车辆数限制的多车型校车路径问题模型及算法研究

为适应校车路径规划中校车有多种车型且每种车型数量受限的需求,建立车辆数限制的多车型校车路径问题(HFSBRP)的数学模型,并提出一种迭代局部搜索算法进行求解。该算法借助邻域随机选择的变邻域下降搜索(VND)算法完成局部提升。局部提升过程中,首先调整车型,然后再混合使用缩减路径数和提高车辆利用率的邻域解接受策略以提高算法的寻优能力,为保证解的多样性,允许接受一定偏差范围内的邻域解。此外,为避免算法过早陷入局部最优,设计了多点交换和移动的扰动规则。基于国际基准测试案例进行模型验证和算法测试,实验结果表明了模型的正确性和算法的有效性。     

求解多车型校车路径问题的带参数选择机制的GRASP算法

考虑到校车路径安排过程中不同车型容量和成本的差异,建立了多车型校车路径问题(SBRP)模型,并提出了一种带参数选择机制的贪婪随机自适应(GRASP)算法进行求解。在初始解构造阶段,设计一组阈值参数控制受限候选列表(RCL)的大小,使用轮盘赌法选择阈值参数。完成初始解构造后,使用可变邻域搜索(VNS)进行邻域解改进,并记录所选择的参数和解的目标值。算法迭代过程中,先设置相同阈值参数的选择概率,每隔若干次迭代后,评估每个阈值参数的性能并修改其选择概率,使得算法能够得到更好的平均解。使用基准测试案例进行了测试,比较了基本GRASP算法与设计的GRASP算法的性能,并与现有求解多车型校车路径问题的算法进行对比,实验结果表明所设计的算法是有效的。     

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。     

航班恢复问题的迭代局部搜索算法

在恶劣天气和机械故障等原因造成航班不能按照原计划执行时,航空公司需要采取相应的措施对航班进行恢复。本文基于经典的资源指派模型,综合考虑了调整时间、换机、联程拉直、取消航班和调机5种恢复策略,提出一种以最小化加权成本为优化目标的航班恢复模型,并设计一种迭代局部搜索算法。首先用构造-修复启发式方法构造可行解,然后从该初始解出发,在飞机路线对的邻域中进行局部搜索。当陷入局部最优后,对解进行扰动,然后从扰动后的解重新出发进行局部搜索。为了提高搜索效率,同时降低陷入局部最优解的概率,局部搜索过程采用模拟退火算法。实例结果表明,本文提出的模型及算法能够在短时间内对受到影响的大规模航班计划进行恢复。     

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.     

改进迭代局部搜索算法在MMTVRP中的应用

为了解决运送不相容货物的带时间窗的多行程车辆路径问题,需要制定一个明确的路径规划来服务一组客户,以满足客户运送不相容的大宗货物的需求。车辆在工作日期间允许执行多个行程,目的就是最大限度地减少使用车辆的数量。通过创建巨网结构并采用辅助分割过程和改进的迭代局部搜索算法获得解决方案,在多个相关约束条件限制下,车辆实现了以最少的数量、最短的行程在规定的时间窗内送达货物,并从车队不同规模的角度分别介绍了采用多行程方式送货的优势。最后通过典型的带时间窗的车辆路径问题的实例分析表明,该算法在某些情况下可以使车队规模减半,从而最大程度上减少了运行成本。     

MAX-SAT问题一种改进的局部搜索算法

局部搜索算法是求解大规模SAT问题的高效算法。经典的局部搜索算法有GSAT、WSAT、TSAT、NSAT等,但这些算法的初始解都是随机产生的。本文提出了用单纯形法产生“初始概率”（每个变量取1的概率）,用“初始概率”对局部搜索算法中变量的初始随机指派进行适当的约束,使在局部搜索的开始阶段,满足的子句数大大增加,加快了收敛的速度。通过对不同规模的随机STA问题实例的实验表明,这些改进有效地提高了局部搜索算法求解SAT问题的效率。     

改进的自适应大规模邻域搜索算法求解动态需求的混合车辆路径问题

为了给物流企业在车辆配送方案制定上提供决策支持,针对电动物流车与燃油物流车混合配送的模式,研究了带时间窗的动态需求车辆路径问题,建立了以配送总成本最小化为目标的两阶段整数规划模型.针对模型特点,设计了改进的自适应大规模邻域搜索(improved adaptive large neighborhood search,IALNS)算法,提出新的删除、修复算子及动态阶段加速策略,分别针对大规模的静态算例与动态算例进行算法性能测试.结果表明,与无改进策略的IALNS(IALNS-ND)相比,静态问题中在相同的求解时间内75％的算例(12个算例中9个)IALNS得到的最小值和平均值优于IALNS-ND,动态问题中95％(60个算例中57个算例)的算例可以得到成本和时间均优于IALNS-ND的解;与三种算法——自适应大规模邻域搜索算法(ALNS)、大规模邻域搜索算法(LNS)以及变邻域搜索算法(VNS)相比,静态问题中所有算例IALNS获得的总成本的最小值和平均值均优于三个对比算法,动态问题中58％(60个算例中35个算例)的算例IALNS能够以少于三个对比算法1.5倍甚至10倍的时间获得更优的解.同时随着问题动态度的提高,IALNS的速度更快,质量更好,证明了该算法在求解时效性要求高的动态需求车辆路径问题的优越性.     

求解旅行锦标赛问题的改进混合局部搜索算法

研究旅行锦标赛问题(Traveling Tournament Problem),属于体育类调试优化问题,涉及到球员、赛程安排和传播权等经济活动.针对体育联赛调度问题中碰到的赛程可行性与联盟队伍旅行总距离最优性的权衡问题,为了改善已有算法的效率及仿真结果,提出了一种全新的混合局部搜索算法:首先,通过改进的全面有效的构造算法以生成高质量的初始解,提出一种利用禁忌搜索和VND启发式算法,并具备迭代次数调整的混合局部搜索算法.改进算法能够通过各种有效的邻域移动遍历庞大的邻域结构.通过对标准问题集的仿真测试与结果对比,证明改进算法能够在合理的时间内实现优化调试,并得出非常具有竞争力的结果.     

需求可拆分车辆路径问题的禁忌搜索算法

为解决实际配送运输中的车辆路径问题（Vehicle Routing Problem,VRP）,通过改进传统的数学模型,解除每个客户需求只能由l辆车配送的约束,建立改进的可拆分车辆路径问题（Split Delivery VRP,SDVRP）数学模型,并利用禁忌搜索算法（Taboo Search Algorithm,TSA）进行求解．在TSA的设计中,根据SDVRP模型的特点对初始解、邻域搜索和解的评价等进行特殊处理．算例表明,该模型不仅可以解决VRP模型中不允许配送点需求量超出装载量的限制,而且通过相应配送点需求量的拆分和重新组合,可节省车辆数目、缩短路线长度、提高车辆装载率．     

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.     

An iterated local search for the multi-commodity multi-trip vehicle routing problem with time windows

The Multi-Commodity Multi-Trip Vehicle Routing Problem with Time Windows calls for the determination of a routing planning to serve a set of customers that require products belonging to incompatible commodities. Two commodities are incompatible if they cannot be transported together into the same vehicle. Vehicles are allowed to perform several trips during the working day. The objective is to minimize the number of used vehicles.We propose an Iterated Local Search that outperforms the previous algorithm designed for the problem. Moreover, we conduct an analysis on the benefit that can be obtained introducing the multi-trip aspect at the fleet dimensioning level. Results on classical VRPTW instances show that, in some cases, the fleet can be halved.     

Multi-start iterated local search for the periodic vehicle routing problem with time windows and time spread constraints on services

In the field of high-value shipment transportation, companies are faced to the malevolence problem. The risk of ambush increases with the predictability of vehicle routes. This paper addresses a very hard periodic vehicle routing problem with time windows, submitted by a software company specialized in transportation problems with security constraints. The hours of visits to each customer over the planning horizon must be spread in the customer's time window. As the aim is to solve real instances, the running time must be reasonable. A mixed integer linear model and a multi-start iterated local search are proposed. Results are reported on instances derived from classical benchmarks for the vehicle routing problem with time windows, and on two practical instances. Experiments are also conducted on a particular case with a single period, the vehicle routing problem with soft time windows: the new metaheuristic competes with two published algorithms and improves six best known solutions.     

An iterated local search algorithm for the permutation flowshop problem with total flowtime criterion

An ILS algorithm is proposed to solve the permutation flowshop sequencing problem with total flowtime criterion. The effects of different initial permutations and different perturbation strengths are studied. Comparisons are carried out with three constructive heuristics, three ant-colony algorithms and a particle swarm optimization algorithm. Experiments on benchmarks and a set of random instances show that the proposed algorithm is more effective. The presented ILS improves the best known permutations by a significant margin.     

A multi-start iterated local search with tabu list and path relinking for the two-echelon location-routing problem

The two-echelon location-routing problem (LRP-2E) is raised by the design of transportation networks with two types of trips: first-level trips serving from one main depot a set of satellite depots, to be located, and second-level trips supplying customers from these satellites. In the proposed multi-start iterated local search (MS-ILS), three greedy randomized heuristics are used cyclically to get initial solutions. Each ILS run alternates between two search spaces: LRP-2E solutions, and travelling salesman (TSP) tours covering the main depot and the customers. The number of iterations allotted to a run is reduced whenever a known solution (stored in a tabu list) is revisited. MS-ILS can be reinforced by a path-relinking procedure (PR), used internally for intensification, as post-optimization, or both. On two sets with 24 and 30 LRP-2E instances, MS-ILS outperforms on average two GRASP algorithms and adding PR brings a further improvement. Our metaheuristic also surpasses a tabu search on 30 instances for a more general problem with several main depots. It is still effective on a particular case, the capacitated location-routing problem (CLRP): In a comparison with four published metaheuristics, only one (LRGTS, Prins et al., 2007) does better.     

A multi-start evolutionary local search for the two-dimensional loading capacitated vehicle routing problem

This paper addresses an extension of the capacitated vehicle routing problem where customer demand is composed of two-dimensional weighted items (2L-CVRP). The objective consists in designing a set of trips minimizing the total transportation cost with a homogenous fleet of vehicles based on a depot node. Items in each vehicle trip must satisfy the two-dimensional orthogonal packing constraints. A GRASP×ELS algorithm is proposed to compute solutions of a simpler problem in which the loading constraints are transformed into resource constrained project scheduling problem (RCPSP) constraints. We denote this relaxed problem RCPSP-CVRP. The optimization framework deals with RCPSP-CVRP and lastly RCPSP-CVRP solutions are transformed into 2L-CVRP solutions by solving a dedicated packing problem. The effectiveness of our approach is demonstrated through computational experiments including both classical CVRP and 2L-CVRP instances. Numerical experiments show that the GRASP×ELS approach outperforms all previously published methods.     

A column generation approach for a school bus routing problem with resource constraints

The Multiple Vehicle Traveling Purchaser Problem describes a school bus routing problem that combines bus stop selection and bus route generation. This problem aims at selecting a set of bus stops from among a group of potential locations to pick up students, and for designing bus routes to visit the selected stops and to carry the students to their school. We address a variation of this problem that considers certain constraints on each bus route, such as bounds on the distances traveled by the students, bounds on the number of visited bus stops, and bounds on the minimum number of students that a vehicle has to pick up.     

Combining biased randomization with iterated local search for solving the multidepot vehicle routing problem

This paper proposes a hybrid approach for solving the multidepot vehicle routing problem (MDVRP) with a limited number of identical vehicles per depot. Our approach, which only uses a few parameters, combines “biased randomization”—use of nonsymmetric probability distributions to generate randomness—with the iterated local search (ILS) metaheuristic. Two biased‐randomized processes are employed at different stages of the ILS framework in order to (a) assign customers to depots following a randomized priority criterion—this allows for fast generation of alternative allocation maps and (b) improving routing solutions associated with a “promising” allocation map—this is done by randomizing the classical savings heuristic. These biased‐randomized processes rely on the use of the geometric probability distribution, which is characterized by a single and bounded parameter. Being an approach with few parameters, our algorithm does not require troublesome fine‐tuning processes, which tend to be time consuming. Using standard benchmarks, the computational experiments show the efficiency of the proposed algorithm. Despite its hybrid nature, our approach is relatively easy to implement and can be parallelized in a very natural way, which makes it an interesting alternative for practical applications of the MDVRP.     

An improved LNS algorithm for real-time vehicle routing problem with time windows

This paper studies the dynamic vehicle routing problem with hard time windows (DVRPTW). The main study course of this problem was briefly reviewed. The solving strategy and algorithm of the problem are put forward. First of all, DVRPTW problem is decomposed into a series of static VRPTW. When and how to decompose the DVRP is the issue, that must be addressed. An event-trigger mechanism has been proposed and used to decompose the DVRPTW into a series of system delay-snapshots. The trigger event to be adopted is a new request arrival during the stable operation. And each snapshot is regarded as a static VRPTW. Whether each static VRPTW can quickly and efficiently be solved within a given time or a shorter time, i.e. the solving time is another issue for the DVRPTW. In the solving process, how to merge the latest requirement to the current solution is the third issue that must be solved. An improved large neighborhood search (LNS) algorithm is proposed to solve the static problem. Utilizing the remove-reinsert process of the LNS, the latest request nodes are regarded as a part of the removed nodes; these nodes can be inserted into the original or current solution in good time in the reinsertion process; meanwhile, its computing speed is high and effective for it does not need to resolve primal problem each time. Computational results of a large number of test problems, which cited from Solomon's static benchmarks and Lacker’s dynamic data set, show that our method is superior to other methods in most instances.