Hybrid large neighbourhood search algorithm for capacitated vehicle routing problem

This paper presents a new hybrid algorithm that executes large neighbourhood search algorithm in combination with the solution construction mechanism of the ant colony optimization algorithm (LNS–ACO) for the capacitated vehicle routing problem (CVRP). The proposed hybrid LNS–ACO algorithm aims at enhancing the performance of the large neighbourhood search algorithm by providing a satisfactory level of diversification via the solution construction mechanism of the ant colony optimization algorithm. Therefore, LNS–ACO algorithm combines its solution improvement mechanism with a solution construction mechanism. The performance of the proposed algorithm is tested on a set of CVRP instances. The hybrid LNS–ACO algorithm is compared against two other LNS variants and some of the formerly developed methods in terms of solution quality. Computational results indicate that the proposed hybrid LNS–ACO algorithm has a satisfactory performance in solving CVRP instances.     

A multi-phase oscillated variable neighbourhood search algorithm for a real-world open vehicle routing problem

The aim of this study is to solve the newspaper delivery optimization problem for a media delivery company in Turkey by reducing the total cost of carriers. The problem is modelled as an open vehicle routing problem (OVRP), which is a variant of the vehicle routing problem. A variable neighbourhood search-based algorithm is proposed to solve a real-world OVRP. The proposed algorithm is tested with varieties of small and large-scale benchmark suites and a very large-scale real-world problem instance. The results of the proposed algorithm provide either the best known solution or a competitive solution for each of the benchmark instances. The algorithm also improves the real-world company’s solutions by more than 10%.     

A large neighbourhood metaheuristic for the risk-constrained cash-in-transit vehicle routing problem

In this paper, we propose a new metaheuristic to solve the Risk constrained Cash-in-Transit Vehicle Routing Problem (Rctvrp). The Rctvrp is a variant of the well-known capacitated vehicle routing problem and models the problem of routing vehicles in the cash-in-transit sector. In the Rctvrp, the risk associated with a robbery represents a critical aspect that is treated as a limiting factor subject to a maximum risk threshold.A new metaheuristic, called aco-lns is developed. It combines the ant colony heuristic for the travelling salesman problem and a variable neighbourhood descent within an large neighbourhood search framework.A new library of Rctvrp instances with known optimal solutions is proposed. The aco-lns is extensively tested on small, medium and large benchmark instances and compared with all existing solution approaches for the Rctvrp.     

An adaptive large neighborhood search heuristic for the cumulative capacitated vehicle routing problem

The cumulative capacitated vehicle routing problem (CCVRP) is a variation of the classical capacitated vehicle routing problem in which the objective is the minimization of the sum of arrival times at customers, instead of the total routing cost. This paper presents an adaptive large neighborhood search heuristic for the CCVRP. This algorithm is applied to a set of benchmark instances and compared with two recently published memetic algorithms.     

A general variable neighborhood search for the swap-body vehicle routing problem

The Swap-Body Vehicle Routing Problem, a generalization of the well known Vehicle Routing Problem, can be stated as follows: the vehicle fleet consisting of trucks, semi-trailers, and swap bodies, is available at a single depot to serve a given set of customers. To serve a subset of customers, one may use either a truck carrying one swap body or a train (a truck with a semi-trailer attached to it) carrying two swap bodies. In both cases, a vehicle (a truck or a train) must perform a route starting and ending at the depot, so to satisfy demands of visited customers, maximal allowed route duration, allowed load on the used vehicle, and accessibility constraint of each customer. The accessibility constraint indicates whether a customer is allowed to be visited by a train or not. In addition, a set of swap locations is given where semi-trailers and swap bodies may be parked or swapped. The goal of the Swap-Body Vehicle Routing Problem is to minimize the total costs consisting of the fixed costs for using vehicles and costs for performing routes. In this paper, we propose two general variable neighborhood search heuristics to solve this problem. The quality of the proposed methods is evaluated on the instances provided by the organizers of VeRolog Solver Challenge 2014.     

A fast two-level variable neighborhood search for the clustered vehicle routing problem

In this paper, we present an improved two-level heuristic to solve the clustered vehicle routing problem (CluVRP). The CluVRP is a generalization of the classical capacitated vehicle routing problem (CVRP) in which customers are grouped into predefined clusters, and all customers in a cluster must be served consecutively by the same vehicle. This paper contributes to the literature in the following ways: (i) new upper bounds are presented for multiple benchmark instances, (ii) good heuristic solutions are provided in much smaller computing times than existing approaches, (iii) the CluVRP is reduced to its cluster level without assuming Euclidean coordinates or distances, and (iv) a new variant of the CluVRP, the CluVRP with weak cluster constraints, is introduced. In this variant, clusters are allocated to vehicles in their entirety, but all corresponding customers can be visited by the vehicle in any order.The proposed heuristic solves the CluVRP by combining two variable neighborhood search algorithms, that explore the solution space at the cluster level and the individual customer level respectively. The algorithm is tested on different benchmark instances from the literature with up to 484 nodes, obtaining high quality solutions while requiring only a limited calculation time.     

A two-level self-adaptive variable neighborhood search algorithm for the prize-collecting vehicle routing problem

This paper investigates the prize-collecting vehicle routing problem (PCVRP), which has a strong background in practical industries. In the PCVRP, the capacities of all available vehicles are not sufficient to satisfy the demands of all customers. Consequently it is not a compulsory requirement that all customers should be visited. However, a prize can be collected once a customer is visited. In addition, it is required that the total demands of visited customers should reach a pre-specified value at least. The objective is to establish a schedule of vehicle routes so as to minimize the total transportation cost and at the same time maximize the prize collected by all vehicles. The total transportation cost consists of the total distance of vehicle routes and the sum of vehicles used in the schedule. To solve the PCVRP, a two-level self-adaptive variable neighborhood search (TLSAVNS) algorithm is developed according to the two levels of decisions in the PCVRP, namely the selection of customers to visit and the visiting sequence of selected customers in each vehicle route. The proposed TLSAVNS algorithm is self-adaptive because the neighborhoods and their search sequence are determined automatically by the algorithm itself based on the analysis of its search history. In addition, a graph extension method is adopted to obtain the lower bound for PCVRP by transforming the proposed mixed integer programming model of PCVRP into an equivalent traveling salesman problem (TSP) model, and the obtained lower bound is used to evaluate the proposed TLSAVNS algorithm. Computational results on benchmark problems show that the proposed TLSAVNS algorithm is efficient for PCVRP.     

A variable neighborhood search for the multi-depot vehicle routing problem with loading cost

The purpose of this paper is to propose a variable neighbourhood search (VNS) for solving the multi-depot vehicle routing problem with loading cost (MDVRPLC). The MDVRPLC is the combination of multi-depot vehicle routing problem (MDVRP) and vehicle routing problem with loading cost (VRPLC) which are both variations of the vehicle routing problem (VRP) and occur only rarely in the literature. In fact, an extensive literature search failed to find any literature related specifically to the MDVRPLC. The proposed VNS comprises three phases. First, a stochastic method is used for initial solution generation. Second, four operators are randomly selected to search neighbourhood solutions. Third, a criterion similar to simulated annealing (SA) is used for neighbourhood solution acceptance. The proposed VNS has been test on 23 MDVRP benchmark problems. The experimental results show that the proposed method provides an average 23.77% improvement in total transportation cost over the best known results based on minimizing transportation distance. The results show that the proposed method is efficient and effective in solving problems.     

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

The 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.     

多舱共配绿色车辆路径问题的改进变邻域搜索算法

针对社区团购前置仓配送场景中“多中心、高时效、多品类、高排放”难题, 本文提出多车场带时间窗的绿色多舱车车辆路径问题(MDMCG-VRPTW), 构建混合整数线性规划模型, 并设计改进的变邻域搜索算法(IVNS)实现求解. 采用两阶段混合算法构造高质量初始解. 提出均衡抖动策略以充分探索解空间, 引入粒度机制以提升局部搜索阶段的寻优效率. 标准算例测试结果验证了两阶段初始解构造算法和IVNS算法的有效性. 仿真实验结果表明,模型与算法能够有效求解MDMCGVRPTW, 且改进策略提高了算法的求解效率和全局搜索能力. 最后, 基于对配送策略和时效性的敏感性分析, 为相关配送企业降本增效提供更多决策依据.     

求解带容量约束车辆路径问题的混合变邻域生物共栖搜索算法

针对带容量约束的车辆路径问题,提出一种混合变邻域生物共栖搜索算法.设计基于客户点优先序列及车辆参考点模拟信息的有序编码,该编码方案使生物共栖搜索算法可以参与CVRP的离散优化;为了提高算法的全局搜索能力,根据有序编码特点构造3种共栖搜索算子,扩大搜索空间;同时,结合变邻域搜索算法设计客户点重置、交换和2-OPT三种局部搜索策略,以提高解方案质量.算例验证分析表明,所提算法能够有效地解决容量约束车辆路径问题,求解质量优于所对比算法,具有可靠的全局稳定性.     

A parallel variable neighborhood search for the vehicle routing problem with divisible deliveries and pickups

A well-known variant of the vehicle routing problem involves backhauls, where vehicles deliver goods from a depot to linehaul customers and pick up goods from backhaul customers to the depot. The vehicle routing problem with divisible deliveries and pickups (VRPDDP) allows vehicles to visit each client once or twice for deliveries or pickups. In this study, a very efficient parallel approach based on variable neighborhood search (VNS) is proposed to solve VRPDDP. In this approach, asynchronous cooperation with a centralized information exchange strategy is used for parallelization of the VNS approach, called cooperative VNS (CVNS). All available problem sets of VRPDDP have been successfully solved with the CVNS, and the best solutions available in the literature have been significantly improved.     

求解冷链物流时间依赖型车辆路径问题的混合自适应大邻域搜索算法

针对单一机制的自适应大邻域搜索算法存在早熟收敛、易陷入局部最优的问题,提出了一种混合自适应大邻域搜索算法来求解冷链物流时间依赖型车辆路径问题（TDVRP）。首先,根据连续型行驶时间依赖函数来刻画时变车速,采用综合油耗模型来评估实时燃油消耗量,并建立了以总成本最小化为目标的路径优化模型;然后,根据问题的NP-hard性质和时间依赖特性设计了多种破坏和修复解的大邻域搜索算子,并将破坏-修复大邻域搜索算子融入到人工蜂群（ABC）算法之中,以提高算法的全局搜索能力。仿真实验结果表明,与自适应可变邻域搜索精英蚁群（AVNS_EAC）算法、自适应大邻域搜索精英蚁群（ALNS_EAC）算法、自适应大邻域搜索精英遗传（ALNS_EG）算法和自适应大邻域搜索模拟退火（ALNS_SA）算法相比,所提出的自适应大邻域搜索人工蜂群（ALNS_ABC）算法在多组测试数据上的最优适应度值分别平均提高了46.3%、5.3%、36.8%和6%。可见所提算法计算性能更高、稳定性更强,能够为冷链物流企业兼顾经济效益和环境效益提供更为合理的决策依据。     

A matheuristic based on large neighborhood search for the vehicle routing problem with cross-docking

The vehicle routing problem with cross-docking (VRPCD) consists in defining a set of routes that satisfy transportation requests between a set of pickup points and a set of delivery points. The vehicles bring goods from pickup locations to a cross-docking platform, where the items may be consolidated for efficient delivery. In this paper we propose a new solution methodology for this problem. It is based on large neighborhood search and periodically solving a set partitioning and matching problem with third-party solvers. Our method improves the best known solution in 19 of 35 instances from the literature.     

A variable neighborhood search heuristic algorithm for the double vehicle routing problem with multiple stacks

This paper addresses the double vehicle routing problem with multiple stacks (DVRPMS) in which a fleet of vehicles must collect items in a pickup region and then travel to a delivery region where all items are delivered. The load compartment of all vehicles is divided into rows (horizontal stacks) of fixed profundity (horizontal heights), and on each row, the unloading process must respect the last‐in‐first‐out policy. The objective of the DVRPMS is to find optimal routes visiting all pickup and delivery points while ensuring the feasibility of the vehicle loading plans. We propose a new integer linear programming formulation, which was useful to find inconsistencies in the results of exact algorithms proposed in the literature, and a variable neighborhood search based algorithm that was able to find solutions with same or higher quality in shorter computational time for most instances when compared to the methods already present in the literature.     

The multi-depot vehicle routing problem with heterogeneous vehicle fleet: Formulation and a variable neighborhood search implementation

The multi-depot fleet size and mix vehicle routing problem, also known as the multi-depot routing with heterogeneous vehicles, is investigated. A mathematical formulation is given and lower as well as upper bounds are produced using a three hour execution time of CPLEX. An efficient implementation of variable neighborhood search that incorporates new features in addition to the adaptation of several existing neighborhoods and local search operators is proposed. These features include a preprocessing scheme for identifying borderline customers, a mechanism that aggregates and disaggregates routes between depots, and a neighborhood reduction test that saves nearly 80% of the CPU time, especially on the large instances. The proposed algorithm is highly competitive as it produces 23 new best results when tested on the 26 data instances published in the literature.     

A multistart adaptive memory-based tabu search algorithm for the heterogeneous fixed fleet open vehicle routing problem

This paper addressed the heterogeneous fixed fleet open vehicle routing problem (HFFOVRP), in which the demands of customers are fulfilled by a fleet of fixed number of vehicles with various capacities and related costs. Moreover, the vehicles start at the depot and terminate at one of the customers. This problem is an important variant of the classical vehicle routing problem and can cover more practical situations in transportation and logistics. We propose a multistart adaptive memory programming metaheuristic with modified tabu search algorithm to solve this new vehicle routing problem. The algorithmic efficiency and effectiveness are experimentally evaluated on a set of generated instances.     

A hybrid variable neighborhood tabu search heuristic for the vehicle routing problem with multiple time windows

This paper presents a new hybrid variable neighborhood-tabu search heuristic for the Vehicle Routing Problem with Multiple Time windows. It also proposes a minimum backward time slack algorithm applicable to a multiple time windows environment. This algorithm records the minimum waiting time and the minimum delay during route generation and adjusts the arrival and departure times backward. The implementation of the proposed heuristic is compared to an ant colony heuristic on benchmark instances involving multiple time windows. Computational results on newly generated instances are provided.     

随机需求车辆路径问题及混合变邻域分散搜索算法求解

随机需求车辆路径问题(capacitated vehicle routing problem with stochastic demand,CVRPSD)是对带容量约束车辆路径问题(capacitated vehicle routing problem,CVRP)的扩展,需求不确定的特点使其较CVRP更复杂,对求解方法要求更高.基于先预优化后重调度思想,提出两阶段的混合变邻域分散搜索算法(variable neighborhood scatter search,VNSS)对该问题进行求解:预优化阶段构建随机机会约束规划模型,对客户点随机需求作机会约束确定型等价处理,生成最优预优化方案;重调度阶段采用新的点重优化策略进行线路调整,降低因失败点而产生的额外成本,减少对人工和车辆的占用.算例验证表明,随机机会约束模型和两阶段变邻域分散搜索算法在求解CVRPSD时较为有效,点重优化策略调整效果较佳.     

An efficient variable neighborhood search heuristic for very large scale vehicle routing problems

In this paper, we present an efficient variable neighborhood search heuristic for the capacitated vehicle routing problem. The objective is to design least cost routes for a fleet of identically capacitated vehicles to service geographically scattered customers with known demands. The variable neighborhood search procedure is used to guide a set of standard improvement heuristics. In addition, a strategy reminiscent of the guided local search metaheuristic is used to help escape local minima. The developed solution method is specifically aimed at solving very large scale real-life vehicle routing problems. To speed up the method and cut down memory usage, new implementation concepts are used. Computational experiments on 32 existing large scale benchmarks, as well as on 20 new very large scale problem instances, demonstrate that the proposed method is fast, competitive and able to find high-quality solutions for problem instances with up to 20,000 customers within reasonable CPU times.