GRASP with path relinking for the selective pickup and delivery problem

Bike sharing systems are very popular nowadays. One of the characteristics is that bikes are picked up from some surplus bike stations and transported to all deficit bike stations by a repositioning vehicle with limited capacity to satisfy the demand of deficit bike stations. Motivated by this real world bicycle repositioning problem, we study the selective pickup and delivery problem, where demand at every delivery node has to be satisfied by the supply collected from a subset of pickup nodes. The objective is to minimize the total travel cost incurred from visiting the nodes. We present a GRASP with path-relinking for solving the described problem. Experimental results show that this simple heuristic improves the existing results in the literature with an average improvement of 5.72% using small computing times. The proposed heuristic can contribute to the development of effective and efficient algorithms for real world bicycle reposition operations.     

一种求解多校多车型校车路径问题的元启发算法

针对多种车型可用的多校校车路径问题(SBRP),建立数学模型,并提出了一种迭代局部搜索(ILS)元启发算法进行求解。该算法引入并改进了带时间窗的装卸一体化问题(PDPTW)求解中的点对邻域算子,并使用可变邻域下降搜索(VND)完成局部提升。局部提升过程中,设计一种基于路径段的车型调整策略,尽可能地调整车型,降低成本,并允许接受一定偏差范围内的邻域解以保证搜索的多样性。对于局部提升得到的最好解,使用多点移动方法对其进行扰动,以避免算法过早陷入局部最优。在国际基准测试案例上分别测试多校混载和不混载模式下算法的性能,实验结果验证了设计算法的有效性。进一步使用提出的算法求解单车型多校SBRP问题,并与后启发算法、模拟退火算法和记录更新法等算法进行比较,实验结果表明该算法仍然能够获得较好的优化效果。     

考虑卸载顺序约束的成品油二次配送车辆路径问题

研究考虑卸载顺序约束的成品油二次配送车辆路径问题,已知油库使用容量有限的多隔舱运输槽车为加油站配送多种类型的成品油,每个隔舱只能装载一种特定的油品,且装载到各个隔舱中的油品具有固定的卸载顺序.已知加油站对各种油品的需求量,假设每个加油站对同一种油品的需求只能由一辆车配送,考虑配送车辆的固定动用成本和运输成本,以总配送成本极小化为目标建立该问题的混合整数规划模型,并设计求解模型的自适应大邻域搜索启发式算法.利用不同规模的算例进行模拟计算与分析,从而验证算法的有效性.实验结果显示:对于小规模算例,大邻域搜索启发式算法能够以较高的概率得到全局最优解;对于中、大规模算例,大邻域搜索启发式算法可以在短时间内得到近似最优解,近似比不超过1.2.所提出的模型和算法可为石油公司制定成品油二次配送计划提供理论依据和决策支持.     

Variable Neighborhood Search heuristic for the Inventory Routing Problem in fuel delivery

In this paper we observe the extension of the vehicle routing problem (VRP) in fuel delivery that includes petrol stations inventory management and which can be classified as the Inventory Routing Problem (IRP) in fuel delivery. The objective of the IRP is to minimize the total cost of vehicle routing and inventory management. We developed a Variable Neighborhood Search (VNS) heuristic for solving a multi-product multi-period IRP in fuel delivery with multi-compartment homogeneous vehicles, and deterministic consumption that varies with each petrol station and each fuel type. The stochastic VNS heuristic is compared to a Mixed Integer Linear Programming (MILP) model and the deterministic “compartment transfer” (CT) heuristic. For three different scale problems, with different vehicle types, the developed VNS heuristic outperforms the deterministic CT heuristic. Also, for the smallest scale problem instances, the developed VNS was capable of obtaining the near optimal and optimal solutions (the MILP model was able to solve only the smallest scale problem instances).     

Iterated local search heuristics for the Vehicle Routing Problem with Cross-Docking

This work addresses the Vehicle Routing Problem with Cross-Docking (VRPCD). The problem consists in defining a minimum cost set of routes for a fleet of vehicles that meets the demands of products for a set of suppliers and customers. The vehicles leave a single Cross-Dock (CD) towards the suppliers, pick up products and return to the CD, where products can be exchanged before being delivered to their customers. The vehicle routes must respect the vehicle capacity constraints, as well as the time window constraints. We adapted a constructive heuristic and six local search procedures from the literature of VRP, and made them efficient in the presence of the synchronization constraints of VRPCD. Besides, we propose three Iterated Local Search (Lourenço et al., 2010) heuristics for VRPCD. The first heuristic is a standard implementation of ILS, while the second extends the classic ILS framework by keeping a set of elite solutions, instead of a single current solution. The latter set is used in a restart procedure. As far as we can tell, this is the first ILS heuristic in the literature that keeps a population of current elite solutions. The third heuristic is an extension of the second that relies on an intensification procedure based on an Integer Programming formulation for the Set Partitioning problem. The latter allows a neighborhood with an exponential number of neighbors to be efficiently evaluated. We report computational results and comparisons with the best heuristics in the literature. Besides, we also present a new set with the largest instances in the literature of VRPCD, in order to demonstrate that the improvements we propose for the ILS metaheuristic are efficient even for large size instances. Results show that the best of our heuristics is competitive with the best heuristics in the literature of VRPCD. Besides, it improved the best solution known for half of the benchmark instances in the literature.     

Genetic algorithm with iterated local search for solving a location-routing problem

This paper deals with a location routing problem with multiple capacitated depots and one uncapacitated vehicle per depot. We seek for new methods to make location and routing decisions simultaneously and efficiently. For that purpose, we describe a genetic algorithm (GA) combined with an iterative local search (ILS). The main idea behind our hybridization is to improve the solutions generated by the GA using a ILS to intensify the search space. Numerical experiments show that our hybrid algorithm improves, for all instances, the best known solutions previously obtained by the tabu search heuristic.     

An iterated local search heuristic for the split delivery vehicle routing problem

This paper concerns the Split Delivery Vehicle Routing Problem (SDVRP). This problem is a relaxation of the Capacitated Vehicle Routing Problem (CVRP) since the customers׳ demands are allowed to be split. We deal with the cases where the fleet is unlimited (SDVRP-UF) and limited (SDVRP-LF). In order to solve them, we implemented a multi-start Iterated Local Search (ILS) based heuristic that includes a novel perturbation mechanism. Extensive computational experiments were carried out on benchmark instances available in the literature. The results obtained are highly competitive, more precisely, 55 best known solutions were equaled and new improved solutions were found for 243 out of 324 instances, with an average and maximum improvement of 1.15% and 2.81%, respectively.     

Capacitated arc routing problem with deadheading demands

Capacitated arc routing problem (CARP) is the determination of vehicle tours that serve all positive-demand edges (required edge) exactly once without exceeding vehicle capacity while minimizing sum of all tour costs. In CARP, total demand of a tour is calculated by means of all required edges on the tour. In this study, a new CARP variation is introduced, which considers not only required edges but also traversed edges while calculating total demand of the tour. The traversing demand occurs when the traversed edge is either servicing or non-servicing (deadheading). Since the new CARP formulation incurs deadheading edge demands it is called CARP with deadheading demands. An integer linear model is given for the problem which is used to solve small-sized instances, optimally. A constructive heuristic is presented to solve the problem which is a modified version of a well-known CARP heuristic. Furthermore, two post-optimization procedures are presented to improve the solution of the heuristic algorithm. The effectiveness of the proposed methods is shown on test problems, which are obtained by modifying CARP test instances.     

TL-FCM: A hierarchical prediction model based on two-level fuzzy c-means clustering for bike-sharing system

In recent years, shared bikes have gradually emerged into public life as a new way to travel and helped solve the last-mile problem of residents’ travel. While this development has brought convenient travel to users, a series of problems exist, a prominent one is the uneven distribution of bikes at each shared bike station. Accurately predicting bike usage in a bike-sharing system can help solve this problem. In this paper, we investigate how to improve the accuracy of predicting the usage of bikes in bike-sharing system. First, considering both geographic location information of shared bike stations and the migration trend of bikes between stations, we design a two-level fuzzy c-means clustering algorithm to cluster shared bicycle stations into groups, which can better capture the connection between shared bicycle stations and improve the clustering accuracy of shared bicycle sites, then, we combine the two-level fuzzy c-means clustering algorithm with the multi-similarity reference model to predict the usage of bikes, which can significantly improve the accuracy of the forecast. To evaluate the performance of our model, we validate our model in the New York Bike-Sharing System. The results shows that our model obtained significantly better results than other models.

     

School bus routing—a column generation approach

The School Bus Routing Problem (SBRP), a generalization of the well‐known Vehicle Routing Problem, involves the routing, planning, and scheduling of public school bus transportation. The problem can be divided into several subproblems, including bus stop selection, assigning students to buses, and determining the bus routes. This work presents an exact branch‐and‐price framework for the SBRP, with a strong emphasis on efficiency issues inherently related to column generation (CG). Experiments are conducted on a set of 128 SBRP instances. Many of these instances are solved optimally; for the remaining instances, strong lower bounds have been derived. Furthermore, better integer solutions were found for a number of instances reported in the literature. Both lower bounds computed on the optimum solution and stabilization added to the CG procedure significantly improved computation times.     

校车路径问题的改进迭代局部搜索算法

针对考虑站点服务时间、学生最大乘车时间约束的校车路径问题(SBRP),提出一种改进迭代局部搜索(ILS)算法以提升求解质量。该算法使用大规模邻域搜索(LNS)算法作为扰动算子;在解的破坏过程中,设计一组解的破坏因子并赋以一定的选择概率,每隔若干次迭代后根据解的质量自适应更改破坏因子的选择概率,进而调整解的破坏程度。为提升ILS解的多样性,算法采用了基于偏差系数的邻域解接受准则。在国际基准测试案例上进行了测试,测试结果表明在ILS算法中使用自适应调整破坏程度的LNS扰动比常规扰动和其他破坏扰动的求解质量有大幅提升;与蚁群算法的比较结果进一步验证了改进算法的有效性。     

Heuristics for tactical time slot management: a periodic vehicle routing problem view

In this study, we consider a tactical problem where a time slot schedule for delivery service over a given planning horizon must be selected in each zone of a geographical area. A heuristic search evaluates each schedule selection by constructing a corresponding tactical routing plan of minimum cost based on demand and service time estimates. At the end, the schedule selection leading to the best tactical routing plan is selected. The latter can then be used as a blueprint when addressing the operational problem (i.e., when real customer orders are received and operational routes are constructed). We propose two heuristics to address the tactical problem. The first heuristic is a three‐phase approach: a periodic vehicle routing problem (PVRP) is first solved, followed by a repair phase and a final improvement phase where a vehicle routing problem (VRP) with time windows is solved for each period of the planning horizon. The second heuristic tackles the problem as a whole by directly solving a PVRP with time windows. Computational results compare the two heuristics under various settings, based on instances derived from benchmark instances for the VRP with time windows.     

Battery swap station location-routing problem with capacitated electric vehicles

In this paper, we present an electric vehicles battery swap stations location routing problem (BSS–EV–LRP), which aims to determine the location strategy of battery swap stations (BSSs) and the routing plan of a fleet of electric vehicles (EVs) simultaneously under battery driving range limitation. The problem is formulated as an integer programming model under the basic and extended scenarios. A four-phase heuristic called SIGALNS and a two-phase Tabu Search-modified Clarke and Wright Savings heuristic (TS-MCWS) are proposed to solve the problem. In the proposed SIGALNS, the BSSs location stage and the vehicle routing stage are alternated iteratively, which considers the information from the routing plan while improving the location strategy. In the first phase, an initial routing plan is generated with a modified sweep algorithm, leading to the BSSs location subproblem, which is then solved by using an iterated greedy heuristic. In the third phase, the vehicle routes resulting from the location subproblem are determined by applying an adaptive large neighborhood search heuristic with several new neighborhood structures. At the end of SIGALNS, the solution is further improved by a split procedure. Compared with the MIP solver of CPLEX and TS-MCWS over three sets of instances, SIGALNS searches the solution space more efficiently, thus producing good solutions without excessive computation on the medium and large instances. Furthermore, we systematically conduct economic and environmental analysis including the comparison between basic and extended scenarios, sensitivity analysis on battery driving range and efficiency analysis about the vehicle emissions reduction when EVs are used in the logistics practice.     

需求点位置随机的分批配送VRP优化

将需求点位置随机的分批配送车辆路径问题视为分区路径问题进行求解。文章建立多目标随机规划模型,并设计改进的局部迭代搜索算法求解。在调整的Solomon算例测试集及调整的Gehring和Homberger算例测试集上进行测试,结果表明本文设计的算法能有效解决此类问题,同时由于分批配送的引入,32个测试算例中50%以上的算例得到更优的解。同时,使用具有实际意义的系数在算例集上进行求解,最优解平均比构造算法提高9.75%和14%的最优解质量。     

Vehicle routing with cross-dock selection

The vehicle routing problem with cross-dock selection is a variant of the vehicle routing problem containing spatial and load synchronization constraints by which products are transferred and processed via at least one cross-dock. This paper presents a mathematical formulation of the problem and an adaptive large neighborhood search heuristic. Computational experiments on a set of benchmark instances demonstrate the efficiency of the proposed methodology.     

The multi-depot split delivery vehicle routing problem: An integer programming-based heuristic, new test problems, and computational results

The multi-depot split delivery vehicle routing problem combines the split delivery vehicle routing problem and the multiple depot vehicle routing problem. We define this new problem and develop an integer programming-based heuristic for it. We apply our heuristic to 30 instances to determine the reduction in distance traveled that can be achieved by allowing split deliveries among vehicles based at the same depot and vehicles based at different depots. We generate new test instances with high-quality, visually estimated solutions and report results on these instances.     

Scatter search for mixed blocking flowshop scheduling

Empty or limited storage capacities between machines introduce various types of blocking constraint in the industries with flowshop environment. While large applications demand flowshop scheduling with a mix of different types of blocking, research in this area mainly focuses on using only one kind of blocking in a given problem instance. In this paper, using makespan as a criterion, we study permutation flowshops with zero capacity buffers operating under mixed blocking conditions. We present a very effective scatter search (SS) algorithm for this. At the initialisation phase of SS, we use a modified version of the well-known Nawaz, Enscore and Ham (NEH) heuristic. For the improvement method in SS, we use an Iterated Local Search (ILS) algorithm that adopts a greedy job selection and a powerful NEH-based perturbation procedure. Moreover, in the reference set update phase of SS, with small probabilities, we accept worse solutions so as to increase the search diversity. On standard benchmark problems of varying sizes, our algorithm very significantly outperforms well-known existing algorithms in terms of both the solution quality and the computing time. Moreover, our algorithm has found new upper bounds for 314 out of 360 benchmark problem instances.     

时空相关的混载校车路径问题邻域搜索

为节约混载校车路径问题求解过程中邻域解搜索的时间,引入时空距离和时空相关度概念,将邻域搜索空间限定在合理的范围内.该算法首先计算站点间的时空距离,再附加上简单约束的预判断,从而得到时空相关度矩阵.然后对于任意学生乘车站点,将其他可能与之直接相连的站点按照时空相关度排序,形成一个邻接列表.在邻域搜索过程中,通过限定邻接列表长度,仅尝试最终接受概率较大的一部分移动操作,以此缩小邻域搜索空间,从而提高算法效率.在国际标准案例上的测试结果表明,基于时空相关度的搜索策略能在基本不降低求解质量的情况下,平均节省50％以上的求解时间.     

The capacitated vehicle routing problem with stochastic demands and time windows

The capacitated vehicle routing problem with stochastic demands and time windows is an extension of the capacitated vehicle routing problem with stochastic demands, in which demands are stochastic and a time window is imposed on each vertex. A vertex failure occurring when the realized demand exceeds the vehicle capacity may trigger a chain reaction of failures on the remaining vertices in the same route, as a result of time windows. This paper models this problem as a stochastic program with recourse, and proposes an adaptive large neighborhood search heuristic for its solution. Modified Solomon benchmark instances are used in the experiments. Computational results clearly show the superiority of the proposed heuristic over an alternative solution approach.     

Balancing bike sharing systems with constraint programming

Bike sharing systems need to be properly rebalanced to meet the demand of users and to operate successfully. However, the problem of Balancing Bike Sharing Systems (BBSS) is a demanding task: it requires the design of optimal tours and operating instructions for relocating bikes among stations to maximally comply with the expected future bike demands. In this paper, we tackle the BBSS problem by means of Constraint Programming (CP). First, we introduce two different CP models for the BBSS problem including two custom branching strategies that focus on the most promising routes. Second, we incorporate both models in a Large Neighborhood Search (LNS) approach that is adapted to the respective CP model. Third, we perform an experimental evaluation of our approaches on three different benchmark sets of instances derived from real-world bike sharing systems. We show that our CP models can be easily adapted to the different benchmark problem setups, demonstrating the benefit of using Constraint Programming to address the BBSS problem. Furthermore, in our experimental evaluation, we see that the pure CP (branch & bound) approach outperforms the state-of-the-art MILP on large instances and that the LNS approach is competitive with other existing approaches.