Solution Of Vehicle Routing Problem Research Articles

Investigation of the robustness of solutions of the problem of transport routing

The article deals with the problem which is of relevance nowadays: vehicle routing problem. This problem is considered in order to reduce delivery costs of the distributor. The solution of this problem allows to optimize and reorganize structure of the company and decrease using of recourses. The model of the vehicle routing problem, i. e. the use of different approaches, tools and algorithms to obtain a better result is investigated. Divid-ing this problem on subproblems gives opportunity for using different approaches in solving vehicle routing problem. The algorithm for solving the vehicle routing problem is proposed. The main idea of this algorithm is to use agglomerative clustering, tabu search, and union of the clusters sequentially. The program module for every method is devel-oped. There is an opportunity to make use of parallel computing, as a result of clustering-based approach. The proposed algorithm of the vehicle routing problem is checked with solving a real problem. Problem location is defined in Dnipro city. The visualization of every step of solving is presented as combining Google Maps API and JavaScript in web implementation. The quasi-optimal solution of the considered problem is obtained and its robustness is checked. The critical values which lead to rapid increase in the transporta-tion cost is found. Randomly data perturbation is also tested. Graphical implementation for every test is considered to create applied interpretation of results. Research results can be applied to obtain a solution to the vehicle routing problem and reduce delivery costs of the distributor. The idea of creating an interface for software, the use of other clustering algorithms, introduction of another algorithm of union of the clusters, and the use of dif-ferent approaches for checking the robustness of vehicle routing problem solution is considered as a further research

A new approach for solution of vehicle routing problem with hard time window: an application in a supermarket chain

In this study, a vehicle routing problem with hard time windows (VRPHTW) that appears to meet demands of customers’ service within time intervals in a supermarket chain is solved. In VRPHTW, to reach a solution by an exact method is quite difficult and sometimes impossible if number of constraints is large enough (i.e., NP-hard), and solution time of a VRPHTW grows exponentially. As the size of the problem grows, a near optimal solution can be found using a heuristic method. A hierarchical approach consisting of two stages as “cluster-first route-second” is proposed. In the first stage, customers are assigned to vehicles using three different clustering algorithms (i.e., K-means, K-medoids and DBSCAN). In the second stage, a VRPHTW is solved using a MILP. The main contribution of the article is that the proposed hierarchical approach enables us to deal with a large size real problem and to solve it in a short time using the exact method. Finally, the proposed approach is employed on a supermarket chain. An instance of the algorithm is demonstrated to illustrate the applicability of the proposed approach and the results obtained are highly favourable.

Collection and distribution of returned-remanufactured products in a vehicle routing problem with pickup and delivery considering sustainable and green criteria

As increasing transportation costs mounts pressure on the businesses, there has been an increasing interest on vehicle routing problem (VRP) as a viable and effective solution. Both industry and academia are continuously looking for new approaches to save transport cost and time while increasing profit margins. This endeavor will eventually reduce costs of delivering goods and services for customers, and therefore enhancing the competitiveness of firms involved. Particularly, transportation cost savings could have potential impacts on marketing activities of remanufactured and recycled products in reverse logistics chains. Therefore, developing practical solutions for VRP of original and remanufactured products is one the emerging topics in the current transportation research. In this article, we propose a multi-objective non-linear programming model for the green vehicle routing problem (GVRP), including original and remanufactured products distribution (both delivery and pickup) of end of life (EOL) products. Through the appropriate fuzzy approach the model is linearized, validated, and solved. The results show considerable level of improved performance under the model configurations and proposed solution approach. The obtained results clearly indicate that the proposed mathematical model is capable of reducing the fuel cost, distribution center set-up cost and supplying vehicles, as well as minimizing air pollution. Finally, using a real case study the reliability and viability of the proposed model is verified.

Solving vehicle routing problem by using improved genetic algorithm for optimal solution

ContextThe Vehicle Routing Problem (VRP) has numerous applications in real life. It clarifies in a wide area of transportation and distribution such as transportation of individuals and items, conveyance service and garbage collection. Thus, an appropriate selecting of vehicle routing has an extensive influence role to improve the economic interests and appropriateness of logistics planning. ProblemIn this study the problem is as follows: Universiti Tenaga Nasional (UNITEN) has eight buses which are used for transporting students within the campus. Each bus starts from a main location at different times every day. The bus picks up students from eight locations inside the campus in two different routes and returns back to the main location at specific times every day, starting from early morning until the end of official working hours, on the following conditions: Every location will be visited once in each route and the capacity of each bus is enough for all students included in each route. ObjectivesOur paper attempt to find an optimal route result for VRP of UNITEN by using genetic algorithm. To achieve an optimal solution for VRP of UNITEN with the accompanying targets: To reduce the time consuming and distance for all paths. which leads to the speedy transportation of students to their locations, to reduce the transportation costs such as fuel utilization and additionally the vehicle upkeep costs, to implement the Capacitated Vehicle Routing Problem (CVRP) model for optimizing UNITEN’s shuttle bus services. To implement the algorithm which can be used and applied for any problems in the like of UNITEN VRP. ApproachThe Approach has been presented based on two phases: firstly, find the shortest route for VRP to help UNITEN University reduce student’s transportation costs by genetic algorithm is used to solve this problem as it is capable of solving many complex problems; secondly, identify The CVRP model is implemented for optimizing UNITEN shuttle bus services. FindingThe findings outcome from this study have shown that: (1) A comprehensive listed of active GACVRP; (2) Identified and established an evaluation criterion for GACVRP of UNITEN; (3) Highlight the methods, based on hybrid crossover operation, for selecting the best way (4) genetic algorithm finds a shorter distance for route A and route B. The proportion of reduction the distance for each route is relatively short, but the savings in the distance becomes greater when calculating the total distances traveled by all buses daily or monthly. This applies also to the time factor that has been reduced slightly based on the rate of reduction in the distances of the routes.

MULTI-OBJECTIVE OPTIMIZATION OF VEHICLE ROUTING PROBLEM USING EVOLUTIONARY ALGORITHM WITH MEMORY

The idea of a new evolutionary algorithm with memory aspect included is proposed to find multiobjective optimized solution of vehicle routing problem with time windows. This algorithm uses population of agents that individually search for optimal solutions. The agent memory incorporates the process of learning from the experience of each individual agent as well as from the experience of the population. This algorithm uses crossover operation to define agents evolution. In the paper we choose as a base the Best Cost Route Crossover (BCRC) operator. This operator is well suited for VPRTW problems. However it does not treat both of parent symmetrically what is not natural for general evolutionary processes. The part of the paper is devoted to find an extension of the BCRC operator in order to improve inheritance of chromosomes from both of parents. Thus, the proposed evolutionary algorithm is implemented with use of two crossover operators: BCRC and its extended-modified version. We analyze the results obtained from both versions applied to Solomon’s and Gehring & Homberger instances. We conclude that the proposed method with modified version of BCRC operator gives statistically better results than those obtained using original BCRC. It seems that evolutionary algorithm with memory and modification of Best Cost Route Crossover Operator lead to very promising results when compared to the ones presented in the literature.

Freight vehicle routing with reliable link travel times: a method based on network fundamental diagram

This paper presents a procedure for the solution of the Vehicle Routing Problem (VRP) based on reliable link travel times. They are obtained as a combination of spatially disaggregated and aggregated data about simulated traffic conditions on an urban road network. The disaggregated data concern the congested link travel times, which are traditionally used as variable to be minimized in VRP. The novelty of this research article consists in the introduction of spatially aggregated data, which are estimated by means of the Network Fundamental Diagram (NFD). In a within-day dynamic context, they are a measure of reliability of travel times because they could anticipate the latter ones’ variation in the short term. The equation of reliable link travel times is composed of a congestion term, expressing the traditional congested link travel times (or generalized costs), and a reliability term, which depends on the fundamental diagram of the link and the NFD of the homogeneous cluster of adjacent links. The proposed procedure has been validated and applied for two real test cases. NFDs data are used in the proposed link travel time function to calculate reliable travel times. The reliable link travel times are used for the solution of VRP to obtain optimal routes of freight vehicles.

Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: A dynamic programming approach based on state–space–time network representations

Optimization of on-demand transportation systems and ride-sharing services involves solving a class of complex vehicle routing problems with pickup and delivery with time windows (VRPPDTW). This paper first proposes a new time-discretized multi-commodity network flow model for the VRPPDTW based on the integration of vehicles’ carrying states within space–time transportation networks, so as to allow a joint optimization of passenger-to-vehicle assignment and turn-by-turn routing in congested transportation networks. Our three-dimensional state–space–time network construct is able to comprehensively enumerate possible transportation states at any given time along vehicle space–time paths, and further allows a forward dynamic programming solution algorithm to solve the single vehicle VRPPDTW problem. By utilizing a Lagrangian relaxation approach, the primal multi-vehicle routing problem is decomposed to a sequence of single vehicle routing sub-problems, with Lagrangian multipliers for individual passengers’ requests being updated by sub-gradient-based algorithms. We further discuss a number of search space reduction strategies and test our algorithms, implemented through a specialized program in C++, on medium-scale and large-scale transportation networks, namely the Chicago sketch and Phoenix regional networks.

A bi-criteria evolutionary algorithm for a constrained multi-depot vehicle routing problem

Most research about the vehicle routing problem (VRP) does not collectively address many of the constraints that real-world transportation companies have regarding route assignments. Consequently, our primary objective is to explore solutions for real-world VRPs with a heterogeneous fleet of vehicles, multi-depot subcontractors (drivers), and pickup/delivery time window and location constraints. We use a nested bi-criteria genetic algorithm (GA) to minimize the total time to complete all jobs with the fewest number of route drivers. Our model will explore the issue of weighting the objectives (total time vs. number of drivers) and provide Pareto front solutions that can be used to make decisions on a case-by-case basis. Three different real-world data sets were used to compare the results of our GA vs. transportation field experts’ job assignments. For the three data sets, all 21 Pareto efficient solutions yielded improved overall job completion times. In 57 % (12/21) of the cases, the Pareto efficient solutions also utilized fewer drivers than the field experts’ job allocation strategies.

Branch-and-price algorithms for the solution of the multi-trip vehicle routing problem with time windows

We investigate the exact solution of the vehicle routing problem with time windows, where multiple trips are allowed for the vehicles. In contrast to previous works in the literature, we specifically consider the case in which it is mandatory to visit all customers and there is no limitation on duration. We develop two branch-and-price frameworks based on two set covering formulations: a traditional one where columns (variables) represent routes, that is, a sequence of consecutive trips, and a second one in which columns are single trips. One important difficulty related to the latter is the way mutual temporal exclusion of trips can be handled. It raises the issue of time discretization when solving the pricing problem. Our dynamic programming algorithm is based on concept of groups of labels and representative labels. We provide computational results on modified small-sized instances (25 customers) from Solomon’s benchmarks in order to evaluate and compare the two methods. Results show that some difficult instances are out of reach for the first branch-and-price implementation, while they are consistently solved with the second.

Achieving Better Solutions for Vehicle Routing Problem Involving Split Deliveries and Pickups Using a Competitive Decision Algorithm

This paper discusses vehicle routing problem involving split deliveries and pickups, in which the customer has pickup and delivery demands that can exceed the capacity of the vehicle, and one customer can be visited by no more than one vehicle or by one vehicle for no more than one time. The objective of the problem is to minimize total travel cost. A new heuristic algorithm, the competitive decision algorithm, is proposed to solve the problem. Computational experiments on the benchmark provided by Mitra are performed to evaluate our algorithm against the previously proposed method. The experiment shows that our algorithm provides the best solutions to a total of 110 problems whether or not the number of vehicles used is restricted to the minimum.

Vehicle routing problem solution considering minimising fuel consumption

Recently, logistics is not only playing more and more important role in social and economic development, but also caused serious energy consumption and environment pollution problems. Reasonable vehicle route planning is viewed as an important solution to reduce logistics enterprises’ operation costs as well as alleviate the energy and environmental problems. This study aims to propose a solution to time-dependent vehicle routing problem with time windows (TDVRPTW) considering minimising fuel consumption. First, a mathematical TDVRPTW model with the minimum fuel consumption as an objective function is established, in which the three-dimensional bin-packing problem is considered as a sub-problem and the alternative stop point concept is newly proposed to reduce the possible detouring distance and fuel consumption of logistic vehicle. Then, an ant colony algorithm is applied to solve the problem, and the departure time optimisation is introduced to further improve the obtained results. Finally, the proposed approach is evaluated with the real road network and traffic data of Beijing. The results show that the method introduced in this study outperforms the existing approaches in reducing fuel consumption as well as route length.

The k-dissimilar vehicle routing problem

Abstract In this paper we define a new problem, the aim of which is to find a set of k dissimilar solutions for a vehicle routing problem (VRP) on a single instance. This problem has several practical applications in the cash-in-transit sector and in the transportation of hazardous materials. A min–max mathematical formulation is proposed which requires a maximum similarity threshold between VRP solutions, and the number k of dissimilar VRP solutions that need to be generated. An index to measure similarities between VRP solutions is defined based on the edges shared between pairs of alternative solutions. An iterative metaheuristic to generate k dissimilar alternative solutions is also presented. The solution approach is tested using large and medium size benchmark instances for the capacitated vehicle routing problem.

The load-dependent vehicle routing problem and its pick-up and delivery extension

The present paper examines a Vehicle Routing Problem (VRP) of major practical importance which is referred to as the Load-Dependent VRP (LDVRP). LDVRP is applicable for transportation activities where the weight of the transported cargo accounts for a significant part of the vehicle gross weight. Contrary to the basic VRP which calls for the minimization of the distance travelled, the LDVRP objective is aimed at minimizing the total product of the distance travelled and the gross weight carried along this distance. Thus, it is capable of producing sensible routing plans which take into account the variation of the cargo weight along the vehicle trips. The LDVRP objective is closely related to the total energy requirements of the vehicle fleet, making it a credible alternative when the environmental aspects of transportation activities are examined and optimized. A novel LDVRP extension which considers simultaneous pick-up and delivery service is introduced, formulated and solved for the first time. To deal with large-scale instances of the examined problems, we propose a local-search algorithm. Towards an efficient implementation, the local-search algorithm employs a computational scheme which calculates the complex weighted-distance objective changes in constant time. Solution results are presented for both problems on a variety of well-known test cases demonstrating the effectiveness of the proposed solution approach. The structure of the obtained LDVRP and VRP solutions is compared in pursuit of interesting conclusions on the relative suitability of the two routing models, when the decision maker must deal with the weighted distance objective. In addition, results of a branch-and-cut procedure for small-scale instances of the LDVRP with simultaneous pick-ups and deliveries are reported. Finally, extensive computational experiments have been performed to explore the managerial implications of three key problem characteristics, namely the deviation of customer demands, the cargo to tare weight ratio, as well as the size of the available vehicle fleet.

Effective Set Covering Approach for Vehicle Routing Based on Artificial Immune

In this paper, a heuristic algorithm to solve the Vehicle Routing Problem (VRP) is proposed based on the Artificial Immune System (AIS). By introducing the route covering methodology, a new encoding and heuristic structure are developed. Routes are constructed primarily by the cluster-first-route-second method, with the network renewal mechanism to generate initial antibodies and the bi-learning with balanced-opportunity approach to expand antibody population. The concentric-circle builder is to identify different customer clusters to further form routes. Upon the elite strategy (AB) and (R), worse antibodies are deleted and routes keep diversified in the pool. By further solving the set covering model, the VRP solution is improved along with increasing route choices. Further, the route combination phase is developed to add promising routes, and it brings the final optimal VRP solution by selecting optimal routes from the final route pool. Finally, experiment tests are carried out to illustrate the effectiveness of the proposed heuristic.

A Vehicle Routing Problem Solution Considering Alternative Stop Points

Logistics, especially the city logistics delivery becomes one of the main contributors of energy consumption and environment pollution in urban transportation system. Reasonable vehicle route planning is viewed as an important solution to lower the energy consumption of delivery vehicle as well as reduce logistics enterprises’ operation costs. However, in most existing vehicle routing problem (VRP) studies, the road networks were simplified and the client points were connected by unidirectional roads, which is obviously inconsistent with the actual conditions of road network. A new VRP solution based on a bi-directional road network, which aims to minimizing fuel consumption for gasoline powered delivery vehicle, is proposed in this paper. First, the mathematic VRP model with the minimal-fuel consumption as optimization objective is established. Then, a bi-directional road network for VRP is constructed, and alternative stop point for each delivery client is formulated according to the weight of package and the walking distance of deliveryman. Finally, the proposed method is evaluated in an actual road network, and the results show that the proposed solution for VRP reduces the distance of roundabout and the fuel consumption of delivery vehicle effectively.

Adaptive Ant Colony Algorithm for the VRP Solution of Logistics Distribution

In order to conquer the premature convergence problem and lower the cost of computing of the basic Ant Colony Algorithm (ACA), we present an adaptive ant colony algorithm, named AACA, coupled with a Pareto Local Search (PLS) algorithm and apply to the Vehicle Routing Problem (VRP) and Capacitated VRP (CVRP). By using the information entropy, the algorithm adjusts the pheromone updating strategy adaptively. Experiments on various aspects of the algorithm and computational results for some benchmark problems are reported. We compare our approach with some classic, powerful meta-heuristics and show that the proposed approach can obtain the better quality of the solutions.

Improved ant colony optimisation for the dynamic multi-depot vehicle routing problem

Dynamic vehicle routing problem (DVRP) with single depot has received increasing interest from engineers and scientists. Dynamic multi-depot vehicle routing problem (DMDVRP), an extension of DVRP, however, has not received much attention. In our paper, a distance-based clustering approach is introduced to simplify the DMDVRP by allocating each customer to its nearest depot. Thus, DMDVRP is decomposed to a sequence of DVRPs. An improved ant colony optimisation (IACO) with ant-weight strategy and mutation operation is presented to optimise vehicle routing problem (VRP) in this paper. Moreover, to satisfy the real-time feature of DMDVRP, the nearest addition approach is used to handle the new orders occurring during a time slice on the basis of VRP solution. Finally, the computational results for 17 benchmark problems are reported to validate that IACO with the distance-based clustering approach is more suitable for solving DMDVRP.

Exact Solution for Vehicle Routing Problem with Soft Time Windows and Dynamic Travel Time

The traffic conditions in urban areas change with time due to varying congestion levels and incidents, resulting in unexpected variations of travel time on the infrastructure links. These conditions lead to the formulation of the Dynamic Vehicle Routing and scheduling Problem with Soft Time Windows (D-VRPSTW) with dynamic travel time in the city logistics field. This paper presents a column generation-based exact solution approach for the D-VRPSTW. The performance evaluation on a test instance under different dynamic travel time events shows that the D-VRPSTW solutions based on the updated travel times result in significant cost savings as compared to the static version.

포병화력 생존성지원을 위한 진지구축경로문제 연구

In this paper, we deal with the vehicle routing problem that could establish operational plan of military engineer for survivability support of artillery position construction. We propose VRPTW(vehicle routing problem with time-window) model of special form that considered service level to reflect the characteristics of military operations rather than the logic of economic efficiencies in the objective function. Furthermore we suggest modified particle swarm optimization algorithm for service based vehicle routing problem solution that can be possible to search in complicated and uncertain area and control relation softly between global and local search.

Research on Particle Swarm Optimization for Vehicle Routing Problem

Logistics Vehicle Routing Problem belongs to a class of NP problem which has important practical value. This article needs to be considered for vehicles path restriction requirements, and have been established in the vehicle routing problem based on the mathematical model, using particle swarm optimization algorithm intelligence (PSO), constructing vehicle routing problem with particle expressions, establishing this problem by particle swarm algorithm, and compared with Genetic algorithms. The simulation results show that the algorithm can quickly and efficiently obtain the optimal vehicle routing problem solution. Therefore, it can be a very effective program to solve the vehicle routing problem.