Showing papers on "Vehicle routing problem published in 2022"

Research on the Time-Dependent Split Delivery Green Vehicle Routing Problem for Fresh Agricultural Products with Multiple Time Windows

Abstract: Due to the diversity and the different distribution conditions of agricultural products, split delivery plays an important role in the last mile distribution of agricultural products distribution. The time-dependent split delivery green vehicle routing problem with multiple time windows (TDSDGVRPMTW) is studied by considering both economic cost and customer satisfaction. A calculation method for road travel time across time periods was designed. A satisfaction measure function based on a time window and a measure function of the economic cost was employed by considering time-varying vehicle speeds, fuel consumption, carbon emissions and customers’ time windows. The object of the TDSDGVRPMTW model is to minimize the sum of the economic cost and maximize average customer satisfaction. According to the characteristics of the model, a variable neighborhood search combined with a non-dominated sorting genetic algorithm II (VNS-NSGA-II) was designed. Finally, the experimental data show that the proposed approaches effectively reduce total distribution costs and promote energy conservation and customer satisfaction.

Vehicle routing problem with drones considering time windows

Abstract: The cooperation of trucks and unmanned aerial vehicles (UAV) has become a new delivery method in the area of logistics and transportation. In this form of cooperation, the trucks are not only able to provide services to the customers, but also serve as a ‘launch pad’ for the drones, in which the drones can be launched to service a customer and then recovered at the rendezvous node. This study intends to explore this cooperation by developing a model for the vehicle routing problem with drones that considers the presence of customer time windows (VRPTWD). A mixed-integer programming (MIP) model is presented to minimize the total travelling costs. Then, a simple yet effective variable neighborhood search (VNS) procedure with a novel solution representation is proposed as a solver. The numerical results indicate the ability of the proposed VNS to solve the VRPTWD, as well as the improvement of delivery performance using drones.

Learning Improvement Heuristics for Solving Routing Problems

Abstract: Recent studies in using deep learning (DL) to solve routing problems focus on construction heuristics, whose solutions are still far from optimality. Improvement heuristics have great potential to narrow this gap by iteratively refining a solution. However, classic improvement heuristics are all guided by handcrafted rules that may limit their performance. In this article, we propose a deep reinforcement learning framework to learn the improvement heuristics for routing problems. We design a self-attention-based deep architecture as the policy network to guide the selection of the next solution. We apply our method to two important routing problems, i.e., the traveling salesman problem (TSP) and the capacitated vehicle routing problem (CVRP). Experiments show that our method outperforms state-of-the-art DL-based approaches. The learned policies are more effective than the traditional handcrafted ones and can be further enhanced by simple diversifying strategies. Moreover, the policies generalize well to different problem sizes, initial solutions, and even real-world data set.

Collaborative truck multi-drone routing and scheduling problem: Package delivery with flexible launch and recovery sites

Abstract: This paper deals with the problem of coordinating a truck and multiple heterogeneous unmanned aerial vehicles (UAVs or drones) for last-mile package deliveries. Existing literature on truck–drone tandems predominantly restricts the UAV launch and recovery operations (LARO) to customer locations. Such a constrained setting may not be able to fully exploit the capability of drones. Moreover, this assumption may not accurately reflect the actual delivery operations. In this research, we address these gaps and introduce a new variant of truck–drone tandem that allows the truck to stop at non-customer locations (referred to as flexible sites) for drone LARO. The proposed variant also accounts for three key decisions — (i) assignment of each customer location to a vehicle, (ii) routing of truck and UAVs, and (iii) scheduling drone LARO and truck operator activities at each stop, which are always not simultaneously considered in the literature. A mixed integer linear programming model is formulated to jointly optimize the three decisions with the objective of minimizing the delivery completion time (or makespan). To handle large problem instances, we develop an optimization-enabled two-phase search algorithm by hybridizing simulated annealing and variable neighborhood search. Numerical analysis demonstrates substantial improvement in delivery efficiency of using flexible sites for LARO as opposed to the existing approach of restricting truck stop locations. Finally, several insights on drone utilization and flexible site selection are provided based on our findings.

A multi-agent approach to the truck multi-drone routing problem

Abstract: • Truck-n-drone routing problem coded as a grid in which locations-agents can move. • Agent-based approach in which locations to be visited are the agents instead of orders or vehicles. • Battery capacity constraints and multiple customer’s visits per flight allowed. • Better performance of agent-based approach than that of other meta-heuristics in large problem instances. In this work, we address the Truck-multi-Drone Team Logistics Problem (TmDTL), devoted to visit a set of points with a truck helped by a team of unmanned aerial vehicles (UAVs) or drones in the minimum time, starting at a certain location and ending at a different one. It is an enhanced version of the multiple Flying Sidekicks Traveling Salesman Problem (mFSTSP) presented in Murray and Raj (2020) wherein drones are allowed to visit several customers per trip. In order to cope with large instances of the complex TmDTL, we have developed a novel agent-based method where agents represent the points that are going to be visited by vehicles. Agents evolve by means of movement inside a grid (locations vs. vehicles) according to a set of rules in the seek of better objective function values. Each agent needs to explore only a fraction of the complete problem, sharing its progress with the rest of the agents which are coordinated by one central agent which helps to maintain an asynchronous memory of solutions – e.g. on the control of the mechanism to escape from local minima. Our agent-based approach is firstly tested using the largest instances of the single TDTL problem reported in the literature, which additionally serves as upper bounds to the TmDTL problem. Secondly, we have solved instances up to 500 locations with up to 6 drones in the fleet. Thirdly, we have tested the behavior of our approach in 500 locations problems with up to 8 drones in order to test the fleet size sensitivity. Our experiments demonstrate the ability of the proposed agent-based system to obtain good quality solutions for complex optimization problems that arise. Further, the abstraction in solutions coding applied makes the agent-based approach scalable and flexible enough to be applied to a wide range of other optimization problems.

A Bilevel Ant Colony Optimization Algorithm for Capacitated Electric Vehicle Routing Problem

Abstract: The development of electric vehicle (EV) techniques has led to a new vehicle routing problem (VRP) called the capacitated EV routing problem (CEVRP). Because of the limited number of charging stations and the limited cruising range of EVs, not only the service order of customers but also the recharging schedules of EVs should be considered. However, solving these two aspects of the problem together is very difficult. To address the above issue, we treat CEVRP as a bilevel optimization problem and propose a novel bilevel ant colony optimization algorithm in this article, which divides CEVRP into two levels of subproblem: 1) capacitated VRP and 2) fixed route vehicle charging problem. For the upper level subproblem, the electricity constraint is ignored and an order-first split-second max-min ant system algorithm is designed to generate routes that fulfill the demands of customers. For the lower level subproblem, a new effective heuristic is designed to decide the charging schedule in the generated routes to satisfy the electricity constraint. The objective values of the resultant solutions are used to update the pheromone information for the ant system algorithm in the upper level. Through good orchestration of the two components, the proposed algorithm can significantly outperform state-of-the-art algorithms on a wide range of benchmark instances.

Collaborative multicenter vehicle routing problem with time windows and mixed deliveries and pickups

Abstract: This study focuses on the collaborative multicenter vehicle routing problem with time windows and mixed deliveries and pickups (CMVRPTWMDP), which is a variant of the vehicle routing problem (VRP) with mixed deliveries and pickups, and VRP with simultaneous deliveries and pickups and time windows. Collaboration and transportation resource sharing are adopted to optimize vehicle routes in the CMVRPTWMDP, to integrate the delivery and pickup services with time windows, and to construct open–closed mixed vehicle routes. First, the CMVRPTWMDP is formulated as a mixed-integer programming model to minimize logistics operating costs. The effect of transportation resource sharing on reducing the number of needed vehicles and the maintenance cost is considered in the model formulation. Second, a two-stage hybrid algorithm combining customer clustering and vehicle routing optimization is designed to solve the CMVRPTWMDP. An improved 3D k-means clustering algorithm based on space–time distances and the customer demand is proposed to reassign customers to logistics facilities (e.g., delivery or pickup centers). Furthermore, a hybrid heuristic algorithm that combines the genetic algorithm (GA) and particle swarm optimization (PSO) algorithm, called GA–PSO, is designed to optimize the vehicle routes. A coordination operator between GA and PSO is designed to allow particles and chromosomes to interact, increasing the diversity of particle swarms and the possibility of finding a feasible solution. Third, the performance and effectiveness of the proposed approach are tested by comparing them with the CPLEX solver using 30 small-scale instances and other existing algorithms using 25 benchmark instances. Fourth, the minimum costs-remaining savings (MCRS) model is adopted to design a fair and reasonable profit allocation scheme for participants in the collaborative alliance and maintain alliance stability. Finally, the optimization results of a real-world case study from Chongqing, China, show that transportation resource misuse and logistics operating costs are significantly reduced, demonstrating the proposed approach’s effectiveness and applicability. This study provides insights for logistics enterprises and transportation departments on effectively allocating and utilizing the transportation resources and optimizing the local logistics network.

The Electric Vehicle Routing Problem with Capacitated Charging Stations

Abstract: Electric vehicle routing problems (E-VRPs) deal with routing a fleet of electric vehicles (EVs) to serve a set of customers while minimizing an operational criterion, for example, cost or time. The feasibility of the routes is constrained by the autonomy of the EVs, which may be recharged along the route. Much of the E-VRP research neglects the capacity of charging stations (CSs) and thus implicitly assumes that an unlimited number of EVs can be simultaneously charged at a CS. In this paper, we model and solve E-VRPs considering these capacity restrictions. In particular, we study an E-VRP with nonlinear charging functions, multiple charging technologies, en route charging, and variable charging quantities while explicitly accounting for the number of chargers available at privately managed CSs. We refer to this problem as the E-VRP with nonlinear charging functions and capacitated stations (E-VRP-NL-C). We introduce a continuous-time model formulation for the problem. We then introduce an algorithmic framework that iterates between two main components: (1) the route generator, which uses an iterated local search algorithm to build a pool of high-quality routes, and (2) the solution assembler, which applies a branch-and-cut algorithm to combine a subset of routes from the pool into a solution satisfying the capacity constraints. We compare four assembly strategies on a set of instances. We show that our algorithm effectively deals with the E-VRP-NL-C. Furthermore, considering the uncapacitated version of the E-VRP-NL-C, our solution method identifies new best-known solutions for 80 of 120 instances.

Deep Reinforcement Learning for the Electric Vehicle Routing Problem With Time Windows

Abstract: The past decade has seen a rapid penetration of electric vehicles (EVs) as more and more logistics and transportation companies start to deploy electric vehicles (EVs) for service provision. In order to model the operations of a commercial EV fleet, we utilize the EV routing problem with time windows (EVRPTW). In this paper, we propose an end-to-end deep reinforcement learning framework to solve the EVRPTW. In particular, we develop an attention model incorporating the pointer network and a graph embedding layer to parameterize a stochastic policy for solving the EVRPTW. The model is then trained using policy gradient with rollout baseline. Our numerical studies show that the proposed model is able to efficiently solve EVRPTW instances of large sizes that are not solvable with current existing approaches.

Deep Reinforcement Learning for Solving the Heterogeneous Capacitated Vehicle Routing Problem

Abstract: Existing deep reinforcement learning (DRL)-based methods for solving the capacitated vehicle routing problem (CVRP) intrinsically cope with a homogeneous vehicle fleet, in which the fleet is assumed as repetitions of a single vehicle. Hence, their key to construct a solution solely lies in the selection of the next node (customer) to visit excluding the selection of vehicle. However, vehicles in real-world scenarios are likely to be heterogeneous with different characteristics that affect their capacity (or travel speed), rendering existing DRL methods less effective. In this article, we tackle heterogeneous CVRP (HCVRP), where vehicles are mainly characterized by different capacities. We consider both min–max and min–sum objectives for HCVRP, which aim to minimize the longest or total travel time of the vehicle(s) in the fleet. To solve those problems, we propose a DRL method based on the attention mechanism with a vehicle selection decoder accounting for the heterogeneous fleet constraint and a node selection decoder accounting for the route construction, which learns to construct a solution by automatically selecting both a vehicle and a node for this vehicle at each step. Experimental results based on randomly generated instances show that, with desirable generalization to various problem sizes, our method outperforms the state-of-the-art DRL method and most of the conventional heuristics, and also delivers competitive performance against the state-of-the-art heuristic method, that is, slack induction by string removal. In addition, the results of extended experiments demonstrate that our method is also able to solve CVRPLib instances with satisfactory performance.

Deep Policy Dynamic Programming for Vehicle Routing Problems

Abstract: AbstractRouting problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical dynamic programming (DP) algorithms guarantee optimal solutions, but scale badly with the problem size. We propose Deep Policy Dynamic Programming (DPDP), which aims to combine the strengths of learned neural heuristics with those of DP algorithms. DPDP prioritizes and restricts the DP state space using a policy derived from a deep neural network, which is trained to predict edges from example solutions. We evaluate our framework on the travelling salesman problem (TSP), the vehicle routing problem (VRP) and TSP with time windows (TSPTW) and show that the neural policy improves the performance of (restricted) DP algorithms, making them competitive to strong alternatives such as LKH, while also outperforming most other ‘neural approaches’ for solving TSPs, VRPs and TSPTWs with 100 nodes.KeywordsDynamic ProgrammingDeep LearningVehicle Routing

A Deep Reinforcement Learning Approach to Ride-Sharing Vehicle Dispatching in Autonomous Mobility-on-Demand Systems

Abstract: This paper investigates a ride-sharing vehicle dispatching and routing problem in ride-sharing autonomous mobility-on-demand systems. We present a new method that can optimize both operation cost and passenger quality of service in a global and farsighted view by leveraging the historical data. It comprises two parts, one for vehicle routing decision making and the other for request-vehicle assignment. In particular, the vehicle routing decision making procedure is formulated as a Markov decision process considering idle vehicle rebalancing, with properly designed states, actions, and rewards. By sampling the future requests according to the historical probability distribution, the look-ahead decision making is realized via a deep reinforcement learning framework, which is composed of a Convolutional Neural Network and a double deep Q-learning module. Then a request-vehicle assignment scheme is presented based on the learning value attained from vehicle routing. Satisfactory performances (e.g, service rate, average waiting time and travel distance) of the method are demonstrated by experimental results under various fleet sizes and different vehicle capacities.

The Electric Vehicle Routing Problem with Drones: An Energy Minimization Approach for Aerial Deliveries

Abstract: This paper introduces the Electric Vehicle Routing Problem with Drones (EVRPD), the first VRP combining electric ground vehicles (EVs) with unmanned aerial vehicles (UAVs), also known as drones, in order to deliver packages to customers. The problem’s objective is to minimize the total energy consumption, focusing on the main non-constant and controllable factor of energy consumption on a delivery vehicle, the payload weight. The problem considers same-sized packages, belonging to different weight classes. EVs serve as motherships, from which drones are deployed to deliver the packages. Drones can carry multiple packages, up to a certain weight limit and their range is depended on their payload weight. For solving the EVRPD, four algorithms of the Ant Colony Optimization framework are implemented, two versions of the Ant Colony System and the Min–Max Ant System. A Variable Neighborhood Descent algorithm is utilized in all variants as a local search procedure. Instances for the EVRPD are created based on the two-echelon VRP literature and are used to test the proposed algorithms. Their computational results are compared and discussed. Practical, real-life scenarios of the EVRPD application are also presented and solved.

Goods Delivery with Electric Vehicles: Electric Vehicle Routing Optimization with Time Windows and Partial or Full Recharge

Abstract: With the rise of the electric vehicle market share, many logistic companies have started to use electric vehicles for goods delivery. Compared to the vehicles with an internal combustion engine, electric vehicles are considered as a cleaner mode of transport that can reduce greenhouse gas emissions. As electric vehicles have a shorter driving range and have to visit charging stations to replenish their energy, the efficient routing plan is harder to achieve. In this paper, the Electric Vehicle Routing Problem with Time Windows (EVRPTW), which deals with the routing of electric vehicles for the purpose of goods delivery, is observed. Two recharge policies are considered: full recharge and partial recharge. To solve the problem, an Adaptive Large Neighborhood Search (ALNS) metaheuristic based on the ruin-recreate strategy is coupled with a new initial solution heuristic, local search, route removal, and exact procedure for optimal charging station placement. The procedure for the O(1) evaluation in EVRPTW with partial and full recharge strategies is presented. The ALNS was able to find 38 new best solutions on benchmark EVRPTW instances. The results also indicate the benefits and drawbacks of using a partial recharge strategy compared to the full recharge strategy.

Vehicle routing problems over time: a survey

Abstract: In vehicle routing problems (VRPs) the decisions to be taken concern the assignment of customers to vehicles and the sequencing of the customers assigned to each vehicle. Additional decisions may need to be jointly taken, depending on the specific problem setting. In this paper, after discussing the different kinds of decisions taken in different classes of VRPs, the class where the decision about when the routes start from the depot has to be taken is considered and the related literature is reviewed. This class of problems, that we call VRPs over time, includes the periodic routing problems, the inventory routing problems, the vehicle routing problems with release dates, and the multi-trip vehicle routing problems.