Generalized Vehicle Routing Problem Research Articles

Solving a real-life roll-on–roll-off waste collection problem with column generation

In this paper, we develop an intelligent solution to a complex, real-life vehicle routing problem in the waste management sector. Waste management companies deliver various types of empty waste containers to industrial customers, to be filled with different types of waste, after which the containers are picked up again. The full containers are transported to a so-called waste management depot or waste handling depot, where they are emptied, after which they are reused. Empty containers are stocked in various stock depots. Time windows in which containers may be picked up and delivered at the customers and opening hours of the different depots have to be taken into account additionally. Very importantly, there are two types of waste collection trucks that can, respectively, carry one or two containers. The resulting vehicle routing problem belongs to a class of so-called roll-on–roll-off problems, characterized by unit demand. Additionally, the problem discussed in this paper has several characteristics (multiple waste types, multiple container types, multiple depots, a heterogeneous fleet, pickup and delivery, time window constraints, and other) that make solving it a difficult task. To solve this problem, we develop a novel column generation scheme that incorporates a heuristic approach to generate new columns. The master problem is solved by linear relaxation of a set partitioning problem. New routes (columns) are generated by a constructive heuristic loosely based on Solomon’s insertion heuristic for the vehicle routing problem with time windows. The construction heuristic operates on a reformulated version of the roll-on–roll-off problem, i.e., a generalized vehicle routing problem with time windows. The algorithm—called wmpopt—is submitted to an extensive sensitivity analysis to determine its response to different parameter settings. After this, we test it on four real-life problem instances and compare its results to those obtained by a commercial solver. We show that wmpopt achieves much better solutions than the commercial solver in similar computing times.

Usulan Rute Optimal Distribusi Sampah Shift I Kota Sumbawa Besar Menggunakan Metode GVRP

Generalized vehicle routing problem (GVRP), for each vertex of the graph is partitioned into vertex sets and called groups, it will be determined the optimal route given to each set group includes exactly one vertex of each group. Furthermore, the cluster generalized vehicle routing problem (CGVRP) was introduced which aims to determine the optimal route for each vertex for each cluster. The optimal route can be solved using the Djikstra Algorithm. The distribution of waste in the city of Sumbawa Besar is still considered to be less than optimal, so this system can be implemented by making direct connections between each polling station. This system produces the shortest route, travel details, distance between polling stations and travel costs.

Routing problems in agricultural cooperatives: a model for optimization of transport vehicle logistics

AbstractThis study considers the problem of optimizing the routes of vehicles used in an agricultural cooperative that distributes animal feed to its customers. Different peculiarities distinguish our problem from the general Vehicle Routing Problem because there exists a type of time window constraint, truck capacity is limited, trucks are compartmentalized, there are access restrictions for trucks to some farms and our problem has the main objective of maximizing the amount of feed distributed every day and an auxiliary criterion of minimizing the transport costs. We present a mathematical programming formulation of the model that represents the logistics management problem. As solving the exact model is computationally expensive, we opt for a hybrid heuristic approach that first uses an insertion heuristic algorithm to obtain an initial solution and then improvement processes are performed using the so-called simulated annealing metaheuristic. We have built a graphical interface that allows easy use of the system and, in particular, efficient post-optimality analysis. Moreover, this interface can easily interface with other management tools. The utility of our model is shown with real and simulated data sets.

A Genetic Algorithm in Combination with a Solution Archive for Solving the Generalized Vehicle Routing Problem with Stochastic Demands

This work presents a steady-state genetic algorithm enhanced by a complete trie-based solution archive for solving the generalized vehicle routing problem with stochastic demands using a preventive restocking strategy. As the necessary dynamic programming algorithm for the solution evaluation is very time consuming, considered candidate solutions are stored in the solution archive. It acts as complete memory of the search history, avoids reevaluations of duplicate solution candidates, and is able to efficiently transform them into guaranteed new ones. This increases the diversity of the population and reduces the risk of premature convergence. Similar to a branch-and-bound algorithm, the tree structure of the solution archive is further exploited to compute lower bounds on the nodes to cut off parts of the solution space that evidently do not contain good solutions. Since in each iteration a not yet considered solution candidate is generated and completeness can be efficiently checked, the overall method is in principle an exact enumeration algorithm, which leads to guaranteed optimal solutions for smaller instances. Computational results of this algorithm show the superiority over the so far state-of-the-art metaheuristic and also prove its effectiveness on the nongeneralized version of this problem.

A branch-cut-and-price algorithm for the generalized vehicle routing problem

We develop a branch-cut-and-price algorithm for the generalized vehicle routing problem (GVRP)—a variant of the vehicle routing problem where customers are partitioned into mutually exclusive clusters. The decision-maker seeks to determine minimum cost routes using a limited number of vehicles such that every cluster is visited by exactly one route, and within any cluster a single customer is visited, subject to vehicle capacity constraints. The pricing subproblem is solved using a specialized dynamic programming algorithm. Computational results show that the proposed algorithm compares favorably against a state-of-the-art branch-and-cut algorithm and solves to optimality eight previously open GVRP instances in the literature.

Distribusi Batik Madura Melalui Penerapan Generalized Vehicle Routing Problem (GVRP)

Product distribution process is an effort to convey a product of consumer handlebar with a planned and programmed system. Cluster method is a grouping of the nearest market location, then analyzed the location of potential facilities through center of gravity. GVRP (Generalized Vehicle Routing Problem) is one of the algorithms in the cluster method [1]. In the GVRP describes the route determination to minimize the required distribution costs. GVRP is a generalization of VRP, so the point of the graph is partitioned into several sets of specific points, called clusters [2]. In this research, modification of GVRP model for multi-capacity vehicle case can determine the route and minimize the cost of distribution. Taken case on UD. Damai Asih for the distribution of Madura writes batik to 25 districts in East Java. From the results of running using MATLAB 7.8.0 obtained the efficiency of the distribution cost of 8.71% of the initial cost before doing the clustering based on distance and maximum capacity of the car of Rp. 6,969,480.00. After the filtering based on the distance and maximum capacity of the car obtained a cost of Rp. 6.365.500.00. The highest value of efficiency is obtained in cluster four, while the lowest efficiency value is obtained in cluster eight. The existence of cost efficiency is due to the different mileage in the clustering process.

Complex vehicle transport problems: taxonomy, new variants, challenges and solution methodology

Due to appeared of several and new alternatives of vehicle routing problems (VRPs) in the last years, the contributions focus on design of traffic flow and transportation systems, vehicle routing, and other important aspects of supply chain management such as dynamic routing, multi commodity problems, inventory management, lot sizing, and lot scheduling. In this paper, we are going to present an extensive review of the general vehicle routing problem then we are going to focus on the problematic approaches in this field. For each one of these problematic, a positioning compared to this state of the art will be developed. In the first part a synthesis of literature review devoted to the complex and logistic transport problems in general and a transport problem with limited fleet and common carrier in particular with stochastic and dynamic vehicle routing problem. In the second part, a description of the vehicle routing problem with mathematical formulations will be presented. The different variants of this problem will be approached.

Adaptive memory programming for the many-to-many vehicle routing problem with cross-docking

This paper presents a new generalized vehicle routing problem with a cross-dock. Basic features of the examined problem are the many-to-many relationship between the suppliers and customers, and the use of different vehicle fleets for performing the inbound and outbound routes. An adaptive memory programming method has been developed coupled with a Tabu Search algorithm. For generating new provisional solutions, elite subroutes with varying lengths are identified from the reference solutions and are used as building blocks, while multiple strategies are applied to maintain an effective interplay between diversification and intensification. Various computational experiments are conducted on existing as well as on new data sets with diverse features, regarding the geographic distribution of the nodes and the density of supplier-customer links. Overall, the proposed method performed very well and new best solutions have been found. Lastly, new insights regarding the impact of split options are reported.

An Integer L-shaped Method for the Generalized Vehicle Routing Problem with Stochastic Demands

In this work we consider the generalized vehicle routing problem with stochastic demands (GVRPSD). This NP-hard problem combines the clustering aspect of the generalized vehicle routing problem with the uncertainty aspect of the vehicle routing problem with stochastic demands. We propose an integer L-shaped method based on decomposition and branch-and-cut. The subproblem of computing the restocking costs is based on dynamic programming. We consider the preventive restocking strategy which is substantially harder than the standard restocking strategy used by the majority of the published articles for stochastic vehicle routing problems. Using this strategy the vehicle can make a return trip to the depot even before an actual stockout occurs and therefore save travel time. The GVRPSD has not been considered in the literature so far and this first exact solution attempt proves to be able to solve small to medium instances.

Differential evolution algorithms for scheduling raw milk transportation

This paper focuses on determining routes for raw milk collection from collection centers to dairy factories with the objective of minimizing the total costs, considering fuel costs and costs of cleaning and sanitizing raw milk tanks on vehicles. This problem is considered to be a special case of the vehicle routing problem (VRP) but it is complex compared to the general VRP, especially since each vehicle contains more than one tank with heterogeneous capacity to collect raw milk and raw milk from different collection centers cannot be transferred into the same compartment. In this paper, a DE metaheuristic was used to solve the problem. In order to improve the solution quality, five modified DE algorithms with two additional steps, reincarnation and survival processes, were proposed. In addition, the skipped customer and multi-route attributes are also developed in the decoding process in order to obtain a shorter traveling distance and lower truck usage in the system, especially if they are used together with the reincarnation and survival processes. The computational results reveal that the modified DE algorithms yield higher relative improvement (RI) on the total costs and also the RI on the number of vehicles used.

Two solution representations for solving multi-depot vehicle routing problem with multiple pickup and delivery requests via PSO

Two solution representations for solving the generalized multi-depot vehicle routing problem with multiple pickup and delivery requests (GVRP-MDMPDR) is presented in this paper. The representations are used in conjunction with GLNPSO, a variant of PSO with multiple social learning terms. The computational experiments are carried out using benchmark test instances for pickup and delivery problem with time windows (PDPTW) and the generalized vehicle routing problem for multi-depot with multiple pickup and delivery requests (GVRP-MDMPDR). The preliminary results illustrate that the proposed method is capable of providing good solutions for most of the test problems.

Efficient elementary and restricted non-elementary route pricing

Column generation is involved in the current most efficient approaches to routing problems. Set partitioning formulations model routing problems by considering all possible routes and selecting a subset that visits all customers. These formulations often produce tight lower bounds and require column generation for their pricing step. The bounds in the resulting branch-and-price are tighter when elementary routes are considered, but this approach leads to a more difficult pricing problem. Balancing the pricing with route relaxations has become crucial for the efficiency of the branch-and-price for routing problems. Recently, the ng-routes relaxation was proposed as a compromise between elementary and non-elementary routes. The ng-routes are non-elementary routes with the restriction that when following a customer, the route is not allowed to visit another customer that was visited before if they belong to a dynamically computed set. The larger the size of these sets, the closer the ng-route is to an elementary route. This work presents an efficient pricing algorithm for ng-routes and extends this algorithm for elementary routes. Therefore, we address the Shortest Path Problem with Resource Constraint (SPPRC) and the Elementary Shortest Path Problem with Resource Constraint (ESPPRC). The proposed algorithm combines the Decremental State-Space Relaxation technique (DSSR) with completion bounds. We apply this algorithm for the Generalized Vehicle Routing Problem (GVRP) and for the Capacitated Vehicle Routing Problem (CVRP), demonstrating that it is able to price elementary routes for instances up to 200 customers, a result that doubles the size of the ESPPRC instances solved to date.

An exact algorithm and a metaheuristic for the generalized vehicle routing problem with flexible fleet size

The generalized vehicle routing problem (GVRP) involves finding a minimum-length set of vehicle routes passing through a set of clusters, where each cluster contains a number of vertices, such that the tour includes exactly one vertex from each cluster and satisfies capacity constraints. We consider a version of the GVRP where the number of vehicles is a decision variable. This paper introduces a new mathematical formulation based on a two-commodity flow model. We solve the problem using a branch-and-cut algorithm and a metaheuristic that is a hybrid of the greedy randomized adaptive search procedure (GRASP) and the evolutionary local search (ELS) proposed in [18]. We perform computational experiments on instances from the literature to demonstrate the performance of our algorithms.

Exact and heuristic algorithms for solving the generalized vehicle routing problem with flexible fleet size

AbstractThe generalized vehicle routing problem with flexible fleet size (GVRP‐flex) extends the classical capacitated vehicle routing problem (CVRP) by partitioning the set of required nodes into clusters and has interesting applications such as humanitarian logistics. The problem aims at minimizing the total cost for a set of routes, such that each cluster is visited exactly once and its total demand is delivered to one of its nodes. An exact method based on column generation (CG) and two metaheuristics derived from iterated local search are proposed for the case with flexible fleet size. On five sets of benchmarks, including a new one, the CG approach often provides good upper and lower bounds, whereas the metaheuristics find, in a few seconds, solutions with small optimality gaps.

Generalized Vehicle Routing Problem for Reverse Logistics Aiming at Low Carbon Transportation

Deployment of green transportation in reverse logistics is a key issue for low carbon technologies. To cope with such logistic innovation, this paper proposes a hybrid approach to solve practical vehicle routing problem (VRP) of pickup type that is common when considering the reverse logistics. Noticing that transportation cost depends not only on distance traveled but also on weight loaded, we propose a hierarchical procedure that can design an economically efficient reverse logistics network even when the scale of the problem becomes very large. Since environmental concerns are of growing importance in the reverse logistics field, we need to reveal some prospects that can reduce CO2 emissions from the economically optimized VRP in the same framework. In order to cope with manifold circumstances, the above idea has been deployed by extending the Weber model to the generalized Weber model and to the case with an intermediate destination. Numerical experiments are carried out to validate the effectiveness of the proposed approach and to explore the prospects for future green reverse logistics.

Artificial bee colony algorithm with scanning strategy for the periodic vehicle routing problem

The periodic vehicle routing problem (PVRP) is an extension of the vehicle routing problem (VRP). Because it extends the single delivery period to a T-day period ( T > 1), PVRP has strong theoretical and practical significance. Since PVRP is an embedded VRP, it is more complex and difficult compared with the general VRP. In this paper, the bee colony algorithm is used to solve the PVRP. To improve the performance of this algorithm, multidimensional heuristic information and a local optimization based on a scanning strategy are used. At the end of this paper, the algorithm is tested by some well-known examples. The results show that the proposed improved bee colony algorithm is a powerful tool for solving the PVRP. It also shows that these two kinds of strategies can significantly improve the performance of the algorithm.

Military aircraft mission planning: a generalized vehicle routing model with synchronization and precedence

We introduce a military aircraft mission planning problem where a given fleet of aircraft should attack a number of ground targets. Due to the nature of the attack, two aircraft need to rendezvous at the target, that is, they need to be synchronized in both space and time. At the attack, one aircraft is launching a guided weapon, while the other is illuminating the target. Each target is associated with multiple attack and illumination options. Further, there may be precedence constraints between targets, limiting the order of the attacks. The objective is to maximize the outcome of the entire attack, while also minimizing the mission timespan. We give a linear mixed-integer programming model of the problem, which can be characterized as a generalized vehicle routing problem with synchronization and precedence side constraints. Numerical results are presented for problem instances of realistic size.

An improved hybrid algorithm for solving the generalized vehicle routing problem

The generalized vehicle routing problem (GVRP) is a natural extension of the classical vehicle routing problem (VRP). In GVRP, we are given a partition of the customers into groups (clusters) and a depot and we want to design a minimum length collection of routes for the fleet of vehicles, originating and terminating at the depot and visiting exactly one customer from each group, subject to capacity restrictions. The aim of this paper is to present an efficient hybrid heuristic algorithm obtained by combining a genetic algorithm (GA) with a local–global approach to the GVRP and a powerful local search procedure. The computational experiments on several benchmark instances show that our hybrid algorithm is competitive to all of the known heuristics published to date.

An incremental tabu search heuristic for the generalized vehicle routing problem with time windows

This paper describes an incremental neighbourhood tabu search heuristic for the generalized vehicle routing problem with time windows. The purpose of this work is to offer a general tool that can be successfully applied to a wide variety of specific problems. The algorithm builds upon a previously developed tabu search heuristic by replacing its neighbourhood structure. The new neighbourhood is exponential in size, but the proposed evaluation procedure has polynomial complexity. Computational results are presented and demonstrate the effectiveness of the approach.

Sensitive Ants in Solving the Generalized Vehicle Routing Problem

The idea of sensitivity in ant colony systems has been exploited in hybrid ant-based models with promising results for many combinatorial optimization problems. Heterogeneity is induced in the ant population by endowing individual ants with a certain level of sensitivity to the pheromone trail. The variable pheromone sensitivity within the same population of ants can potentially intensify the search while in the same time inducing diversity for the exploration of the environment. The performance of sensitive ant models is investigated for solving the generalized vehicle routing problem. Numerical results and comparisons are discussed and analysed with a focus on emphasizing any particular aspects and potential benefits related to hybrid ant-based models.