Cumulative Capacitated Vehicle Routing Problem Research Articles

A Dynamic and Stochastic Cumulative Capacitated Vehicle Routing Problem

A Dynamic and Stochastic Cumulative Capacitated Vehicle Routing Problem

Solving the cumulative capacitated vehicle routing problem with drones

ABSTRACT In this paper, we consider the Cumulative Capacitated Vehicle Routing Problem (CCVRP), which is used to model many real-world applications, especially in the area of supplying humanitarian aid after a natural disaster. Interestingly, in this study, Unmanned Aerial Vehicles (UAVs) so-called drones are used to assist the trucks in delivering parcels to customers. Each of them travels to different locations to perform specified tasks and meet periodically with the vehicle from which it takes off to swap its battery. In this paper, a mathematical model is formulated which is then tested with small-sized problems using CPLEX software. Due to the difficulty of solving large instances to optimality, we propose a heuristic algorithm based on a well-established type of cluster-first, route-second approach. Then, it is enhanced by some proposed properties. Hereafter, we develop a minimum spanning tree based-lower bound. Finally, extensive computational experiments are carried out by using instances from the literature. They show the good performance of the proposed heuristic algorithm to solve large instances in a very competitive running time.

An iterated local search algorithm for latency vehicle routing problems with multiple depots

The Multi-depot Cumulative Capacitated Vehicle Routing Problem (MDCCVRP) extends the recently proposed Cumulative Capacitated Vehicle Routing Problem (CCVRP). The aim is to minimize the sum of the arrival times at the customers considering a fleet of Nv capacitated vehicles and a set of Nd uncapacitated depots. This paper proposes valid lower bounds and a novel metaheuristic algorithm for the solution of the MDCCVRP. The initial solution is obtained by combining different heuristic approaches, while the improving phase consists of an iterated local search algorithm (ILS). Computational experiments on 78 MDCCVRP benchmark instances show that the proposed algorithm is able to find, within reasonable computing times, solution values globally better than those obtained by the state-of-the-art heuristic algorithms. For challenging instances (having a large number of customers and a small fleet size), the algorithm can find, within short computing times, solutions globally better than those obtained by the published exact algorithms. The proposed algorithm has also been applied to the recently introduced Multi-depot k-traveling Repairman Problem (MDk-TRP) and the Latency Location Routing Problem (LLRP). The MDk-TRP is a particular case of the MDCCVRP arising when the vehicles are uncapacitated, while the LLRP is a generalization of the MDCCVRP in which, at most, p of the Nd available depots can be used. The computational experiments performed on 87 MDk-TRP benchmark instances and 76 LLRP benchmark instances show that the proposed algorithm globally outperforms the state-of-the-art metaheuristic algorithms for what concerns both the solution quality and the computing time. For large-size instances, the computing time required to provide a good quality solution is considerably smaller than that required by the previously published heuristic and exact algorithms. For all the problems, the proposed algorithm is able to find better solution values than those obtained by the respective state-of-the-art metaheuristic algorithms when it is executed for the same computing time as the respective competitor.

Effective metaheuristics for the latency location routing problem

AbstractThe latency location routing problem (LLRP), a combination of the facility location problem and the cumulative capacitated vehicle routing problem, is a recently proposed variant of location routing problems. It corresponds to a customer‐centric problem, in which the aim is to minimize the sum of the arrival times at the customers. This paper proposes three novel metaheuristic algorithms to solve the LLRP. They use a simulated annealing framework, which after each temperature reduction is intensified through a variable neighborhood descent procedure. Each algorithm uses a different search strategy as intensification. Results on 76 benchmark instances indicate that the proposed metaheurstics outperform the state‐of‐the‐art algorithms, finding new best solutions for all the large‐sized instances (over 100 customers), or the currently known optimal ones for most of the small‐ and medium‐sized instances, in comparable computing times. Furthermore, in more than 80% of the instances the average value of the solutions found by the proposed algorithms is better than or equal to that of the current best known solution.

New formulations and solution approaches for the latency location routing problem

The Latency Location Routing Problem (LLRP) belongs to a relatively new branch of routing problems, where latency, defined as the sum of the arrival times at customers, is the objective function to be minimized. Introduced by Moshref-Javadi and Lee (2016), this problem optimizes the location of depots, the vehicles allocation to open depots, the customers’ assignment to vehicles and the routing strategy in a customer-oriented framework. In this paper, we address the problem from a modeling and computational viewpoint. From a modeling point of view, we propose two new mixed-integer formulations and introduce a general variant of the problem, which considers the presence of opening costs associated to the depots. Under this assumption, the optimal selection of suitable locations for depots is driven not only by the total latency but also by fixed costs related, for instance, to the construction/renting cost of depots. From a methodological standpoint, we propose different exact solution methods and a metaheuristic algorithm able to obtain near-optimal solutions for both variants, with and without opening costs. Extensive numerical experiments validate the effectiveness of the proposed models and the efficiency of the solution approaches. As a byproduct of the research, by slightly adapting our models, we obtained an effective mathematical formulation for the multi-depot cumulative capacitated vehicle routing problem, which outperformed the state-of-the-art model, providing new optimal solutions in the benchmark dataset.

A hybrid Tabu search – Variable neighborhood descent algorithm for the cumulative capacitated vehicle routing problem with time windows in humanitarian applications

The paper presents a Hybrid Tabu Search - Variable Neighborhood Descent (HTS-VND) metaheuristic algorithm for the Cumulative Capacitated Vehicle Routing Problem with Time Windows (CCVRPTW). The algorithm is also used to solve the Cumulative Capacitated Vehicle Routing Problem (CCVRP) without the time widow constraints. Its effectiveness is tested against well known benchmark instances from the literature and the results are compared with the results of other state-of-the-art approaches. The proposed metaheuristic was able to find new best known solutions in two instances of the CCVRP. For the CCVRPTW, two additional algorithms, a Tabu Search algorithm and a Variable Neighborhood Descent algorithm, were implemented to provide benchmark values for results obtained with HTS-VND. Overall, on the 92 CCVRP instances tested, the best known solutions were reached in 84 of them. For the CCVRPTW, 56 instances were tested and the proposed HTS-VND obtained better results than the two pure implementations, reaching the instance specified number of vehicles in 41 of them. The paper also provides solution cost values for the CCVRPTW, which are not included in approaches in the literature.

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

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

A cumulative unmanned aerial vehicle routing problem approach for humanitarian coverage path planning

This paper presents a Cumulative Unmanned Aerial Vehicle Routing Problem (CUAVRP) approach to optimize Humanitarian Coverage Path Planning (HCPP). Coverage path planning consists of finding the route which covers every point of a certain area of interest. This paper considers a Search & Rescue mission, using a homogeneous fleet of Unmanned Aerial Vehicles (UAVs). In this scenario, the objective is to minimize the sum of arrival times at all points of the area of interest, thus, completing the search with minimum latency. The HCPP problem is transformed into a Vehicle Routing Problem by using an approximate cellular decomposition technique to discretize the area into a grid, where the rectangles represent the UAV sensor’s field of view. The center points of the formed rectangles, become the nodes used for a UAV routing problem. This approach uses the objective of minimizing the sum of arrival times at customers, found in the Cumulative Capacitated Vehicle Routing Problem (CCVRP), adjusted for the Search & Rescue Coverage Path Planning using UAVs. The Min-max objective is also implemented and tested. Three versions of a Parallel Weighted Greedy Randomized Adaptive Search Procedure - Variable Neighborhood Decent (GRASP-VND) algorithm is implemented to solve the Cumulative UAV Routing Problem for Humanitarian Coverage Path Planning.

A hybrid ant colony optimization-variable neighborhood descent approach for the cumulative capacitated vehicle routing problem

In this paper, we present two swarm intelligence algorithms for the solution of the Cumulative Capacitated Vehicle Routing Problem. In particular, two hybrid algorithms of the Ant Colony Optimization family have been implemented, the Ant Colony System-Variable Neighborhood Decent and the Max-Min Ant System-Variable Neighborhood Decent. In this novel implementation, the ant-solution population, in both algorithms, is generated by applying local search operators on a single solution generated by the ant transition rules. This method of generating the population is compared to the traditional ACO population generation method. Their effectiveness is tested against well known benchmark instances in the literature and the results are compared to other approaches. The Ant Colony System-Variable Neighborhood Decent provided the best results among the two implemented versions and was able to find a new best known solution for two instances. Overall, on the 112 instances tested, best known solutions were reached in 92 of them. From the 20 instances in which the best known solution was not reached, 19 are instances with over 220 customers. The average gap from the best known solution in those instances is 0.35% and the maximum gap is 0.98%.

Emergency Logistics Scheduling Under Uncertain Transportation Time Using Online Optimization Methods

In the immediate aftermath of large-scale disasters, emergency logistics services play important roles in saving lives and reducing losses. Efficient relief logistics scheduling depends on the accurate transport time information for available routes. However, this information cannot be obtained precisely until a vehicle uses the road. Considering the correlation between information acquisition and logistics operations, this paper focuses on a multiperiod online decision-making problem to simulate the information acquiring process. This problem can be referenced for emergency resource scheduling scenarios in which previous decisions impact knowledge for future logistics plans. A multi-trip cumulative capacitated vehicle routing problem with uncertain transportation time is investigated as the basic model. The tradeoff between transportation efficiency and the unknown transport time discovery rate is considered in a multiobjective evolutionary algorithm (MOEA). A memetic algorithm (MA) and a robust optimization (RO) -MA for single-period post-disaster emergency logistics are also proposed to solve the problem for comparison. In these algorithms, evolutionary operators that benefit solution fixing and variation are proposed. In the experiments, a real-world instance is employed. A simulative experimental environment is established. Dynamic information gained within the process of logistics scheduling is highlighted via multi-period online optimization. Different scenarios corresponding to estimates in emergency situations are provided to validate the performance of the algorithms. The experimental results show that the hybrid strategy, MOEA+MA, can obtain the best result in more than half of the considered cases which demonstrates the necessary balance between obtaining information and transportation efficiency.

A Memetic Algorithm for the Cumulative Capacitated Vehicle Routing Problem Including Priority Indexes

This paper studies the Cumulative Capacitated Vehicle Routing Problem, including Priority Indexes, a variant of the classical Capacitated Vehicle Routing Problem, which serves the customers according to a certain level of preference. This problem can be effectively implemented in commercial and public environments where customer service is essential, for instance, in the delivery of humanitarian aid or in waste collection systems. For this problem, we aim to minimize two objectives simultaneously, the total latency and the total tardiness of the system. A Mixed Integer formulation is developed and solved using the AUGMECON2 approach to obtain true efficient Pareto fronts. However, as expected, the use of commercial software was able to solve only small instances, up to 15 customers. Therefore, two versions of a Memetic Algorithm with Random Keys (MA-RK) were developed to solve the problem. The computational results show that both algorithms provided good solutions, although the second version obtained denser and higher quality Pareto fronts. Later, both algorithms were used to solve larger instances (20–100 customers). The results were mixed in terms of quality but, in general, the MA-RK v2 consistently outperforms the first version. The models and algorithms proposed in this research provide useful insights for the decision-making process and can be applied to solve a wide variety of business situations where economic, customer service, environmental, and social concerns are involved.

An Effective Local Search Algorithm for the Multidepot Cumulative Capacitated Vehicle Routing Problem

The cumulative capacitated vehicle routing problem (CCVRP) focuses on minimizing the sum of arrival times at the customers. An important application of the CCVRP arises in the procurement of humanitarian aid when natural disasters occur. In this article, the multidepot CCVRP (MDCCVRP) is investigated, and its mathematical model is developed. Moreover, an effective perturb-based local search (PLS) algorithm is proposed to solve the problem. The proposed PLS algorithm starts from having a feasible solution. Regarding the PLS, the perturbing operators help to explore the searching space, while the six local search operators help to exploit the best solution within each searching basin. To test the performance, the proposed PLS is applied to a set of standard benchmark instances and compared with the recently published algorithms. Extensive computational studies reveal that the proposed PLS algorithm is able to attain better solutions with less computational time for most testing instances, and thus competes very favorably with the previously proposed approaches. A stability analysis is also presented to shed light on the robust behavior of the proposed algorithm. The results of the two-sided Wilcoxon rank sum tests clearly show that the algorithms (our PLS and other published methods) have performed with statistically significant differences.

A hybrid large-neighborhood search algorithm for the cumulative capacitated vehicle routing problem with time-window constraints

This paper introduces a special vehicle routing problem, i.e. the cumulative capacitated vehicle routing problem with time-window constraints (Cum-CVRPTW). The problem can be defined as designing least-cost delivery routes from a depot to a set of geographically-scattered customers, subject to the constraint that each customer has to be served within a time window; accordingly, the objective costs are computed as the sum of arrival times at all the customers. The Cum-CVRPTW finds practical utility in many situations, e.g. the provision of humanitarian aids in the context of natural disasters. The Cum-CVRPTW can be viewed as a combination of two NP-hard problems, i.e. the vehicle routing problem with time windows and the cumulative vehicle routing problem. To effectively address this problem, an effective algorithm is designed, which is based on the frameworks of Large Neighborhood Search Algorithm and hybridizes with Genetic Algorithm. The proposed algorithm adopts a constraint-relaxation scheme to extend the search space, enabling the iterative exploration of both the feasible and infeasible neighborhood solutions of an incumbent solution. Furthermore, some speed-up techniques are designed to reduce the computational complexity. To elucidate its effectiveness, the proposed algorithm is examined on the benchmark instances from the literature. The resultant numerical findings show that the algorithm is able to improve and obtain some best-known solutions found by existing state-of-the-art methods.

A POPMUSIC approach for the Multi-Depot Cumulative Capacitated Vehicle Routing Problem

The Multi-Depot Cumulative Capacitated Vehicle Routing Problem is a variation of the recently proposed Capacitated Cumulative Vehicle Routing Problem, where several depots can be considered as starting points of routes. Its objective aims at minimizing the sum of arrival times at customers for providing service. Practical considerations imply to address the delivery of customers from multiple depots where the service quality level depends on the customer waiting time and the delivering vehicles may be able to depart from different points. Those scenarios require theoretical models to support the decision-making process as well as for measuring the quality of the solutions provided by approximate approaches. In the present work, we formalize this new problem variant by means of a mathematical formulation and propose a matheuristic approach (POPMUSIC) for solving it.

The cumulative capacitated vehicle routing problem: New formulations and iterated greedy algorithms

In this work, we address the Cumulative Capacitated Vehicle Routing Problem (CCVRP), a variant of the classical CVRP, which aims to minimize the sum of the arrival times to customers instead of the total traveled distance. This problem is relevant due to its applications in fields such as emergency logistics, transportation, wireless network and computing, among others. This paper presents the first two tractable integer formulations capable of solving instances with up to 44 nodes and two versions of an Iterated Greedy procedure for dealing with larger instances. Experimental results show that both formulations obtain optimal solutions in a reasonable amount of computational time. Regarding the two metaheuristic procedures, they were able to reach optimal and best known solutions and, in some cases, outperform the bounds obtained by exact methods for tested instances with up to 199 customers. Using larger instances, the proposed metaheuristics showed competitive results when compared to the best known values reported in the literature, with a significant reduction in computational time.

A brain storm optimization approach for the cumulative capacitated vehicle routing problem

The cumulative capacitated vehicle routing problem (CCVRP) is a combinatorial optimization problem which aims to minimize the sum of arrival times at customers. This paper presents a brain storm optimization algorithm to solve the CCVRP. Based on the characteristics of the CCVRP, we design new convergent and divergent operations. The convergent operation picks up and perturbs the best-so-far solution. It decomposes the resulting solution into a set of independent partial solutions and then determines a set of subproblems which are smaller CCVRPs. Instead of directly generating solutions for the original problem, the divergent operation selects one of three operators to generate new solutions for subproblems and then assembles a solution to the original problem by using those new solutions to the subproblems. The proposed algorithm was tested on benchmark instances, some of which have more than 560 nodes. The results show that our algorithm is very effective in contrast to the existing algorithms. Most notably, the proposed algorithm can find new best solutions for 8 medium instances and 7 large instances within short time.

Skewed general variable neighborhood search for the cumulative capacitated vehicle routing problem

AbstractThe cumulative capacitated vehicle routing problem (CCVRP) is a relatively new version of the classical capacitated vehicle routing problem, and it is equivalent to a traveling repairman problem with capacity constraints and a homogeneous vehicle fleet, which aims to minimize the total arrival time at customers. Many real‐world applications can be modeled by this problem, such as the important application resulting from the humanitarian aid following a natural disaster. In this paper, two heuristics are proposed. The first one is a constructive heuristic to generate an initial solution and the second is the skewed variable neighborhood search (SVNS) heuristic. The SVNS algorithm starts with the initial solution. At each iteration, the perturbation phase and the local search phase are used to improve the solution of the CCVRP, and the distance function in acceptance criteria phase is used to improve the exploration of faraway valleys. This algorithm is applied to a set of benchmarks, and the comparison results show that the proposed algorithms provide better solutions than those reported in the previous literature on memetic algorithms and adaptive large neighborhood search heuristics.

The cumulative capacitated vehicle routing problem with min-sum and min-max objectives: An effective hybridisation of adaptive variable neighbourhood search and large neighbourhood search

The cumulative capacitated vehicle routing problem (CCVRP) is a relatively new variant of the classical capacitated vehicle routing problem in which the objective is to minimise the sum of arrival times at customers (min-sum) instead of the total route distance. While the literature for the CCVRP is scarce, this problem has useful applications especially in the area of supplying humanitarian aid after a natural disaster. In this paper, a two-stage adaptive variable neighbourhood search (AVNS) algorithm that incorporates large neighbourhood search (LNS) as a diversification strategy is proposed. When tested on the benchmark data sets, the results show that the proposed AVNS is highly competitive in producing new best known solutions to more than half of the instances. An alternative but related objective that minimises the maximum arrival time (min-max) is also explored in this study demonstrating the flexibility and the effectiveness of the proposed metaheuristic. To the best of our knowledge, this is the first study that exploits the min-max objective of the CCVRP in addition to providing extensive computational results for a large number of instances for the min-sum. As a by-product of this study, managerial insights for decision making are also presented.

A mixed integer formulation and an efficient metaheuristic procedure for the k-Travelling Repairmen Problem

In this paper, we study a k-Travelling Repairmen Problem where the objective is to minimize the sum of clients waiting time to receive service. This problem is relevant in applications that involve distribution of humanitarian aid in disaster areas, delivery and collection of perishable products and personnel transportation, where reaching demand points to perform service, fast and fair, is a priority. This paper presents a new mixed integer formulation and a simple and efficient metaheuristic algorithm. The proposed formulation consumes less computational time and allows solving to optimality more than three times larger data instances than the previous formulation published in literature, even outperforming a recently published Branch and Price and Cut algorithm for this problem. The proposed metaheuristic algorithm solved to optimality 386 out of 389 tested instances in a very short computational time. For larger instances, the algorithm was assessed using the best results reported in the literature for the Cumulative Capacitated Vehicle Routing Problem.

TWO-PHASE ALGORITHM FOR SOLVING HETEROGENEOUS TRAVELLING REPAIRMEN PROBLEM WITH TIME WINDOWS

Heterogeneous travelling repairmen problem with time windows (hetTRPTW) is customer oriented problem with large possibilities for practical applications in logistics area. Models and algorithms developed for solving one problem with a cumulative objective function may be, with a little effort, transformed for solving similar problem with a cumulative function. In that sense, aim of this paper is to present results obtained by implementing an algorithm developed for solving cumulative capacitated vehicle routing problem in solving hetTRPTW.