VRPDiv: A Divide and Conquer Framework for Large Vehicle Routing Problems

2021 ◽  
Vol 7 (4) ◽  
pp. 1-41
Author(s):  
Radu Mariescu-Istodor ◽  
Alexandru Cristian ◽  
Mihai Negrea ◽  
Peiwei Cao
Keyword(s):  
Vehicle Routing ◽  
Real World ◽  
Time Windows ◽  
Clustering Algorithms ◽  
Scale Up ◽  
Divide And Conquer ◽  
Clustering Methods ◽  
Online Service ◽  
Routing Problem ◽  
Public Datasets

The Vehicle Routing Problem (VRP) is an NP hard problem where we need to optimize itineraries for agents to visit multiple targets. When considering real-world travel (road-network topology, speed limits and traffic), modern VRP solvers can only process small instances with a few hundred targets. We propose a framework (VRPDiv) that can scale any solver to support larger VRP instances with up to ten thousand targets (10k) by dividing them into smaller clusters. VRPDiv supports the multiple VRP scenarios and contains a pool of clustering algorithms from which it chooses the ideal one depending on properties of the instance. VRPDiv assigns agents based on cluster demand and targets compatibility (i.e. realizable time-windows and capacity limitations). We incorporate the framework into the Bing Maps Multi-Itinerary Optimization (MIO) 1 online service. This architecture allows MIO to scale up from solving instances with a few hundred to over 10k targets in under 10 minutes. We evaluate our framework on public datasets and publish a new dataset ourselves, as large enough instances supporting real-world travel were impossible to find. We investigate multiple clustering methods and show that choosing the correct one is critical with differences of up to 60% in quality. We compare with relevant baselines and report a 40% improvement in target allocation and a 9.8% improvement in itinerary durations. We compare with existing scores and report an average delta of 10%, with lower values (<5%) in instances with low workload (few targets per agent), which are acceptable for an online service.

scholarly journals Solving Practical Vehicle Routing Problem with Time Windows Using Metaheuristic Algorithms

1970 ◽  
Vol 24 (4) ◽  
pp. 343-351 ◽  
Author(s):  
Filip Taner ◽  
Ante Galić ◽  
Tonči Carić
Keyword(s):  
Vehicle Routing ◽  
Real World ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Iterated Local Search ◽  
Metaheuristic Algorithms ◽  
Benchmark Problems ◽  
Routing Problem ◽  
Constructive Heuristics ◽  
Initial Feasible Solution

This paper addresses the Vehicle Routing Problem with Time Windows (VRPTW) and shows that implementing algorithms for solving various instances of VRPs can significantly reduce transportation costs that occur during the delivery process. Two metaheuristic algorithms were developed for solving VRPTW: Simulated Annealing and Iterated Local Search. Both algorithms generate initial feasible solution using constructive heuristics and use operators and various strategies for an iterative improvement. The algorithms were tested on Solomon’s benchmark problems and real world vehicle routing problems with time windows. In total, 44 real world problems were optimized in the case study using described algorithms. Obtained results showed that the same distribution task can be accomplished with savings up to 40% in the total travelled distance and that manually constructed routes are very ineffective.

scholarly journals POPMUSIC for a real-world large-scale vehicle routing problem with time windows

2009 ◽  
Vol 60 (7) ◽  
pp. 934-943 ◽  
Author(s):  
A Ostertag ◽  
K F Doerner ◽  
R F Hartl ◽  
E D Taillard ◽  
P Waelti
Keyword(s):  
Vehicle Routing ◽  
Real World ◽  
Vehicle Routing Problem ◽  
Large Scale ◽  
Time Windows ◽  
Routing Problem

GVNS for a real-world Rich Vehicle Routing Problem with Time Windows

2015 ◽  
Vol 42 ◽  
pp. 45-56 ◽  
Author(s):  
Jesica de Armas ◽  
Belén Melián-Batista ◽  
José A. Moreno-Pérez ◽  
Julio Brito
Keyword(s):  
Vehicle Routing ◽  
Real World ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Routing Problem

scholarly journals Tackling the rich vehicle routing problem with nature-inspired algorithms

2022 ◽  
Author(s):  
Veronika Lesch ◽  
Maximilian König ◽  
Samuel Kounev ◽  
Anthony Stein ◽  
Christian Krupitzer
Keyword(s):  
Vehicle Routing ◽  
Real World ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Routing Problem ◽  
Real World Applications ◽  
Np Complete ◽  
The Rich ◽  
Nature Inspired Algorithms ◽  
Problem Instances

AbstractIn 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 an NP-complete problem, the application of these algorithms in practice often fails to take into account the constraints and restrictions that apply in real-world applications, the so called rich VRP (rVRP) and are limited to single aspects. In this work, we incorporate the main relevant real-world constraints and requirements. We propose a two-stage strategy and a Timeline algorithm for time windows and pause times, and apply a Genetic Algorithm (GA) and Ant Colony Optimization (ACO) individually to the problem to find optimal solutions. Our evaluation of eight different problem instances against four state-of-the-art algorithms shows that our approach handles all given constraints in a reasonable time.

scholarly journals A mixed integer programming model for a continuous move transportation problem with service constraints

2017 ◽  
Vol 7 (13) ◽  
Author(s):  
J. Fabián López
Keyword(s):  
Vehicle Routing ◽  
Real World ◽  
Large Scale ◽  
Programming Model ◽  
Time Windows ◽  
Mixed Integer ◽  
Pickup And Delivery ◽  
Np Hard ◽  
Routing Problem ◽  
Service Constraints

Key words: Genetic algorithms, logistics routing, metaheuristics, scheduling, time windowsAbstract. We consider a Pickup and Delivery Vehicle Routing Problem (PDP) commonly encountered in real-world logistics operations. The problem involves a set of practical complications that have received little attention in the vehicle routing literature. In this problem, there are multiple vehicle types available to cover a set of pickup and delivery requests, each of which has pickup time windows and delivery time windows. Transportation orders and vehicle types must satisfy a set of compatibility constraints that specify which orders cannot be covered by which vehicle types. In addition we include some dock servicecapacity constraints as is required on common real world operations. This problem requires to be attended on large scale instances (orders ≥ 500), (vehicles ≥ 150). As a generalization of the traveling salesman problem, clearly this problem is NP-hard. The exact algorithms are too slow for large scale instances. The PDP-TWDS is both a packing problem (assign order tovehicles), and a routing problem (find the best route for each vehicle). We propose to solve the problem in three stages. The first stage constructs initials solutions at aggregate level relaxing some constraints on the original problem. The other two stages imposes time windows and dock service constraints. Our results are favorable finding good quality solutions in relatively short computational times.Palabras claves. Algoritmos genéticos, logística de ruteo, metahurística, programación, ventana de horarioResumen. En la solución de problemas combinatorios, es importante evaluar el costobeneficio entre la obtención de soluciones de alta calidad en detrimento de los recursos computacionales requeridos. El problema planteado es para el ruteo de un vehículo con entrega y recolección de producto y con restricciones de ventana de horario. En la práctica, dicho problema requiere ser atendido con instancias de gran escala (nodos ≥100). Existe un fuerte porcentaje de ventanas de horario activas (≥90%) y con factores de amplitud ≥75%. El  problema es NP-hard y por tal motivo la aplicación de un método de solución exacta para resolverlo en la práctica, está limitado por el tiempo requerido para la actividad de ruteo. Se propone un algoritmo genético especializado, el cual ofrece soluciones de buena calidad (% de optimalidad aceptables) y en tiempos de ejecución computacional que hacen útil su aplicación en la práctica de la logística. Para comprobar la eficacia de la propuesta algorítmica se desarrolla un diseño experimental el cual hará uso de las soluciones óptimas obtenidas mediante un algoritmo de ramificación y corte sin límite de tiempo. Los resultados son favorables.

scholarly journals A hybrid ant colony algorithm based on multiple strategies for the vehicle routing problem with time windows

2021 ◽  
Author(s):  
Hongguang Wu ◽  
Yuelin Gao ◽  
Wanting Wang ◽  
Ziyu Zhang
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Ant Colony Algorithm ◽  
Time Window ◽  
Time Windows ◽  
Ant Colony ◽  
Routing Problem ◽  
Multiple Strategies ◽  
Hard Time ◽  
Mutation Operation

AbstractIn this paper, we propose a vehicle routing problem with time windows (TWVRP). In this problem, we consider a hard time constraint that the fleet can only serve customers within a specific time window. To solve this problem, a hybrid ant colony (HACO) algorithm is proposed based on ant colony algorithm and mutation operation. The HACO algorithm proposed has three innovations: the first is to update pheromones with a new method; the second is the introduction of adaptive parameters; and the third is to add the mutation operation. A famous Solomon instance is used to evaluate the performance of the proposed algorithm. Experimental results show that HACO algorithm is effective against solving the problem of vehicle routing with time windows. Besides, the proposed algorithm also has practical implications for vehicle routing problem and the results show that it is applicable and effective in practical problems.

scholarly journals The last-mile vehicle routing problem with delivery options

OR Spectrum ◽  
2021 ◽  
Author(s):  
Christian Tilk ◽  
Katharina Olkis ◽  
Stefan Irnich
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Resource Constraints ◽  
Time Window ◽  
Time Windows ◽  
Service Level ◽  
Optimal Solutions ◽  
Routing Problem ◽  
Common Location ◽  
Delivery Options

AbstractThe ongoing rise in e-commerce comes along with an increasing number of first-time delivery failures due to the absence of the customer at the delivery location. Failed deliveries result in rework which in turn has a large impact on the carriers’ delivery cost. In the classical vehicle routing problem (VRP) with time windows, each customer request has only one location and one time window describing where and when shipments need to be delivered. In contrast, we introduce and analyze the vehicle routing problem with delivery options (VRPDO), in which some requests can be shipped to alternative locations with possibly different time windows. Furthermore, customers may prefer some delivery options. The carrier must then select, for each request, one delivery option such that the carriers’ overall cost is minimized and a given service level regarding customer preferences is achieved. Moreover, when delivery options share a common location, e.g., a locker, capacities must be respected when assigning shipments. To solve the VRPDO exactly, we present a new branch-price-and-cut algorithm. The associated pricing subproblem is a shortest-path problem with resource constraints that we solve with a bidirectional labeling algorithm on an auxiliary network. We focus on the comparison of two alternative modeling approaches for the auxiliary network and present optimal solutions for instances with up to 100 delivery options. Moreover, we provide 17 new optimal solutions for the benchmark set for the VRP with roaming delivery locations.

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