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The capacitated vehicle routing problem (CVRP) involves distributing (identical) items from a depot to a set of demand locations, using a single capacitated vehicle. We study a generalization of this problem to the setting of multiple…

Data Structures and Algorithms · Computer Science 2010-12-09 Inge Li Gortz , Marco Molinaro , Viswanath Nagarajan , R. Ravi

SNCF, the French public train company, is experimenting to develop new types of transportation services by tackling vehicle routing problems. While many deep learning models have been used to tackle efficiently vehicle routing problems, it…

Artificial Intelligence · Computer Science 2023-01-11 Baptiste Rabecq , Rémy Chevrier

In the last decades, the classical Vehicle Routing Problem (VRP), i.e., assigning a set of orders to vehicles and planning their routes has been intensively researched. As only the assignment of order to vehicles and their routes is already…

Neural and Evolutionary Computing · Computer Science 2022-01-13 Veronika Lesch , Maximilian König , Samuel Kounev , Anthony Stein , Christian Krupitzer

Unlike traditional homogeneous routing problems, the Heterogeneous Fleet Vehicle Routing Problem (HFVRP) involves heterogeneous fixed costs, variable travel costs, and capacity constraints, rendering solution quality highly sensitive to…

Machine Learning · Computer Science 2026-04-08 Shihong Huang , Shengjie Wang , Lei Gao , Hong Ma , Zhanluo Zhang , Feng Zhang , Weihua Zhou

The Vehicle Routing Problem (VRP) is the combinatorial optimization problem of designing routes for vehicles to visit customers in such a fashion that a cost function, typically the number of vehicles, or the total travelled distance is…

Artificial Intelligence · Computer Science 2021-07-01 Sabino Francesco Roselli , Martin Fabian , Knut Åkesson

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 a fixed number of customers with optimal…

Quantum Physics · Physics 2022-01-14 Nishikanta Mohanty , Bikash K. Behera

Existing GFlowNet-based methods for vehicle routing problems (VRPs) typically employ Trajectory Balance (TB) to achieve global optimization but often neglect important aspects of local optimization. While Detailed Balance (DB) addresses…

Artificial Intelligence · Computer Science 2025-10-07 Ni Zhang , Zhiguang Cao

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…

Machine Learning · Computer Science 2023-10-02 Jonas K. Falkner , Lars Schmidt-Thieme

We study the structure of solutions to linear programming formulations for the traveling salesperson problem (TSP). We perform a detailed analysis of the support of the subtour elimination linear programming relaxation, which leads to…

Data Structures and Algorithms · Computer Science 2015-03-27 Matthias Mnich , Tobias Mömke

The Orienteering Problem with Time Windows (OPTW) is a combinatorial optimization problem where the goal is to maximize the total score collected from different visited locations. The application of neural network models to combinatorial…

Machine Learning · Computer Science 2021-07-01 Ricardo Gama , Hugo L. Fernandes

The Capacitated Vehicle Routing Problem (CVRP) underpins modern last-mile logistics. Current Neural Combinatorial Optimization (NCO) methods construct CVRP solutions autoregressively, inheriting sequential decoding bottlenecks, sensitivity…

Machine Learning · Computer Science 2026-05-12 Samuel J. K. Chin , Maximilian Schiffer

The capacitated vehicle routing problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. In this problem, we are given a depot and a set of customers, each with a demand, embedded in a metric space. The…

Data Structures and Algorithms · Computer Science 2026-01-30 Jingyang Zhao , Mingyu Xiao

The Profiled Vehicle Routing Problem (PVRP) extends the classical VRP by incorporating vehicle-client-specific preferences and constraints, reflecting real-world requirements such as zone restrictions and service-level preferences. While…

Machine Learning · Computer Science 2025-08-26 Chuanbo Hua , Federico Berto , Zhikai Zhao , Jiwoo Son , Changhyun Kwon , Jinkyoo Park

We present an end-to-end framework for the Assignment Problem with multiple tasks mapped to a group of workers, using reinforcement learning while preserving many constraints. Tasks and workers have time constraints and there is a cost…

Artificial Intelligence · Computer Science 2021-06-08 Sharmin Pathan , Vyom Shrivastava

There have been recent efforts for incorporating Graph Neural Network models for learning full-stack solvers for constraint satisfaction problems (CSP) and particularly Boolean satisfiability (SAT). Despite the unique representational power…

Machine Learning · Computer Science 2019-03-06 Saeed Amizadeh , Sergiy Matusevych , Markus Weimer

Branch-and-bound is a systematic enumerative method for combinatorial optimization, where the performance highly relies on the variable selection strategy. State-of-the-art handcrafted heuristic strategies suffer from relatively slow…

Machine Learning · Computer Science 2022-06-15 Tianyu Zhang , Amin Banitalebi-Dehkordi , Yong Zhang

Reinforcement learning has been applied in operation research and has shown promise in solving large combinatorial optimization problems. However, existing works focus on developing neural network architectures for certain problems. These…

Optimization and Control · Mathematics 2023-03-24 Ching Pui Wan , Tung Li , Jason Min Wang

This paper presents a new method for solving an orienteering problem (OP) by breaking it down into two parts: a knapsack problem (KP) and a traveling salesman problem (TSP). A KP solver is responsible for picking nodes, while a TSP solver…

Neural and Evolutionary Computing · Computer Science 2023-02-23 Wei Liu , Tao Zhang , Rui Wang , Kaiwen Li , Wenhua Li , Kang Yang

Much combinatorial optimisation problems constitute a non-polynomial (NP) hard optimisation problem, i.e., they can not be solved in polynomial time. One such problem is finding the shortest route between two nodes on a graph.…

Machine Learning · Statistics 2017-09-08 Alessandro Bay , Biswa Sengupta

The vehicle routing problem is a well known class of NP-hard combinatorial optimisation problems in literature. Traditional solution methods involve either carefully designed heuristics, or time-consuming metaheuristics. Recent work in…

Artificial Intelligence · Computer Science 2022-06-15 Harshad Khadilkar