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The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem with wide-ranging applications in logistics, routing, and intelligent systems. Due to its factorial complexity, solving large-scale instances…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-27 Rabab Alkhalifa , Fatima Alkhomayes , Boushra Almazroua , Dana Alhaidan , Maryam Alothman , Jumana Almuhaidib

This paper deals with generating of an optimized route for multiple Vehicle routing Problems (mVRP). We used a methodology of clustering the given cities depending upon the number of vehicles and each cluster is allotted to a vehicle. k-…

Distributed, Parallel, and Cluster Computing · Computer Science 2010-01-26 R. Nallusamy , K. Duraiswamy , R. Dhanalaksmi , P. Parthiban

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

Many real-world scenarios involve solving bi-level optimization problems in which there is an outer discrete optimization problem, and an inner problem involving expensive or black-box computation. This arises in space-time dependent…

Optimization and Control · Mathematics 2024-07-12 Isaac Rudich , Quentin Cappart , Manuel López-Ibáñez , Michael Römer , Louis-Martin Rousseau

We present a trajectory optimization algorithm for the traveling salesman problem (TSP) in graphs of convex sets (GCS). Our framework uses an augmented graph of convex sets to encode the TSP specification and solve it exactly as a shortest…

Systems and Control · Electrical Eng. & Systems 2026-04-09 Gael Luna , Tyler Summers

In this paper we present distributed and adaptive algorithms for motion coordination of a group of m autonomous vehicles. The vehicles operate in a convex environment with bounded velocity and must service demands whose time of arrival,…

Robotics · Computer Science 2016-11-17 Marco Pavone , Emilio Frazzoli , Francesco Bullo

We consider the NP-hard 2-period balanced travelling salesman problem. In this problem the salesman needs to visit a set of customers in two time periods. A given subset of the customers has to be visited in both periods while the rest of…

Optimization and Control · Mathematics 2022-03-14 Vladimir Deineko , Bettina Klinz , Mengke Wang

Nowadays, the transport goods problem occupies an important place in the economic life of modern societies. The pickup and delivery problem with time windows (PDPTW) is one of the problems which a large part of the research was interested.…

Neural and Evolutionary Computing · Computer Science 2010-10-06 Imen Harbaoui Dridi , Ryan Kammarti , Mekki Ksouri , Pierre Borne

The capacitated Vehicle Routing Problem with structured Time Windows (cVRPsTW) is concerned with finding optimal tours for vehicles with given capacity constraints to deliver goods to customers within assigned time windows. In our problem…

Optimization and Control · Mathematics 2019-10-10 Christoph Hertrich , Philipp Hungerländer , Christian Truden

The number of optimization techniques in the combinatorial domain is large and diversified. Nevertheless, there is still a lack of real benchmarks to validate optimization algorithms. In this work we introduce VRPBench, a tool to create…

Artificial Intelligence · Computer Science 2016-10-19 Guilherme A. Zeni , Mauro Menzori , P. S. Martins , Luis A. A. Meira

The increasing adoption of Electric Vehicles (EVs) for service and goods distribution operations has led to the emergence of Electric Vehicle Routing Problems (EVRPs), a class of vehicle routing problems addressing the unique challenges…

Optimization and Control · Mathematics 2025-12-04 Andrea Spinelli , Dario Bezzi , Ola Jabali , Francesca Maggioni

Most neural methods for Vehicle Routing Problems (VRPs) are limited to Euclidean settings or simple graphs. In this work, we instead consider multigraphs, where parallel edges represent distinct travel options with varying trade-offs (e.g.,…

Machine Learning · Computer Science 2026-05-08 Filip Rydin , Morteza Haghir Chehreghani , Balázs Kulcsár

Multi-depot vehicle routing problems (MDVRPs) are prevalent in a variety of practical applications. However, they are computationally challenging to solve due to their inherent complexity. This paper proposes an effective hybrid algorithm…

Robotics · Computer Science 2026-05-08 Zhenyu Lei , Jin-Kao Hao

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

We study the Travelling Salesperson (TSP) and the Steiner Tree problem (STP) in graphs of low highway dimension. This graph parameter was introduced by Abraham et al. [SODA 2010] as a model for transportation networks, on which TSP and STP…

Data Structures and Algorithms · Computer Science 2019-07-15 Yann Disser , Andreas Emil Feldmann , Max Klimm , Jochen Konemann

In this paper, we study the Maximum-Profit Routing Problem with Variable Supply (MPRP-VS). This is a more general version of the Maximum-Profit Public Transportation Route Planning Problem, or simply Maximum-Profit Routing Problem (MPRP),…

Data Structures and Algorithms · Computer Science 2020-07-21 Bogdan Armaselu

We consider the Single School Routing Problem (SSRP) where students from a single school are picked up by a fleet of school buses, subject to a set of constraints. The constraints that are typically imposed for school buses are bus…

Optimization and Control · Mathematics 2022-10-03 Xiaotong Guo , Samitha Samaranayake

Neural solvers based on the divide-and-conquer approach for Vehicle Routing Problems (VRPs) in general, and capacitated VRP (CVRP) in particular, integrates the global partition of an instance with local constructions for each subproblem to…

Machine Learning · Computer Science 2025-02-13 Yuxin Pan , Ruohong Liu , Yize Chen , Zhiguang Cao , Fangzhen Lin

In dynamic vehicle routing problems (DVRPs), some part of the information is revealed or changed on the fly, and the decision maker has the opportunity to re-plan the vehicle routes during their execution, reflecting on the changes.…

Optimization and Control · Mathematics 2025-05-13 Markó Horváth , Tímea Tamási

In this paper we present a new approach to tackle complex routing problems with an improved state representation that utilizes the model complexity better than previous methods. We enable this by training from temporal differences.…

Machine Learning · Computer Science 2021-04-27 Ahmad Bdeir , Simon Boeder , Tim Dernedde , Kirill Tkachuk , Jonas K. Falkner , Lars Schmidt-Thieme