Algorithm For Vehicle Routing Problem Research Articles

A competitive heuristic algorithm for vehicle routing problems with drones

We propose a heuristic algorithm capable of handling multiple variants of the vehicle routing problem with drones (VRPD). Assuming that the drone may be launched from a node and recovered at another, these variants are characterized by three axes, (1) minimizing the transportation cost or minimizing the makespan, (2) the drone is either allowed or not allowed to land while awaiting recovery, and (3) single or multiple trucks each equipped with a drone. In our algorithm, we represent a VRPD solution as a set of customer sequences and evaluate it via local search procedures solving for each sequence a problem that we refer to as the fixed route drone dispatch problem (FRDDP). Given a sequence of customers to be served by a single truck and its drone, the FRDDP selects a subset of customers to be served by the drone and determines drone launch and recovery nodes, while ensuring that each such customer is positioned between two nodes in the initial sequence. We introduce a heuristic dynamic program (HDP) to solve the FRDDP with reduced computational complexity compared to an exact solution algorithm for the problem. We reinforce our algorithm by developing filtering strategies based on the HDP. We benchmark the performance of our algorithm on nine benchmark sets pertaining to four VRPD variants resulting in 932 instances. Our algorithm computes 651 of 680 optimal solutions and identifies 189 new best-known solutions.

A discrete Jaya algorithm for vehicle routing problems with uncertain demands

Vehicle Routing Problem with Uncertain Demands (VRPUD) is one of the research hotspots in the field of logistics scheduling. In this paper, a Discrete Jaya (DJaya) algorithm is presented for the VRPUD to minimize the total cost. A novel dividing-point-based coding scheme is designed to represent solutions with higher robustness. In addition, an efficient repair strategy is embedded into the decoding process to avoid the failure of producing feasible solutions. The best and worst solutions are employed to generate offspring solutions in DJaya. Several efficient local search methods are also presented to enhance the exploitation ability and increase the diversity of solutions. Based on the benchmark data sets of the VRPUD, numerical simulations are carried out for the proposed DJaya algorithm with uncertain demands. Computational results and comparisons with the state-of-the-art algorithms demonstrate the superiority of the proposed algorithm in solving VRPUD.

Three-stage multi-modal multi-objective differential evolution algorithm for vehicle routing problem with time windows

In this paper, the mathematical model of Vehicle Routing Problem with Time Windows (VRPTW) is established based on the directed graph, and a 3-stage multi-modal multi-objective differential evolution algorithm (3S-MMDEA) is proposed. In the first stage, in order to expand the range of individuals to be selected, a generalized opposition-based learning (GOBL) strategy is used to generate a reverse population. In the second stage, a search strategy of reachable distribution area is proposed, which divides the population with the selected individual as the center point to improve the convergence of the solution set. In the third stage, an improved individual variation strategy is proposed to legalize the mutant individuals, so that the individual after variation still falls within the range of the population, further improving the diversity of individuals to ensure the diversity of the solution set. Based on the synergy of the above three stages of strategies, the diversity of individuals is ensured, so as to improve the diversity of solution sets, and multiple equivalent optimal paths are obtained to meet the planning needs of different decision-makers. Finally, the performance of the proposed method is evaluated on the standard benchmark datasets of the problem. The experimental results show that the proposed 3S-MMDEA can improve the efficiency of logistics distribution and obtain multiple equivalent optimal paths. The method achieves good performance, superior to the most advanced VRPTW solution methods, and has great potential in practical projects.

A Discrete Salp Swarm Algorithm for Vehicle Routing Problem with Time Windows

A Discrete Salp Swarm Algorithm for Vehicle Routing Problem with Time Windows

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

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

An Integer L-shaped algorithm for vehicle routing problem with simultaneous delivery and stochastic pickup

This paper addresses an exact algorithm for vehicle routing problem with simultaneous pickup and delivery in which customer demands to be collected are stochastic. The problem is modeled as a two-stage stochastic programming problem with recourse, in which routing decisions are made based on known delivery demand and deterministic expected pickup demand in the first stage and recourse actions are made in the second stage when stochastic pickup quantities have been revealed. However, failures happen when the load of the vehicle is insufficient to meet the observed pickup demand of a customer. Three recourse policies are proposed to help deal with the failures to proceed with the routing decisions in the first stage. The Integer L-shaped algorithmic framework is used to solve this two-stage stochastic programming problems with recourse. Furthermore, effective lower bounding of the expected recourse cost of partial routes is designed for the three recourse policies, respectively. Computational experiments on the newly generated instances compare the performance of the Integer L-shaped algorithm under the three recourse policies, and the conclusion is validated via numerous simulations. The effectiveness of the proposed lower bounding functionals is confirmed through reduced optimality gaps and lower computing times.

A two‐stage algorithm for vehicle routing problem with charging relief in post‐disaster

AbstractThis paper first investigates emergency transportation for power recovery in post‐disaster. The problem is formulated as a mixed‐integer linear programming model called vehicle routing problem with charging relief (VRPCR). The battery state of charge () implies the working hours that the battery can provide. The goal is to make a set of shelters charge before the battery of shelters reaches the minimum bound over time. To this end, a two‐stage algorithm is developed to deal with the problem. In stage I, a reduced road network is obtained from a leading road network by the A‐star search algorithm. Subsequently, to determine the order of power delivery with charging operations at shelters by enhanced genetic algorithm (EGA) in stage II. To evaluate this strategy, the detailed complexity analysis of the three algorithms and results tested on a realistic disaster scenario shows the performance of the A‐star search algorithm for VRPCR that outperforms the Dijkstra and Floyd algorithms. In addition, the EGA is applied to Solomon's benchmarks compared with the state‐of‐the‐art heuristic algorithms, which indicates a better performance of EGA. A real case obtained from a disaster scenario in Ichihara City, Japan is also conducted. Simulation results demonstrate that the method can achieve satisfactory solutions.

Solution Algorithm for Vehicle Routing Problem with Stochastic Demand

Solution Algorithm for Vehicle Routing Problem with Stochastic Demand

Solution Algorithm for Vehicle Routing Problem with Stochastic Demand

Solution Algorithm for Vehicle Routing Problem with Stochastic Demand

An adaptive large neighborhood search algorithm for Vehicle Routing Problem with Multiple Time Windows constraints

<p style='text-indent:20px;'>The Vehicle Routing Problem with Multiple Time Windows (VRPMTW) is a generalization of problems in real life logistics distribution, which has a wide range of applications and research values. Several neighborhood search based methods have been used to solve this kind of problem, but it still has drawbacks of generating numbers of infeasible solutions and falling into local optimum easily. In order to solve the problem of arbitrary selection for neighborhoods, a series of neighborhoods are designed and an adaptive strategy is used to select the neighborhood, which constitute the Adaptive Large Neighborhood Search(ALNS) algorithm framework. For escaping from the local optimum effectively in the search process, a local search based on destroy and repair operators is applied to shake the solution by adjusting the number of customers. The proposed method allows infeasible solutions to participate in the iterative process to expand the search space. At the same time, an archive is set to save the high-quality feasible solutions during the search process, and the infeasible solutions are periodically replaced. Computational experimental results on VRPMTW benchmark instances show that the proposed algorithm is effective and has obtained better solutions.</p>

Fuzzy c-means and simulated annealing for planar location-routing problem

Location-routing problem (LRP) contains two Np-hard problems as, facility location (FL) and vehicle routing problem (VRP), in the same content. Since both problems directly affect the cost of distributions of the products and supply chain, the decision of location and routing is important for the success of companies. Therefore, many attempts are made to solve LRP problem in the literature. Researchers proposed exact and heuristic methods for LRP. However, exact methods cannot provide solutions for considerably large instances. In this paper, a new heuristic method is proposed for continuous or planar LRP. The proposed method contains fuzzy c-means for continuous location problem and simulated annealing algorithm for vehicle routing problem, respectively. The proposed method is applied to both capacitated and uncapacitated LRP instances that are widely used in the literature. Results of the proposed method are compared with successful researches that are made on this problem in terms of the total cost.

An improved multi-directional local search algorithm for vehicle routing problem with time windows and route balance

An improved multi-directional local search algorithm for vehicle routing problem with time windows and route balance

An Improved Ant Colony Optimization Algorithm for Vehicle Routing Problem with Time Windows

Distribution plays an important role in the supply chain system. One of the critical problems in distribution is the vehicle routing problem. This research proposes the Improved Ant Colony Optimization (IACO) algorithm to solve the Vehicle Routing Problem with Time Windows (VRPTW). The main objective is to minimize the total vehicle mileage by considering the vehicle capacity and customer time windows. The proposed IACO algorithm is inspired by the conventional Ant Colony Optimization (ACO) algorithm by adding local search and mutation processes. Numerical experiments were conducted to test that the routes generated did not violate the customer's time window constraints. In addition, this study also compares the proposed IACO algorithm routes with other metaheuristic algorithms, namely ACO classic and Tabu Search. In addition, this investigation was carried out by experimenting with the number of iterations. The results of numerical experiments prove that the proposed IACO algorithm can minimize the total vehicle mileage without violating capacity constraints and time windows.

An Estimated-Travel-Time Data Scraping and Analysis Framework for Time-Dependent Route Planning

Generally, a courier company needs to employ a fleet of vehicles to travel through a number of locations in order to provide efficient parcel delivery services. The route planning of these vehicles can be formulated as a vehicle routing problem (VRP). Most existing VRP algorithms assume that the traveling durations between locations are time invariant; thus, they normally use only a set of estimated travel times (ETTs) to plan the vehicles’ routes; however, this is not realistic because the traffic pattern in a city varies over time. One solution to tackle the problem is to use different sets of ETTs for route planning in different time periods, and these data are collectively called the time-dependent estimated travel times (TD-ETTs). This paper focuses on a low-cost and robust solution to effectively scrape, process, clean, and analyze the TD-ETT data from free web-mapping services in order to gain the knowledge of the traffic pattern in a city in different time periods. To achieve the abovementioned goal, our proposed framework contains four phases, namely, (i) Full Data Scraping, (ii) Data Pre-Processing and Analysis, (iii) Fast Data Scraping, and (iv) Data Patching and Maintenance. In our experiment, we used the above framework to obtain the TD-ETT data across 68 locations in Penang, Malaysia, for six months. We then fed the data to a VRP algorithm for evaluation. We found that the performance of our low-cost approach is comparable with that of using the expensive paid data.

Meta Heuristic Algorithm for Vehicle Routing Problem with Uncertainty in Customer Demand

The Vehicle Routing Problem is an optimization problem with number of applications in the transportation field. In this paper, Vehicle Routing Problem (VRP) with uncertainty in customer demand is considered. Often in real world situation, the information on demand on each customer is not accurate enough. Here, in this article we are assuming that the customer demands in each time period are uncertain and are considered as fuzzy variables. This kind of problem is known as an NP-hard problem. The main purpose of this article is to give conceptual and practical idea on how fuzzy logic with meta heuristic algorithm can be implemented to improve the optimization of vehicle routing problem with uncertainty in customer demand. To solve this problem, a hybrid Meta heuristic algorithm (HMHA) including clustering is proposed, with the objective of determining an optimal route to minimize the total cost.

A fuzzy multi-criteria approach based on Clarke and Wright savings algorithm for vehicle routing problem in humanitarian aid distribution

A fuzzy multi-criteria approach based on Clarke and Wright savings algorithm for vehicle routing problem in humanitarian aid distribution

Adapted Fuzzy Multi-Objective Programming Algorithm for Vehicle Routing

The vehicle routing problem (VRP) is a well-known problem in the logistics sector. In this study, two objectives, minimizing the total distance and maximizing the saving value, were considered in VRP with a fuzzy environment. The game theory approach is proposed for determining the weights of objectives when decision-makers have insufficient knowledge of assigning the weights. Thus, a fuzzy pay-off matrix is proposed for determining the weights of objectives by combining the fuzzy two-person zero-sum game with mixed strategies (FTZG with MS) and membership functions. Therefore, the fuzzy multi-objective programming (FMOP) model is adapted to the VRP model, which is named Adapted FMOP algorithm for VRP. Proposed algorithm clusters customers according to two objectives and by using four fuzzy operators, and routes customers with the traveling salesman problem (TSP) model in order to avoid the non-deterministic polynomial-time hardness (NP-hard) structure of VRP. In the end, the results are improved using local search methods. The main contribution of the Adapted FMOP algorithm for VRP is that it provides a solution that considers more than one objective without the need for decision makers’ view on the weights of objectives in all decision models in the fuzzy environment. Also, the proposed algorithm can find the solution with the help of a mathematical model without requiring any heuristics or metaheuristics, since it primarily performs clustering. Firstly, the efficiency of this algorithm was tested on problems in the literature. The Adapted FMOP algorithm for VRP achieved the best-known solutions by some small margins and exceeded the best-known solution for one problem in the literature. After seeing that the performance of the algorithm was sufficient, a data set of a firm in the construction sector was implemented to see how the algorithm works in real life and the obtained results were discussed. The solutions demonstrate that the Adapted FMOP algorithm for VRP also works well for real-world problems.

Alibaba Vehicle Routing Algorithms Enable Rapid Pick and Delivery

Alibaba Group pioneered integrated online and offline retail models to allow customers to place online orders of e-commerce and grocery products at its participating stores or restaurants for rapid delivery—in some cases, in as little as 30 minutes after an order has been placed. To meet these service commitments, quick online routing decisions must be made to optimize order picking routes at warehouses and delivery routes for drivers. The solutions to these routing problems are complicated by stringent service commitments, uncertainties, and complex operations in warehouses with limited space. Alibaba has developed a set of algorithms for vehicle routing problems (VRPs), which include an open-architecture adaptive large neighborhood search to support the solution of variants of routing problems and a deep learning-based approach that trains neural network models offline to generate almost instantaneous solutions online. These algorithms have been implemented to solve VRPs in several Alibaba subsidiaries, have generated more than $50 million in annual financial savings, and are applicable to the broader logistics industry. The success of these algorithms has fermented an inner-source community of operations researchers within Alibaba, boosted the confidence of the company’s executives in operations research, and made operations research one of the core competencies of Alibaba Group.

Flower Pollination Algorithm for Vehicle Routing Problem with Time Windows (VRPTW)

Vehicle Routing Problem with Time Windows (VRPTW) is a vehicle route deciding problem that is used in order to serve customer who involved more than one vehicle with a limited time, so as a minimum distance route is obtained without disobeying vehicle capacity cargo restriction and time range. Flower Pollination Algorithm (FPA) is an algorithm which inspires from nature and that is flower pollination process toward a plant. Within an FPA, there are two main steps to use, they are global flower pollination and local flower pollination. Those two steps are determined by using switch probability parameter. This program is made in Java language program to apply FPA in solving VRPTW which is implemented in three example cases, they are small-scale datum with 25 customers, medium-scale datum with 50 customers, and big-scale datum with 100 customers. According to the results, it can be concluded that the larger number of flowers and iterations can affect the number of total minimum travel distance become smaller. Furthermore, a better total minimum travel distances also will be obtained if the value of switch probability parameter is larger.

Multi-objective evolutionary algorithm for vehicle routing problem with time window under uncertainty

Multi-objective evolutionary algorithm for vehicle routing problem with time window under uncertainty