheuristics are widely employed to solve hard optimization problems, like vehicle routing problems (VRP), for which exact solution methods are impractical. In particular, local search-based metaheuristics have been successfully applied…

Optimization and Control · Mathematics 2022-04-12 Vinícius R. Máximo , Mariá C. V. Nascimento

While large language models (LLMs) are increasingly used as automated heuristic designers for vehicle routing problems (VRPs), current state-of-the-art methods predominantly rely on prompting massive, general-purpose models like GPT-4. This…

Machine Learning · Computer Science 2025-10-14 Rongjie Zhu , Cong Zhang , Zhiguang Cao

This paper develops an inherently parallelised, fast, approximate learning-based solution to the generic class of Capacitated Vehicle Routing Problems with Time Windows and Dynamic Routing (CVRP-TWDR). Considering vehicles in a fleet as…

Artificial Intelligence · Computer Science 2021-04-15 Nazneen N Sultana , Vinita Baniwal , Ansuma Basumatary , Piyush Mittal , Supratim Ghosh , Harshad Khadilkar

Complex vehicle routing problems (VRPs) remain a fundamental challenge, demanding substantial expert effort for intent interpretation and algorithm design. While large language models (LLMs) offer a promising path toward automation, current…

Artificial Intelligence · Computer Science 2026-02-17 Ni Zhang , Zhiguang Cao , Jianan Zhou , Cong Zhang , Yew-Soon Ong

Recent advance in classical reinforcement learning (RL) and quantum computation (QC) points to a promising direction of performing RL on a quantum computer. However, potential applications in quantum RL are limited by the number of qubits…

Quantum Physics · Physics 2022-03-07 Samuel Yen-Chi Chen , Chih-Min Huang , Chia-Wei Hsing , Hsi-Sheng Goan , Ying-Jer Kao