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The Split algorithm is an essential building block of route-first cluster-second heuristics and modern genetic algorithms for vehicle routing problems. The algorithm is used to partition a solution, represented as a giant tour without…

Data Structures and Algorithms · Computer Science 2018-05-08 Thibaut Vidal

The Clustered Vehicle Routing Problem (CluVRP) is a variant of the Capacitated Vehicle Routing Problem in which customers are grouped into clusters. Each cluster has to be visited once, and a vehicle entering a cluster cannot leave it until…

Artificial Intelligence · Computer Science 2014-04-29 Thibaut Vidal , Maria Battarra , Anand Subramanian , Güneş Erdoǧan

This paper deals with the Pollution-Routing Problem (PRP), a Vehicle Routing Problem (VRP) with environmental considerations, recently introduced in the literature by [Bektas and Laporte (2011), Transport. Res. B-Meth. 45 (8), 1232-1250].…

Data Structures and Algorithms · Computer Science 2014-04-22 Raphael Kramer , Anand Subramanian , Thibaut Vidal , Lucídio dos Anjos Formiga Cabral

We consider the multi-vehicle one-to-one pickup and delivery problem with split loads, a NP-hard problem linked with a variety of applications for bulk product transportation, bike-sharing systems and inventory re-balancing. This problem is…

Recent studies in maritime logistics have introduced a general ship routing problem and a benchmark suite based on real shipping segments, considering pickups and deliveries, cargo selection, ship-dependent starting locations, travel times…

Data Structures and Algorithms · Computer Science 2019-12-18 Gabriel Homsi , Rafael Martinelli , Thibaut Vidal , Kjetil Fagerholt

We consider a family of Rich Vehicle Routing Problems (RVRP) which have the particularity to combine a heterogeneous fleet with other attributes, such as backhauls, multiple depots, split deliveries, site dependency, open routes, duration…

Optimization and Control · Mathematics 2018-03-07 Puca Huachi Vaz Penna , Anand Subramanian , Luiz Satoru Ochi , Thibaut Vidal , Christian Prins

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

Shortest path (SP) computation is the building block for many location-based services, and achieving high throughput SP query processing with real-time response is crucial for those services. However, existing solutions can hardly handle…

Databases · Computer Science 2025-02-18 Xinjie Zhou , Mengxuan Zhang , Lei Li , Xiaofang Zhou

Hybridizing machine learning techniques with metaheuristics has attracted significant attention in recent years. Many attempts employ supervised or reinforcement learning to support the decision-making of heuristic methods. However, in some…

Machine Learning · Computer Science 2026-02-25 Bruna C. B. Charytitsch , Mariá C. V. Nascimento

This is a comprehensive review of the Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic and its hybridization with Path Relinking (PR) over the past two decades. GRASP with PR has become a widely adopted approach for solving…

Optimization and Control · Mathematics 2023-12-21 Manuel Laguna , Rafael Martí , Anna Martinez-Gavara , Sergio Perez-Peló , Mauricio G. C. Resende

We consider several Vehicle Routing Problems (VRP) with profits, which seek to select a subset of customers, each one being associated with a profit, and to design service itineraries. When the sum of profits is maximized under distance…

Data Structures and Algorithms · Computer Science 2014-07-29 Thibaut Vidal , Nelson Maculan , Puca Huachi Vaz Penna , Luis Satoru Ochi

We study shortest-path routing in large weighted, undirected graphs, where expanding search frontiers raise time and memory costs for exact solvers. We propose \emph{SPHERE}, a query-aware partitioning heuristic that adaptively splits the…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-03-16 Robert Fabian Lindermann , Paul-Niklas Ken Kandora , Simon Caspar Zeller , Adrian Asmund Fessler , Steffen Rebennack

Several metaheuristics use decomposition and pruning strategies to solve large-scale instances of the vehicle routing problem (VRP). Those complexity reduction techniques often rely on simple, problem-specific rules. However, the growth in…

Artificial Intelligence · Computer Science 2025-09-18 Christoph Kerscher , Stefan Minner

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

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

This work is motivated by solving a problem faced by big agriculture companies implementing precision agriculture operations for spraying practices using two types of operators, namely a tender tanker and a fleet of sprayers. We model this…

Optimization and Control · Mathematics 2023-12-18 Faisal Alkaabneh

For many kinds of vehicle routing problems (VRPs), a popular heuristic approach involves constructing a Traveling Salesman Problem (TSP) solution, referred to as a long tour, then partitioning segments of the solution into routes for…

Data Structures and Algorithms · Computer Science 2026-01-27 Ethan Gibbons , Mario Ventresca , Beatrice M. Ombuki-Berman

Traveling Salesman Problem (TSP) is a classic NP-hard problem that has garnered significant attention from both academia and industry. While neural-based methods have shown promise for solving TSPs, they still face challenges in scaling to…

Machine Learning · Computer Science 2026-04-16 Tongkai Lu , Shuai Ma , Chongyang Tao

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

Facility location problems (FLPs) are a family of optimisation problems with significant social impact. This class of problems has been the subject of study since the 1960s, with classical approaches including the Weber problem and the…

Optimization and Control · Mathematics 2026-02-26 Sergio Salazar , Abraham Duarte , Mauricio G. C. Resende , J. Manuel Colmenar
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