Large-scale Vehicle Routing Problems Research Articles

An efficient heuristic for very large-scale vehicle routing problems with simultaneous pickup and delivery

The paper discusses two variants of the Capacitated Vehicle Routing Problem (CVRP), in which each customer to be visited can require both pickup and delivery, or only either pickup and delivery but not both. These problems are referred to, respectively, as the Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD) and as the Vehicle Routing Problem with Mixed Pickup and Delivery (VRPMPD). Both VRPSPD and VRPMPD are particularly relevant in practical logistics distribution scenarios, especially when dealing with a substantial number of pickup and delivery locations. The aim of this work is to provide an algorithm which extends, through a variety of specializations, the FILO framework, originally proposed and specifically designed for the CVRP. This variant, called FSPD, has been developed to accomplish two objectives: first, being competitive with the state-of-the-art algorithms for the VRPSPD and VRPMPD; second, efficiently solving new benchmark instances for these problems with a very large number of customers, while maintaining linear scalability of the computing time with respect to the problem size. The extensive computational study and detailed analysis of the algorithm components conducted in this paper demonstrate the successful achievement of both objectives.

Knowledge-driven ant colony optimization algorithm for vehicle routing problem in instant delivery peak period

Instant delivery is an important part of urban logistics distribution, which realizes point-to-point distribution between merchants and customers. During the peak period of orders, instant delivery is a large-scale variable NP-hard combinatorial optimization problem, which increases the difficulty and complexity of scheduling greatly. To solve the large-scale vehicle routing problem of instant delivery in peak periods, a knowledge-driven ant colony optimization (KDACO) algorithm is proposed in this paper. First, the knowledge base is established to guide evolutionary search, including the knowledge of order priority and the feature knowledge of feasible schemes. Second, the pheromone supplementation strategy is designed based on the knowledge of order priority, enhancing the guiding ability of the pheromone table. Third, the adaptive evolutionary operator is designed based on the feature knowledge of feasible schemes, improving the optimization efficiency of the algorithm. Finally, numerical experiments on extensive classical datasets show that the proposed KDACO can obtain superior performance to other state-of-the-art algorithms in the instant delivery peak period.

Multi-Agent Inspection Path Planning with Large-Scale Vehicle Routing Problem

A path planning problem involving multiple vehicles for a large and complex structure inspection is challenging owing to its high computational complexity. This occurs from the large and sparse nature of the inspection graph as it requires heavy computation for both preprocessing the graph and solving the problem. However, there have been fewer research efforts that focus on the computation inefficiency occurring from graph preprocessing, which is an important issue that needs to be addressed for practical application. This research proposes an algorithm that fuses a graph clustering algorithm with an ant colony system algorithm. It effectively reduces the computation required for preprocessing the graph and accelerates the vehicle routing problem (VRP) solving process by narrowing down a search space. A series of numerical experiments has shown that the proposed algorithm is capable of handling a large and sparsely connected graph VRP within a significantly reduced computation time. In addition, the algorithm yields a superior solution quality as compared to that of the conventional algorithm.

An adaptive ant colony algorithm for crowdsourcing multi-depot vehicle routing problem with time windows

Logistics distribution faces difficulties such as increasing delivery demands, demanding delivery time and lower delivery costs. However, the routing optimization for logistic distribution is not a simple vehicle routing problem (VRP). This study focuses on crowdsourcing multi-depot vehicle routing problem with time windows (MDVRPTW) problem, permitting one crowdsourcing driver to deliver multiple customers, which has not been covered yet. To quickly distribute many delivery tasks within a certain time, this paper proposes a two-stage MDVRPTW framework. The first stage is the division stage in which a k-means algorithm based on the elbow method is used to transform the multi-depot problem into several single-depot problems. Then a crowdsourcing VRPTW model is developed, which is a mixed-integer linear programming model. The second stage is the optimization stage, for which an adaptive ant colony (ADACO) algorithm is proposed to determine the most reasonable distribution routes for each distribution center. Solomons classic VRP data is then used to validate the models’ effectiveness, with the results confirming that the crowdsourcing MDVRPTW strategy could save 10.02% costs than traditional MDVRPTW strategy. By comparison, the ADACO algorithm could significantly improve the ACO’s weakness of falling into a local optimum, and would be more suitable for solving large-scale vehicle routing problems than the GUROBI solver.

Metaheuristics for a Large-Scale Vehicle Routing Problem of Same-Day Delivery in E-Commerce Logistics System

In this paper, we introduce a new variant of large-scale vehicle routing problem that arises in the goods distribution of city e-commerce logistics, the multi-depot vehicle routing problem with order split and allocation (MD-CVRP-OSA), which incorporates the issue of split and allocation of online orders into traditional VRP. A mathematical formulation is constructed for the MD-CVRP-OSA, and an efficient metaheuristics algorithm based on a variable neighborhood search (VNS) solution framework is designed to solve it. The proposed method is tested on a large family of instances, including real-world data collected from JD.com, and the effectiveness of the VNS algorithm and also the algorithm components are analyzed.

Solving Large Scale Vehicle Routing Problems with Hard Time Windows under Travel Time Uncertainty

Vehicle routing problems have been receiving more attention lately with more importance being given to last-mile and door deliveries by e-commerce players in logistics services, retail & consumer goods, etc. Many of these applications require solving routing problems with tens of thousands of customers with multiple objectives. This paper aims at solving very large-scale capacitated vehicle routing problems with hard delivery windows under travel time uncertainty. We attempt to build robust optimization model using route dependent uncertainty sets. The large-scale problems are solved using two-stage heuristic that comprises of a sweep algorithm and a very large-scale neighborhood search with the objectives of minimizing the number of routes and the total travel distance ensuring delivery windows are not violated. The experiments were carried out on real-life data sets with tens of thousands of customer orders focusing on quality and robustness of solutions, solution time, and scalability, thus providing key insights in solving larger problems for logistics industry.

Large-scale vehicle routing problem with massive precedence and cluster constraints

Large-scale vehicle routing problem with massive precedence and cluster constraints

Large-Scale Vehicle Routing Problem with Massive Precedence and Cluster Constraints

Large-Scale Vehicle Routing Problem with Massive Precedence and Cluster Constraints

Solving Large-Scale Vehicle Routing Problems with Unsplittable Demands via Limited Information

Solving Large-Scale Vehicle Routing Problems with Unsplittable Demands via Limited Information

A construction heuristic for finding an initial solution to a very large-scale capacitated vehicle routing problem

In this paper, a deterministic heuristic method is developed for obtaining an initial solution to an extremely large-scale capacitated vehicle routing problem (CVRP) having thousands of customers. The heuristic has three main objectives. First, it should be able to withstand the computational and memory problems normally associated with extremely large-scale CVRP. Secondly, the outputs should be reasonably accurate and should have a minimum number of vehicles. Finally, it should be able to produce the results within a short duration of time. The new method, based on the sweep algorithm, minimizes the number of vehicles by loading the vehicles nearly to their full capacity by skipping some of the customers as and when necessary. To minimize the total traveled distance, before the sweeping starts the customers are ordered based on both the polar angle and the distance of the customer from the depot. This method is tested on 10 sets of standard benchmark instances found in the literature. The results are compared with the results of the CW100 method by Arnold et al. [Comput. Oper. Res. 107 (2019) 32–42]. The results indicate that the new modified sweep algorithm produces an initial solution with a minimum number of vehicles and with reasonable accuracy. The deviation of the output from the best-known solution (BKS) is reasonable for all the test instances. When compared with the CW100 the modified sweep provides a better initial solution than CW100 whenever the capacity of the vehicle is more and the depot is located eccentrically. The heuristic does not face any memory problems normally associated with the solving of an extremely large-scale CVRP.

A responsive ant colony optimization for large-scale dynamic vehicle routing problems via pheromone diversity enhancement

Large-scale dynamic vehicle routing problem (LSDVRP) is exhibiting extensive application prospect with the rapid growth of online logistics, whereas a few approaches have been developed to address LSDVRPs. The difficulty in solving LSDVRPs lies in that it requires quick response and high adaptability to numerous newly appeared customers in LSDVRPs. To overcome this difficulty, in this paper, we propose a responsive ant colony optimization algorithm, termed as RACO, for efficiently addressing LSDVRPs. In the proposed RACO, a pheromone diversity enhancing method is suggested to generate diverse pheromone matrices for quickly responding to newly appeared customer requests in solving LSDVRPs. A pheromone ensemble technique is further designed to produce a high-quality initial population that well adapts to the new customer requests by making use of diverse pheromone matrices. Empirical results on a set of 12 LSDVRP test instances demonstrate the effectiveness of the suggested pheromone diversity enhancing method in quickly responding to newly appeared customer requests for solving LSDVRPs. Moreover, we investigate the computational cost and the traveling cost obtained by the proposed RACO to evaluate responsiveness and adaptability of the proposed RACO, respectively. Comparison with four state-of-the-art approaches to DVRPs validates the superiority of the proposed RACO in addressing LSDVRPs in terms of responsiveness and adaptability.

Case Article—Route Planning at an Animal Husbandry Department

The case provides an opportunity for undergraduate, graduate, and doctoral students to demonstrate a practical application of supply chain modeling in the area of livestock management for a group of rural communities in India. An animal husbandry department needs to ensure timely replenishment of liquid nitrogen to several livestock locations to preserve semen straws, which are frozen for artificial insemination. The department wishes to explore a possible route redesign for cost reduction. The description in the case, as well as the presented data, is based on a real project undertaken by the authors. The case enables students to conceptualize and design sample routes manually to meet the cost objective. However, the main objective is to make students understand and implement solution heuristics for large-scale vehicle routing problems. It also allows students to compare various designs trying not only possible vehicle capacities but also three solution heuristics. Nevertheless, students can also realize the importance of the spreadsheet as a decision support tool for evaluating several options by integrating the chosen heuristic. An important milestone of the case project was the implementation of our recommendations by the animal husbandry department.

Extremely Fast “Solution” to the Large-Scale and Very Large-Scale Vehicle Routing Problem

A solution to the vehicle routing problem (VRP) is presented that takes only quadratic space, <i>O(n²),</i> and quadratic time, <i>O(n²)</i>, if <i>n</i> is the number of stops on a route. The input is assumed to be a list of stops of length <i>n</i> in longitude, latitude format. The output is an origin-destination (OD) matrix of size <i>O(n²)</i>, which takes <i>O(n²)</i> time to build. The element <i>(i, j)</i> in the matrix is the approximate driving distance between stop <i>i</i> and stop <i>j</i> on the route. Each approximate driving distance takes constant or <I>O(1)</I> time to compute. (The approximate driving distance appears in previous work by the author, published in URISA GIS-Pro ‘19 and CalGIS 2020.) This OD matrix is well-suited for solving large-scale and very large-scale VRP problems, since computing approximate driving distances is lightning fast. For instance, using real-world data, it took less than one (1) second to produce a route with 5,156 stops. The OD matrix can be used with any exact or approximation algorithm to find a route, including the nearest-neighbor approximation algorithm: Starting at an origin, the next closest stop is visited repeatedly, ending at the destination once all stops have been visited. Determining the next stop to visit takes linear or <i>O(n)</i> time to compute, and this is done <i>O(n)</i> times. This solution to the VRP is a polynomial-time, <i>O(n²)</i>, approximation; it is not exact, but is extremely fast.

A VNS solution and objectives tradeoffs for real-life large-scale vehicle routing problems

A VNS solution and objectives tradeoffs for real-life large-scale vehicle routing problems

Investigation of methods for solving a large dimensional routing problem

In this paper, we researched methods for solving a large-scale vehicle routing problem. First, we provided the description of the problem that modern logistic companies encounter during the planning of transportations. As a solution for this problem, we used meta-heuristics and clustering algorithms. Existing studies and publications in the field of large-scale routing were analyzed, giving us the opportunity to assess the quality of the presented meta-heuristics and select those that lead to the best results. The definition of the routing problem is presented, as well as the description of requirements and limitations for the final solution. Then, in the main part of the work, we offer a brief overview of the Clark-Wright heuristic, which we use to build initial solutions. Also we give a brief description of Guided Local Search and Tabu Search algorithms. Both meta-heuristics help to improve the initial solution obtained using the local search algorithms, while avoiding falling into local minima. The K-Means and Mean-Shift clustering algorithms are described and used to speed up the calculation of the solution and eliminate unnecessary costs during routes optimization. Finally, to check the quality of the proposed solution, we developed software that implements the described meta-heuristics and clustering algorithms, and provides the routing results in the form of a route graph and its total length. The program was tested on the set of benchmarks of the Belgian roads, which were provided in the work of F. Arnold, M. Gendreau, K. Sorensen K. The results of comparison with the best solutions are provided along with the conclusion on the optimality of the results obtained. That allows us to assert that in less than ten minutes of solving a problem on each of the clusters, the developed software gives results that differ from the best known only by 5-7%. Further work will be aimed at improving the results by exchanging points between neighboring clusters.

Estimating Emissions from Regional Freight Delivery under Different Urban Development Scenarios

This study aims to develop a regional freight-shipment model to forecast freight movement within freight-delivery regions and examine the relationship between regional freight-shipment activities and the related environmental problems such as air pollution and greenhouse gas emissions. A methodology for freight distribution and collection within geographical regions is proposed, in which a significantly large number of freight demand or supply points needs to be served. This problem can be considered as a large-scale vehicle routing problem and solved by an asymptotic approximation method. A set of closed-form formulas is constructed to obtain a near-optimal total travel distance of a fleet of trucks from multiple distribution centers. A case study is conducted to forecast regional freight-delivery cost in the selected metropolitan areas in the United States. Numerical results under three urban development scenarios show that the proposed methodology can be used to estimate the total cost and related vehicle emissions effectively.

Large-scale vehicle routing problems: Quantum Annealing, tunings and results

Quantum Annealing was previously applied to the vehicle routing problem and the results were promising. For all benchmark instances in the study, optimal results were obtained. However, 100% success rate was not achieved in every case, and tuning the control parameters for larger instances proved cumbersome. This work addresses these remaining difficulties. An empirical approach is taken wherein measurements of run-time behaviour are exploited to transform existing good values of control parameters so that they can be used successfully for other problem instances. The course of this work shows a method which simplifies hand-tuning so that the heuristic performs successfully when applied to larger instances, and also demonstrates a tuning method which establishes control parameter values for instances which belong in broadly defined groupings. In addition, new best known solutions for large-scale instances, and initial results for the distance-constrained variant of the vehicle routing problem are presented.

Multiconstrained Network Intensive Vehicle Routing Adaptive Ant Colony Algorithm in the Context of Neural Network Analysis

Neural network models have recently made significant achievements in solving vehicle scheduling problems. Adaptive ant colony algorithm provides a new idea for neural networks to solve complex system problems of multiconstrained network intensive vehicle routing models. The pheromone in the path is changed by adjusting the volatile factors in the operation process adaptively. It effectively overcomes the tendency of the traditional ant colony algorithm to fall easily into the local optimal solution and slow convergence speed to search for the global optimal solution. The multiconstrained network intensive vehicle routing algorithm based on adaptive ant colony algorithm in this paper refers to the interaction between groups. Adaptive transfer and pheromone update strategies are introduced based on the traditional ant colony algorithm to optimize the selection, update, and coordination mechanisms of the algorithm further. Thus, the search task of the objective function for a feasible solution is completed by the search ants. Through the division and collaboration of different kinds of ants, pheromone adaptive strategy is combined with polymorphic ant colony algorithm. It can effectively overcome some disadvantages, such as premature stagnation, and has a theoretical significance to the study of large-scale multiconstrained vehicle routing problems in complex traffic network systems.

Modelling and solution of a large-scale vehicle routing problem at GE appliances & lighting

We consider a special case of the vehicle routing problem where not only each customer has specified delivery time window, but each route has limited time duration. We propose a solution algorithm using network reduction techniques and simulated annealing meta-heuristic. The objective is twofold: minimising the travel time and minimising the total number of vehicles required. The time-window constraint ensures delivery without delay, thus, a potentially higher level of customer satisfaction. The algorithm has helped the transportation planning team at General Electric Appliances & Lighting to significantly reduce the number of required trucks in two real cases, while its performance on randomly generated cases is also efficient when compared to properly selected benchmarking algorithms.

大規模Vehicle Routing Problemに対する部分問題化と適応的問題統合に基づく新たな探索フレームワークの提案

大規模Vehicle Routing Problemに対する部分問題化と適応的問題統合に基づく新たな探索フレームワークの提案