Solving Vehicle Routing Problem Research Articles

AN APPROACH FOR VEHICLE ROUTING PROBLEM USING GRASSHOPPER OPTIMIZATION ALGORITHM AND SIMULATED ANNEALING

This paper is focused on the study of the basic problem of the vehicle for reducing the cost factor and increasing efficiency of the solution. Features and constraint uses some capabilities of the algorithm used to modify it dynamically between the nodes and depot. This is demonstrated with a feasible schedule for every node and minimizes the total cost as much as possible. The analysis is based on the address of the given model and solution procedure.The purpose of this research paper is to provide examples of models and applications which include the profits, extensions and partitioned features. The objective is to minimize the traveled distance that visits every subset of nodes one after another while maximizing or satisfying a minimum collected profit from each visited node. The concepts of VRP are discussed in Section I and the issues discussed in paper are in Section VI. Section VI also contains the modeling aspects and constraints that can be used in solving VRP in this paper. Simulated annealing and grasshopper optimization algorithm are combined for solving vehicle routing problem as discussed in Section VII. This study investigates both the variants of algorithm for the clustering nodes and different methods for the generation of routes to overcome optimal VRP solution. In conventional grasshopper algorithm, shortest path for certain node that starts from center depot is calculated by means of local search algorithms. Few methods such as ant colony optimization and genetic algorithm are considered for the route optimization. We can compare the performance of these methods to solve the VRP. Therefore, performance of the proposed method is able to produce better solutions than the other methods which reveal a large number of benchmark experimental results and is very promising.

An Adaptive Variable Neighborhood Search Ant Colony Algorithm for Vehicle Routing Problem With Soft Time Windows

In this paper, an adaptive variable neighborhood search ant colony algorithm (AVNSACA) is proposed to solve the vehicle routing problem with soft time windows (VRPSTW). The ant colony algorithm’s pheromone update strategy is improved to make up for the lack of pheromone in the algorithm’s early stage. In order to avoid the algorithm falling into local optimum, two variable neighborhood search operators are designed, and the conditions for the algorithm to enter the variable neighborhood search are set. The effectiveness of AVNSACA in solving vehicle routing problem with soft time windows is verified by Solomon benchmark problem. Through the comparative analysis of the experimental results of the two algorithms, the advantages of the improved ant colony algorithm are illustrated. The experimental results show that the proposed algorithm can effectively obtain better solutions.

Solving vehicle routing problems with stochastic and correlated travel times and makespan objectives

In this paper, we examine a vehicle routing problem with a makespan objective incorporating both stochastic and correlated travel times, which is usually not considered in routing problems. As an alternative to simulation, we develop an approach based on extreme-value theory to estimate the expected makespan (and standard deviation) and show how this approach can be embedded within an existing routing heuristic. We present results that demonstrate the impact of different correlation patterns and levels of correlation on route planning using real-world motivated instances. Depending on the particular objective, cost savings of up to 13.76% can be obtained by considering correlation.

Optimisation and application research of ant colony algorithm in vehicle routing problem

In this paper, an improved ant colony algorithm based on ant system is proposed in order to solve vehicle routing problem. When choosing the path, the 2-opt method is used to explore the reasonable selection of the parameters of the algorithm for vehicle routing problem taking the path savings among customers as heuristic information. The performance of ant colony algorithm is affected by the information heuristic factor α, expectation heuristic factor β and pheromone volatile factor ρ. The method breaks through empirically setting the ant colony algorithm parameter values. By calculation, the optimal parameters of the ant colony algorithm in solving the vehicle routing problem are: α e [1.0, 1.7], β e [4.5, 8.5], ρ e [0.5, 0.6]. At last, an exploration is established to find the optimal solution by combining three parameters and the ant colony algorithm will have a better effect in the actual optimisation problem.

Selective arc‐ng pricing for vehicle routing

AbstractColumn generation algorithms for solving vehicle routing problems often rely on a relaxed pricing subproblem where routes may be nonelementary and which is solved by a labeling algorithm. This pricing algorithm is said to be selective if it can discard nonelementary paths that may be Pareto‐optimal but guarantees finding at least one (not necessarily elementary) path of negative reduced cost when there exists at least one elementary path of negative reduced cost. In this paper, we propose a selective pricing mechanism for a recently introduced variant of the ng‐route relaxation, in which the neighborhoods are associated with arcs instead of nodes. We extend a state‐of‐the‐art set‐based dominance criterion for this problem and show, by means of an exhaustive computational campaign, that the resulting mechanism is effective at reducing the number of nondominated labels as compared to the original pricing algorithm for the same problem. As a result, typically shorter computing times are required to compute similar lower bounds when the proposed mechanism is embedded within a column generation solver.

Overview of fuzzy vehicle routing problems

Introduction. Various algorithms for solving fuzzy vehicle routing problems are considered. The work objective was to study modern methods for the optimal solution to fuzzy, random and rough vehicle routing problems. Materials and Methods. The paper reviews fuzzy vehicle routing problems, existing methods and approaches to their solution. The most effective features of some approaches to solving fuzzy vehicle routing problems considering their specificity, are highlighted. Results. The Fuzzy Vehicle Routing Problem (FVRP) occurs whenever the routing data is vague, unclear, or ambiguous. In many cases, these fuzzy elements can better reflect reality. However, it is very difficult to use Vehicle Routing Problem (VRP) solving algorithms to solve FVRP since several fundamental properties of deterministic problems are no longer fulfilled in FVRP. Therefore, it is required to introduce new models and algorithms of fuzzy programming to solve such problems. Thus, the use of methods of the theory of fuzzy sets will provide successful simulation of the problems containing elements of uncertainty and subjectivity. Discussion and conclusions. As a result of reviewing various methods and approaches to solving vehicle routing problems, it is concluded that the development and study of new solutions come into sharp focus of researchers nowadays, but the degree of elaboration of various options varies. Methods for the optimal solution of FVRP are limited, in general, to some single fuzzy variable. There is a very limited number of papers that consider a large number of fuzzy variables.

Developing Genetic Algorithm to Solve Vehicle Routing Problem with Simultaneous Pickup and Delivery

Developing Genetic Algorithm to Solve Vehicle Routing Problem with Simultaneous Pickup and Delivery

Research on Vehicle Routing Planning Based on Adaptive Ant Colony and Particle Swarm Optimization Algorithm

Aiming at vehicle routing problem and combining the advantages of ant colony and particle swarm optimization, an intelligent optimization algorithm of adaptive ant colony and particle swarm optimization is proposed. Through the simulation of ant colony and bird swarm intelligence mechanism, the particle swarm algorithm and the ant colony algorithm heuristic strategy are combined, and different search strategies are used in different stages of the algorithm. The adaptive adjustment is adopted, and the feedback information is obtained by dynamic interaction with the environment, thus speeding up the convergence speed, improving the learning ability, avoiding the local optimum, getting the best solution and improving the efficiency. The simulation experiment shows that the algorithm has fast convergence speed, strong optimization ability, and can obtain better optimization results. It has some advantages in solving vehicle routing problem.

Differential Evolution Algorithm Based on Sort Mutation Operation for Vehicle Routing Problem with Time Windows

In order to solve vehicle routing problem with time windows, a new sort-based differential evolution algorithm is proposed in this paper. First, Pareto dominates the idea to perform dual-objective optimization and natural number encoding to reflect the order of solutions; at the same time, in order to balance the global exploration and local development capabilities of the algorithm, a new sort-based mutation operation DE/sort/1 is proposed And adopts an innovative dual-strategy evolutionary method based on Pareto frontier selection, and chooses different crossover operations during the crossover process. Finally, this paper uses the standard Solomon test set. Experimental results show that the algorithm is an effective method for solving the vehicle routing problem with time windows.

Comparison of Simulated Annealing, Nearest Neighbour, and Tabu Search Methods to Solve Vehicle Routing Problems

The high cost of logistics is often caused by the determination of distribution routes, vehicle selection, and vehicle scheduling which is often referred to as Vehicle Routing Problem (VRP). VRP can be interpreted as determining the route with minimal costs to deliver goods from a depot to several different customers with different requests. PT Polar Ice Crystal Semarang is a company producing crystal ice that distributes crystal ice in the Semarang area. PT Polar Ice Crystal Semarang does not have a structured and systematic method in determining distribution routes so the company cannot calculate or know how effective the route travelled by the fleet. So far, the determination of distribution routes is left entirely to the driver of the fleet without any route instructions from the company. Therefore we need a method that can determine the distribution route so that the route passed can be effective in terms of cost and time of distribution. In this research, the determination of the optimal distribution route uses three different methods, namely the Simulated Annealing Algorithm, Tabu Search, and Nearest Neighbour. Then the best method is chosen that can produce the optimal route for the company. Based on the calculation results, it can be seen that the optimal route is obtained using the simulated annealing algorithm with estimated travel costs incurred in the amount of Rp. 293,000.17, with a distance of 88.66 km and a travel time of 9 hours 56 minutes using one large vehicle.

Evolutionary ant colony algorithm using firefly-based transition for solving vehicle routing problems

In this paper, we propose an evolutionary optimisation algorithm which adapts the advantages of ant colony optimisation, firefly optimisation algorithms and simulated annealing to solve vehicle routing problem and its variants. Firefly optimisation (FA) along with simulated annealing tries to avoid local optima stagnation of ant colony optimisation. Whereas multi-modal nature of FA helps in exploring the search space, pheromone shaking avoids the stagnation of pheromone deposit on the exploited paths. This is expected to improve the working of ant colony system (ACS). Performance of the proposed algorithm has been compared with the performance of some of other available meta-heuristic approaches currently being used for solving vehicle routing problems on some benchmark problems. Results show the consistency of the proposed approach. Moreover, its convergence rate is also faster and the obtained solutions are closer to optimal as compared to solutions obtained using certain other existing meta-heuristic approaches in use. The results also demonstrate the effectiveness of the presented algorithm over other existing FA-based algorithms for solving vehicle routing problems.

Using the Operations Research Methods to Address Distribution Tasks at a City Logistics Scale

The manuscript discusses the overview and specification of the existing Operations Research methods for their implementation in terms of addressing distribution tasks, in particular to optimize delivery routes at a City logistics scale. First of all, a detailed literature review in a given context is elaborated, while the description of potentially relevant techniques to be applied is presented. The manuscript objective is to identify the most appropriate and benefit methods for their implementation to solve vehicle routing problem (hereinafter as VRP) at a City logistics scale and related optimization operations; i.e. to seek the shortest possible routes during the customer’s delivery activities. In this matter, it is important to state that relevant distribution (pick-up and delivery) tasks can be expressed in a form of graphs on specified transport networks, and thereby use the individual techniques of graph theory. The particular transport network, as the basic concept of transport theory, is defined as a finite set of vertices and edges representing the infrastructure of roads of a network. Each network must be coherent, i.e. there must be at least one path for each vertex pair connecting these two vertices. Each network edge as well as vertex is defined by a certain value or set of values, for example, the edge length, the time it takes to pass, the amount of work that needs to be done on the edge, etc.

Evolutionary ant colony algorithm using firefly-based transition for solving vehicle routing problems

Evolutionary ant colony algorithm using firefly-based transition for solving vehicle routing problems

Meta-heuristic algorithm for solving vehicle routing problems with time windows and synchronized visit constraints in prefabricated systems

Prefabricated construction has attracted research interest as it can significantly improve the energy, cost, and time efficiency of construction. However, dispatching the required prefabricated components to construction sites in a prefabricated system is challenging. To address this issue, we modeled the dispatching problem as a special type of vehicle routing problem with time windows (VRPTW) and solved it by using an improved artificial bee colony (IABC) algorithm. First, to efficiently solve the cross-synchronization problem that occurs in prefabricated systems, two problem-specific lemmas were derived. Then, a hybrid initialization strategy was developed to generate feasible and efficient solutions and a well-designed encoding repair strategy was utilized to make solutions feasible. Finally, a variable length local search strategy was embedded to enhance the exploitation ability. To verify the performance of the proposed IABC algorithm, 55 instances were generated and used for simulation tests. Three efficient algorithms, including the two-phase genetic algorithm (TPGA), improved tabu search algorithm (ITSA), and adaptive large neighborhood search (ALNS) heuristic, were selected for detailed comparisons. Our simulation results show that, considering the energy consumption metric, the proposed algorithm yields average deviations of about 0.099, 0.096, and 0.143 times the values obtained with the TPGA, ITSA, and ALNS heuristic, respectively. The simulation results confirmed that the proposed algorithm can solve the VRPTW in prefabricated systems with high efficiency.

A Review of Genetic Algorithm Applications in Solving Vehicle Routing Problem

A Review of Genetic Algorithm Applications in Solving Vehicle Routing Problem

An Adaptive Spiking Neural P System for Solving Vehicle Routing Problems

The capabilities of membrane computing frameworks in solving multi-objective constrained optimization problems have invited many researchers to focus their efforts on developing new methods and computational paradigms. Getting motivated from the computational completeness of membrane computing systems (P systems), this paper proposes a new way of solving vehicle routing problems (VRP) using one of the most eminent membrane computing frameworks called spiking neural P systems (SNPS). A new model for SNPS has been recommended both for finding the optimal solutions and for optimizing the parameters that are used in the calculation of minimum feasible insertion cost of the customer insertion phase of VRP without using any heuristic operators. The SNPS suggested here is an adaptive SNPS in which some potentials (ATSNPS) with learning and training facilities are incorporated. Being an NP-hard problem with numerous applications in many areas such as gas distribution management, postal delivery, and truck dispatching, the benefits of this study are far-reaching. Here, a variant of VRP called VRP with time windows (VRPTW) has been used in the proposed system. Since this is the first attempt to find solutions of VRP using ATSNPS, a comparison has been made with the algorithms used over VRPTW. The analysis of results proved that the proposed ATSNPS is substantially superior to the state-of-the-art algorithms in terms of computational time and optimizing the attributes such as the average number of vehicles used and the total distance traveled.

Solving vehicle routing problem for multistorey buildings using iterated local search

Vehicle routing problem (VRP) which is a well-known combinatorial optimisation problem that has many applications used in industry is also a generalised form of the travelling salesman problem. In this study, we defined and formulated the VRP in multistorey buildings (Multistorey VRP) for the first time and proposed a solving method employing iterated local search metaheuristic algorithm. This variant of VRP has a great potential for turning the direction of optimisation research and applications to the vertical cities area as well as the horizontal ones. Routes of part picking or placing vehicles/humans in multistorey plants can be minimised by this way. VRP can also be applied to the optimisation of delivering the packages (goods, meals, folders, mails, etc.) to rooms or locations of the structures such as buildings, and skyscrapers for travelling robots/humans using elevators and stairs. The first detailed multistorey building optimisation experiments were conducted by designing a series of scenarios with different parameter values (number of storeys, connections between storeys and customers). The results were presented and the effects of the various building structures over the performance were discussed.

An optimization model for the transportation network with hierarchical structure: the case of China Post

We study the vehicle routing problem of China Post Group with time windows (VRP_CPG_TW). A three-level hub model is established, which includes the determination of the number, location of hubs and their service area as well as routes between hubs and local post office. We propose a comprehensive approach by integrating the center distribution method, and the Taboo and Genetic algorithm to solve the VRP_CPG_TW. The proposed algorithm is divided into two phase. The first phase includes initial site selection and regional division and the second phase is responsible for solving vehicle routing problem with time constraint. The two phases are iterated alternately until the feasible solution comes out. Our scheme is compared with the real scheme of Guizhou Post and about 25% operation fee is reduced. The test results confirm that our model has high potential to be applied to optimize the transportation network of China Post. Moreover, the proposed model also provides an effective solution for optimizing the transportation network with hierarchical structure.

A new metaheuristics for solving vehicle routing problem: Partial Comparison Optimization

Vehicle Routing Problem (VRP) is a problem of selecting shortest route from a depot to serve several nodes by considering transport capacity. In this study, a new metaheuristcs algorithm is proposed to solve VRP in order to achieve optimal solution. This metaheuristics algorithm is Partial Comparison Optimization (PCO). This new optimization algorithm was developed to solve combinatorial optimization problems such as VRP. In this study, PCO was tested to solve the problems that existed in the origin VRP. To prove PCO is a good metaheuristics for solving VRP, several of instances of symmetrical VRP were selected from the VRP library to evaluate its performance. The numerical results obtained from the calculation indicated that the proposed optimization method could achieve results that almost similar with the best-known solutions within a reasonable time calculation. It showed that PCO was a good metaheuristics to solve VRP.

Evolutionary Ant Colony Algorithm Using Firefly Based Transition for Solving Vehicle Routing Problems

Vehicle routing problems are a classical NP-hard optimization problem. In this article we propose an evolutionary optimization algorithm which adapts the advantages of ant colony optimization and firefly optimization to solve vehicle routing problem and its variants. Firefly optimization (FA) based transition rules and a novel pheromone shaking rule is proposed to escape local optima. Whereas the multi-modal nature of FA explores the search space, pheromone shaking avoids the stagnation of pheromones on the exploited paths. This is expected to improve working of an ant colony system (ACS). Performance of the proposed algorithm is compared with the performance of some of other currently available meta-heuristic approaches for solving vehicle routing problems (VRP) by applying it to certain standard benchmark datasets. Results show that the proposed approach is consistent and its convergence rate is faster. The results also demonstrate the superiority of the proposed approach over some of the other existing FA-based approaches for solving such type of discrete optimization problems.