Showing papers on "Vehicle routing problem published in 2019"

Attention, learn to solve routing problems!

Abstract: The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of training. We contribute in both directions: we propose a model based on attention layers with benefits over the Pointer Network and we show how to train this model using REINFORCE with a simple baseline based on a deterministic greedy rollout, which we find is more efficient than using a value function. We significantly improve over recent learned heuristics for the Travelling Salesman Problem (TSP), getting close to optimal results for problems up to 100 nodes. With the same hyperparameters, we learn strong heuristics for two variants of the Vehicle Routing Problem (VRP), the Orienteering Problem (OP) and (a stochastic variant of) the Prize Collecting TSP (PCTSP), outperforming a wide range of baselines and getting results close to highly optimized and specialized algorithms.

Vehicle routing problem with drones

Abstract: The vehicle routing problem with drones (VRPD) is an extension of the classic capacitated vehicle routing problem, where not only trucks but drones are used to deliver parcels to customers. One distinctive feature of the VRPD is that a drone may travel with a truck, take off from its stop to serve customers, and land at a service hub to travel with another truck as long as the flying range and loading capacity limitations are satisfied. Routing trucks and drones in an integrated manner makes the problem much more challenging and different from classical vehicle routing literature. We propose a mixed integer programming model, and develop a branch-and-price algorithm. Extensive experiments are conducted on the instances randomly generated in a practical setting, and the results demonstrate the good computational performance of the proposed algorithm. We also conduct sensitivity analysis on a key factor that may affect the total cost of a solution.

An adaptive large neighborhood search metaheuristic for the vehicle routing problem with drones

Abstract: Unmanned Aerial Vehicles, commonly known as drones, have attained considerable interest in recent years due to the potential of revolutionizing transport and logistics. Amazon were among the first to introduce the idea of using drones to deliver goods, followed by several other distribution companies working on similar services. The Traveling Salesman Problem, frequently used for planning last-mile delivery operations, can easily be modified to incorporate drones, resulting in a routing problem involving both the truck and aircraft. Introduced by Murray and Chu (2015) , the Flying Sidekick Traveling Salesman Problem considers a drone and truck collaborating. The drone can be launched and recovered at certain visits on the truck route, making it possible for both vehicles to deliver goods to customers in parallel. This generalization considerably decreases the operational cost of the routes, by reducing the total fuel consumption for the truck, as customers on the routes can be serviced by drones without covering additional miles for the trucks, and hence increase productivity. In this paper a mathematical model is formulated, defining a problem similar to the Flying Sidekick Traveling Salesman Problem, but for the capacitated multiple-truck case with time limit constraints and minimizing cost as objective function. The corresponding problem is denoted the Vehicle Routing Problem with Drones. Due to the difficulty of solving large instances to optimality, an Adaptive Large Neighborhood Search metaheuristic is proposed. Finally, extensive computational experiments are carried out. The tests investigate, among other things, how beneficial the inclusion of the drone-delivery option is compared to delivering all items using exclusively trucks. Moreover, a detailed sensitivity analysis is performed on several drone-parameters of interest.

Learning to Perform Local Rewriting for Combinatorial Optimization

Abstract: Search-based methods for hard combinatorial optimization are often guided by heuristics. Tuning heuristics in various conditions and situations is often time-consuming. In this paper, we propose NeuRewriter that learns a policy to pick heuristics and rewrite the local components of the current solution to iteratively improve it until convergence. The policy factorizes into a region-picking and a rule-picking component, each parameterized by a neural network trained with actor-critic methods in reinforcement learning. NeuRewriter captures the general structure of combinatorial problems and shows strong performance in three versatile tasks: expression simplification, online job scheduling and vehicle routing problems. NeuRewriter outperforms the expression simplification component in Z3; outperforms DeepRM and Google OR-tools in online job scheduling; and outperforms recent neural baselines and Google OR-tools in vehicle routing problems.

Online Vehicle Routing With Neural Combinatorial Optimization and Deep Reinforcement Learning

Abstract: Online vehicle routing is an important task of the modern transportation service provider. Contributed by the ever-increasing real-time demand on the transportation system, especially small-parcel last-mile delivery requests, vehicle route generation is becoming more computationally complex than before. The existing routing algorithms are mostly based on mathematical programming, which requires huge computation time in city-size transportation networks. To develop routes with minimal time, in this paper, we propose a novel deep reinforcement learning-based neural combinatorial optimization strategy. Specifically, we transform the online routing problem to a vehicle tour generation problem, and propose a structural graph embedded pointer network to develop these tours iteratively. Furthermore, since constructing supervised training data for the neural network is impractical due to the high computation complexity, we propose a deep reinforcement learning mechanism with an unsupervised auxiliary network to train the model parameters. A multisampling scheme is also devised to further improve the system performance. Since the parameter training process is offline, the proposed strategy can achieve a superior online route generation speed. To assess the proposed strategy, we conduct comprehensive case studies with a real-world transportation network. The simulation results show that the proposed strategy can significantly outperform conventional strategies with limited computation time in both static and dynamic logistic systems. In addition, the influence of control parameters on the system performance is investigated.

A Survey on the Electric Vehicle Routing Problem: Variants and Solution Approaches

Abstract: In order to ensure high-quality and on-time delivery in logistic distribution processes, it is necessary to efficiently manage the delivery fleet. Nowadays, due to the new policies and regulations related to greenhouse gas emission in the transport sector, logistic companies are paying higher penalties for each emission gram of /km. With electric vehicle market penetration, many companies are evaluating the integration of electric vehicles in their fleet, as they do not have local greenhouse gas emissions, produce minimal noise, and are independent of the fluctuating oil price. The well-researched vehicle routing problem (VRP) is extended to the electric vehicle routing problem (E-VRP), which takes into account specific characteristics of electric vehicles. In this paper, a literature review on recent developments regarding the E-VRP is presented. The challenges that emerged with the integration of electric vehicles in the delivery processes are described, together with electric vehicle characteristics and recent energy consumption models. Several variants of the E-VRP and related problems are observed. To cope with the new routing challenges in E-VRP, efficient VRP heuristics and metaheuristics had to be adapted. An overview of the state-of-the-art procedures for solving the E-VRP and related problems is presented.

A concise guide to existing and emerging vehicle routing problem variants.

Abstract: Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem variants with different attributes. In this article, we provide a concise overview of existing and emerging problem variants. Models are typically refined along three lines: considering more relevant objectives and performance metrics, integrating vehicle routing evaluations with other tactical decisions, and capturing fine-grained yet essential aspects of modern supply chains. We organize the main problem attributes within this structured framework. We discuss recent research directions and pinpoint current shortcomings, recent successes, and emerging challenges.

Exact Branch-Price-and-Cut Algorithms for Vehicle Routing

Abstract: Vehicle routing problems (VRPs) are among the most studied problems in operations research. Nowadays, the leading exact algorithms for solving many classes of VRPs are branch-price-and-cut algorith...

The electric vehicle routing problem with energy consumption uncertainty

Abstract: Compared with conventional freight vehicles, electric freight vehicles create less local pollution and are thus generally perceived as a more sustainable means of goods distribution. In urban areas, such vehicles must often perform the entirety of their delivery routes without recharging. However, their energy consumption is subject to a fair amount of uncertainty, which is due to exogenous factors such as the weather and road conditions, endogenous factors such as driver behaviour, and several energy consumption parameters that are difficult to measure precisely. Hence we propose a robust optimization framework to take into account these energy consumption uncertainties in the context of an electric vehicle routing problem. The objective is to determine minimum cost delivery routes capable of providing strong guarantees that a given vehicle will not run out of charge during its route. We formulate the problem as a robust mixed integer linear program and solve small instances to optimality using robust optimization techniques. Furthermore, we develop a two-phase heuristic method based on large neighbourhood search to solve larger instances of the problem, and we conduct several numerical tests to assess the quality of the methodology. The computational experiments illustrate the trade-off between cost and risk, and demonstrate the influence of several parameters on best found solutions. Furthermore, our heuristic identifies 42 new best solutions when tested on instances of the closely related robust capacitated vehicle routing problem.

A Branch-and-Bound Approach to the Traveling Salesman Problem with a Drone

Abstract: The Traveling Salesman Problem with a Drone (TSP-D) is a hybrid truck and drone model of delivery, in which the drone rides on the truck and launches from the truck to deliver packages. Our approac...

A Hybrid Genetic Algorithm, Simulated Annealing and Tabu Search Heuristic for Vehicle Routing Problems with Time Windows

Abstract: The Vehicle Routing Problem with Time Windows (VRPTW) involves servicing a set of customers, with earliest and latest time deadlines, with varying demands using capacitated vehicles with limited travel times. The objective of the problem is to service all customers while minimizing the number of vehicles and travel distance without violating the capacity and travel time of the vehicles and customer time constraints. In this paper we describe a λ-interchange mechanism that moves customers between routes to generate neighborhood solutions for the VRPTW. The λ-interchange neighborhood is searched using Simulated Annealing and Tabu Search strategies. The initial solutions to the VRPTW are obtained using the Push-Forward Insertion heuristic and a Genetic Algorithm based sectoring heuristic. The hybrid combination of the implemented heuristics, collectively known as the GenSAT system, were used to solve 60 problems from the literature with customer sizes varying from 100 to 417 customers. The computational results of GenSAT obtained new best solutions for 40 test problems. For the remaining 20 test problems, 11 solutions obtained by the GenSAT system equal previously known best solutions. The average performance of GenSAT is significantly better than known competing heuristics. For known optimal solutions to the VRPTW problems, the GenSAT system obtained the optimal number of vehicles.

Energy consumption estimation integrated into the Electric Vehicle Routing Problem

Abstract: When planning routes for fleets of electric commercial vehicles, it is necessary to precisely predict the energy required to drive and plan for charging whenever needed, in order to manage their driving range limitations. Although there are several energy estimation models available in the literature, so far integration with Vehicle Routing Problems has been limited and without demonstrated accuracy. This paper introduces the Two-stage Electric Vehicle Routing Problem (2sEVRP) that incorporates improved energy consumption estimation by considering detailed topography and speed profiles. First, a method to calculate energy cost coefficients for the road network is outlined. Since the driving cycle is unknown, the model generates an approximation based on a linear function of mass, as the latter is only determined while routing. These coefficients embed information about topography, speed, powertrain efficiency and the effect of acceleration and braking at traffic lights and intersections. Secondly, an integrated two-stage approach is described, which finds the best paths between pairs of destinations and then finds the best routes including battery and time-window constraints. Energy consumption is used as objective function including payload and auxiliary systems. The road cost coefficients are aggregated to generate the path cost coefficients that are used in the routing problem. In this way it is possible to get a proper approximation of the complete driving cycle for the routes and accurate energy consumption estimation. Lastly, numerical experiments are shown based on the road network from Gothenburg-Sweden. Energy estimation is compared with real consumption data from an all-electric bus from a public transport route and with high-fidelity vehicle simulations. Routing experiments focus on trucks for urban distribution of goods. The results indicate that time and energy estimations are significantly more precise than existing methods. Consequently the planned routes are expected to be feasible in terms of energy demand and that charging stops are properly included when necessary.

A matheuristic for the vehicle routing problem with drones and its variants

Abstract: In this work, we are interested in studying the Vehicle Routing Problem with Drones (VRPD). Given a fleet of trucks, where each truck carries a given number of drones, the objective consists in designing feasible routes and drone operations such that all customers are served and minimal makespan is achieved. We formulate the VRPD as a Mixed Integer Linear Program (MILP), which can be solved by any standard MILP solver. Moreover, with the aim of improving the performance of solvers, we introduce several sets of valid inequalities (VIEQ). Due to limited performance of the solvers in addressing large instances, we propose a matheuristic approach that effectively exploits the problem structure of the VRPD. Integral to this approach, we propose the Drone Assignment and Scheduling Problem (DASP) that, given an existing routing of trucks, looks for an optimal assignment and schedule of drones such that the makespan is minimized. In this context, we propose two MILP formulations for the DASP. In order to evaluate the performance of a state-of-the-art solver in tackling the MILP formulation of the VRPD, the benefit of the proposed VIEQs, and the performance of the matheuristic, we carried out extensive computational experiments. According to the numerical results, the use of drones can significantly reduce the makespan and the proposed VIEQ as well as the matheuristic approach have a significant contribution in solving the VRPD effectively.

A Discrete and Improved Bat Algorithm for solving a medical goods distribution problem with pharmacological waste collection

Abstract: The work presented in this paper is focused on the resolution of a real-world drugs distribution problem with pharmacological waste collection. With the aim of properly meeting all the real-world restrictions that comprise this complex problem, we have modeled it as a multi-attribute or rich vehicle routing problem (RVRP). The problem has been modeled as a Clustered Vehicle Routing Problem with Pickups and Deliveries, Asymmetric Variable Costs, Forbidden Roads and Cost Constraints. To the best of authors knowledge, this is the first time that such a RVRP problem is tackled in the literature. For this reason, a benchmark composed of 24 datasets, from 60 to 1000 customers, has also been designed. For the developing of this benchmark, we have used real geographical positions located in Bizkaia, Spain. Furthermore, for the proper dealing of the proposed RVRP, we have developed a Discrete and Improved Bat Algorithm (DaIBA). The main feature of this adaptation is the use of the well-known Hamming Distance to calculate the differences between the bats. An effective improvement has been also contemplated for the proposed DaIBA, which consists on the existence of two different neighborhood structures, which are explored depending on the bat's distance regarding the best individual of the swarm. For the experimentation, we have compared the performance of our presented DaIBA with three additional approaches: an evolutionary algorithm, an evolutionary simulated annealing and a firefly algorithm. Additionally, with the intention of obtaining rigorous conclusions, two different statistical tests have been conducted: the Friedman's non-parametric test and the Holm's post-hoc test. Furthermore, an additional experimentation has been performed in terms of convergence. Finally, the obtained outcomes conclude that the proposed DaIBA is a promising technique for addressing the designed problem.

Vehicle Routing and Location Routing with Intermediate Stops: A Review

Abstract: This paper reviews the literature on vehicle routing problems and location routing problems with intermediate stops. We classify publications into different categories from both an application-base...

Learning Improvement Heuristics for Solving Routing Problems

Abstract: Recent studies in using deep learning to solve routing problems focus on construction heuristics, the solutions of which are still far from optimality. Improvement heuristics have great potential to narrow this gap by iteratively refining a solution. However, classic improvement heuristics are all guided by hand-crafted rules which may limit their performance. In this paper, we propose a deep reinforcement learning framework to learn the improvement heuristics for routing problems. We design a self-attention based deep architecture as the policy network to guide the selection of next solution. We apply our method to two important routing problems, i.e. travelling salesman problem (TSP) and capacitated vehicle routing problem (CVRP). Experiments show that our method outperforms state-of-the-art deep learning based approaches. The learned policies are more effective than the traditional hand-crafted ones, and can be further enhanced by simple diversifying strategies. Moreover, the policies generalize well to different problem sizes, initial solutions and even real-world dataset.

A robust optimization for a home health care routing and scheduling problem with consideration of uncertain travel and service times

Abstract: In today’s competitive environment, one of the most critical objectives for Home Health Care (HHC) companies is to meet the demand of patients in a timely fashion. According to the feedback from HHC companies, caregivers have to deal with some uncertainties when carrying out a given schedule to visit their patients. However, a majority of the previous work only considers the deterministic models which ignore the uncertainties, and solutions obtained by these deterministic models are usually less robust in case of any possible changes in practical situations. Inspired by this point, in this work, we formulate a model for an HHC Routing and Scheduling Problem with taking into account uncertain travel and service times, from the perspective of Robust Optimization (RO). Specifically, the non-deterministic variables are defined based on the theory of budget uncertainty, and then the arrival time of each caregiver is rewritten as a complicated recursive function. After that, Gurobi Solver, Simulated Annealing, Tabu Search, and Variable Neighborhood Search are adapted to solve the model respectively. Finally, a series of experiments have been performed to validate the proposed models and algorithms. Experimental results from Monte Carlo simulation highlight the strength of considering uncertainties when modeling the problem. Additional, the influences of other characters in instances, like the width of time-window, distributed location have also been empirically analyzed. Finally, the comparison performed between the solutions obtained by the stochastic model and the RO model also demonstrates the advantage of the RO model. This work provides a valuable framework for HHC companies to make a robust schedule when arranging the caregivers.

A Survey of Recent Extended Variants of the Traveling Salesman and Vehicle Routing Problems for Unmanned Aerial Vehicles

Abstract: The use of Unmanned Aerial Vehicles (UAVs) is rapidly growing in popularity. Initially introduced for military purposes, over the past few years, UAVs and related technologies have successfully transitioned to a whole new range of civilian applications such as delivery, logistics, surveillance, entertainment, and so forth. They have opened new possibilities such as allowing operation in otherwise difficult or hazardous areas, for instance. For all applications, one foremost concern is the selection of the paths and trajectories of UAVs, and at the same time, UAVs control comes with many challenges, as they have limited energy, limited load capacity and are vulnerable to difficult weather conditions. Generally, efficiently operating a drone can be mathematically formalized as a path optimization problem under some constraints. This shares some commonalities with similar problems that have been extensively studied in the context of urban vehicles and it is only natural that the recent literature has extended the latter to fit aerial vehicle constraints. The knowledge of such problems, their formulation, the resolution methods proposed—through the variants induced specifically by UAVs features—are of interest for practitioners for any UAV application. Hence, in this study, we propose a review of existing literature devoted to such UAV path optimization problems, focusing specifically on the sub-class of problems that consider the mobility on a macroscopic scale. These are related to the two existing general classic ones—the Traveling Salesman Problem and the Vehicle Routing Problem. We analyze the recent literature that adapted the problems to the UAV context, provide an extensive classification and taxonomy of their problems and their formulation and also give a synthetic overview of the resolution techniques, performance metrics and obtained numerical results.

A Two-Stage Multiobjective Evolutionary Algorithm for Multiobjective Multidepot Vehicle Routing Problem With Time Windows

Abstract: This paper proposes a multiobjective multidepot vehicle routing problem with time windows and designs some real-world test instances. It develops a two-stage multiobjective evolutionary algorithm (TS-MOEA) for dealing with the problem. Stage I of our proposed algorithm focuses on finding extreme solutions, and forms a coarse Pareto front, while stage II extends the found extreme solutions for approximating the whole Pareto front. The two-stage strategy provides a new method to balance convergence and diversity. Moreover, a hybrid neighborhood structure is designed for solution improvement. Experimental result shows that TS-MOEA significantly outperforms two other representative algorithms.