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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

Learning how to automatically solve optimization problems has the potential to provide the next big leap in optimization technology. The performance of automatically learned heuristics on routing problems has been steadily improving in…

Artificial Intelligence · Computer Science 2020-12-01 André Hottung , Kevin Tierney

The Heterogeneous Fleet Vehicle Routing Problem (HFVRP) is an important variant of the classical Capacitated Vehicle Routing Problem (CVRP) that aims to find routes that minimize the total traveling cost of a heterogeneous fleet of…

Optimization and Control · Mathematics 2021-11-29 Vinícius R. Máximo , Jean-François Cordeau , Mariá C. V. Nascimento

A recent study on the classical Capacitated Vehicle Routing Problem (CVRP) introduced an adaptive version of the widely used Iterated Local Search (ILS) paradigm, hybridized with a path-relinking strategy (PR). The solution method, called…

Optimization and Control · Mathematics 2025-07-22 Vinícius R. Máximo , Jean-François Cordeau , Mariá C. V. Nascimento

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 Capacitated Vehicle Routing Problem (CVRP) is a fundamental NP-hard problem in logistics. Augmented Lagrangian Methods (ALM) for solving CVRP performance depends heavily on well-tuned penalty parameters. In this paper, we propose a…

Physics and Society · Physics 2025-09-22 Monit Sharma , Hoong Chuin Lau

Designing high-performing metaheuristics for NP-hard combinatorial optimization problems, such as the Vehicle Routing Problem (VRP), remains a significant challenge, often requiring extensive domain expertise and manual tuning. Recent…

Neural and Evolutionary Computing · Computer Science 2026-04-10 Manuj Malik , Jianan Zhou , Shashank Reddy Chirra , Zhiguang Cao

While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing approaches typically formulate AHD around constructive priority rules or parameterized local search guidance, thereby restricting…

Artificial Intelligence · Computer Science 2026-02-10 Baoyun Zhao , He Wang , Liang Zeng

Real-world Vehicle Routing Problems (VRPs) are characterized by a variety of practical constraints, making manual solver design both knowledge-intensive and time-consuming. Although there is increasing interest in automating the design of…

Artificial Intelligence · Computer Science 2025-05-20 Kai Li , Fei Liu , Zhenkun Wang , Xialiang Tong , Xiongwei Han , Mingxuan Yuan , Qingfu Zhang

Solving NP-hard combinatorial optimization problems (COPs) (e.g., traveling salesman problems (TSPs) and capacitated vehicle routing problems (CVRPs)) in practice traditionally involves handcrafting heuristics or specifying a search space…

Machine Learning · Computer Science 2025-05-27 Nguyen Thach , Aida Riahifar , Nathan Huynh , Hau Chan

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

Designing high-performing heuristics for vehicle routing problems (VRPs) is a complex task that requires both intuition and deep domain knowledge. Large language model (LLM)-based code generation has recently shown promise across many…

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,…

Machine Learning · Computer Science 2022-03-08 Jingwen Li , Yining Ma , Ruize Gao , Zhiguang Cao , Andrew Lim , Wen Song , Jie Zhang

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

We investigate a structural decomposition for the capacitated vehicle routing problem (CVRP) based on vehicle-to-customer "assignment" and visits "sequencing" decision variables. We show that an heuristic search focused on assignment…

Optimization and Control · Mathematics 2018-03-19 Túlio A. M. Toffolo , Thibaut Vidal , Tony Wauters

Capacitated vehicle routing problem (CVRP) is being one of the most common optimization problems in our days, considering the wide usage of routing algorithms in multiple fields such as transportation domain, food delivery, network routing,…

Artificial Intelligence · Computer Science 2021-12-28 Hassan Moussa

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

Solving large-scale CVRP (LSCVRP) with hundreds to thousands of nodes remains difficult for even state-of-the-art solvers. Divide-and-conquer can scale by decomposing the instance into size-reduced subproblems, but designing decomposition…

Artificial Intelligence · Computer Science 2026-05-06 Tong Guo , Caishun Chen , Yew Soon Ong

The Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) is a classic NP-hard combinatorial optimization problem widely applied in logistics distribution and transportation management. Its complexity stems from the constraints of…

Machine Learning · Computer Science 2025-07-22 Linjiang Cao , Maonan Wang , Xi Xiong

We investigate the capacitated vehicle routing problem (CVRP) under a robotics context, where a vehicle with limited payload must complete delivery (or pickup) tasks to serve a set of geographically distributed customers with varying…

Robotics · Computer Science 2021-07-27 Kai Gao , Jingjin Yu
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