A Particle Swarm Optimization Algorithm with Path Relinking for the Location Routing Problem

This paper introduces a new hybrid algorithmic nature inspired approach based on particle swarm optimization, for solving successfully one of the most popular logistics management problems, the location routing problem (LRP). The proposed algorithm for the solution of the location routing problem, the hybrid particle swarm optimization (HybPSO-LRP), combines a particle swarm optimization (PSO) algorithm, the multiple phase neighborhood search – greedy randomized adaptive search procedure (MPNS-GRASP) algorithm, the expanding neighborhood search (ENS) strategy and a path relinking (PR) strategy. The algorithm is tested on a set of benchmark instances. The results of the algorithm are very satisfactory for these instances and for six of them a new best solution has been found.      

Solving the unconstrained optimization problem by a variable neighborhood search

This paper presents variable neighborhood search (VNS) for the problem of finding the global minimum of a nonconvex function. The variable neighborhood search, which changes systematically neighborhood structures in the search for finding a better solution, is used to guide a set of standard improvement heuristics. This algorithm was tested on some standard test functions, and successful results were obtained. Its performance was compared with the other algorithms, and observed to be better.     

变邻域模拟退火算法求解速度时变的VRPTW问题

本文在经典的带时间窗的车辆路径问题(VRPTW)的基础上,考虑不同时间段车辆行驶速度不同的情况,研究速度时变的带时间窗车辆路径问题(TDVRPTW),使问题更具实际意义。本文用分段函数表示不同时间段下的车辆行驶速度,并解决了速度时变条件下行驶时间计算的问题。针对模拟退火算法(SA)在求解VRPTW问题时易陷入局部最优解,变邻域搜索算法(VNS)在求解VRPTW问题时收敛速度慢的问题,本文将模拟退火算法以一定概率接受非最优解的思想和变邻域搜索算法系统地改变当前解的邻域结构以拓展搜索范围的思想结合起来,提出了一种改进的算法——变邻域模拟退火算法(SAVN),使算法在退火过程中一陷入局部最优解就改变邻域结构,更换搜索范围,以此提升算法跳出局部最优解的能力,加快收敛速度。通过在仿真实验中将SAVN算法的求解结果与VNS算法、SA算法进行对比,验证了SAVN算法确实能显著提升算法跳出局部最优解的能力。     

Variable neighborhood search: Principles and applications

Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization, called variable neighborhood search (VNS). We present a basic scheme for this purpose, which can easily be implemented using any local search algorithm as a subroutine. Its effectiveness is illustrated by solving several classical combinatorial or global optimization problems. Moreover, several extensions are proposed for solving large problem instances: using VNS within the successive approximation method yields a two-level VNS, called variable neighborhood decomposition search (VNDS); modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed VNS (SVNS) heuristic. Finally, we show how to stabilize column generation algorithms with help of VNS and discuss various ways to use VNS in graph theory, i.e., to suggest, disprove or give hints on how to prove conjectures, an area where metaheuristics do not appear to have been applied before.     

The two-echelon capacitated electric vehicle routing problem with battery swapping stations: Formulation and efficient methodology

In this paper, we present a two-echelon capacitated electric vehicle routing problem with battery swapping stations (2E-EVRP-BSS), which aims to determine the delivery strategy under battery driving range limitations for city logistics. The electric vehicles operating in the different echelons have different load capacities, battery driving ranges, power consumption rates, and battery swapping costs. We propose an integer programming formulation and a hybrid algorithm that combines a column generation and an adaptive large neighborhood search (CG-ALNS) to solve the problem. We conducted extensive computational experiments, demonstrate the applicability of the proposed model, and show the efficiency of the CG-ALNS algorithm. In addition, we explore the interplay between battery driving range and the effectiveness of vehicle emission reduction through sensitivity analysis.     

一类多对多物流系统的运送频率选择优化问题研究

多供应商多客户物流系统的周期运送库存决策问题是一个非常复杂的问题,但它在供应链管理中又极其重要.本文主要考虑一个由多个供应商、一个联运中心和多个客户组成的三级物流系统的运送频率选择优化问题.假定两级库存均采用周期补货策略,且补货周期满足二次幂(POT)策略,每个客户处的产品需求为确定性需求.假设给定一套可行频率的情况下,选择使整个系统总的长期平均成本最小化的联运中心的补货策略和联运中心到各客户的配送策略.分为单频率配送和多频率配送两种情况分别建立了数学模型,并设计了相应的近似算法——基于支配性的邻域搜索启发式算法和基于饱和性的邻域搜索启发式算法.计算试验显示,本文所设计的近似算法对于求解多对多配送这样的大型组合优化问题是有效的.     

A general variable neighborhood search for solving the uncapacitated single allocation p-hub median problem

We present a new general variable neighborhood search approach for the uncapacitated single allocation p-hub median problem in networks. This NP hard problem is concerned with locating hub facilities in order to minimize the traffic between all origin-destination pairs. We use three neighborhoods and efficiently update data structures for calculating new total flow in the network. In addition to the usual sequential strategy, a new nested strategy is proposed in designing a deterministic variable neighborhood descent local search. Our experimentation shows that general variable neighborhood search based heuristics outperform the best-known heuristics in terms of solution quality and computational effort. Moreover, we improve the best-known objective values for some large Australia Post and PlanetLab instances. Results with the new nested variable neighborhood descent show the best performance in solving very large test instances.     

A variable neighborhood-based heuristic for the heterogeneous fleet vehicle routing problem

The heterogeneous fleet vehicle routing problem is investigated using some adaptations of the variable neighborhood search (VNS). The initial solution is obtained by Dijkstra’s algorithm based on a cost network constructed by the sweep algorithm and the 2-opt. Our VNS algorithm uses several neighborhoods which are adapted for this problem. In addition, a number of local search methods together with a diversification procedure are used. Two VNS variants, which differ in the order the diversification and Dijkstra’s algorithm are used, are implemented. Both variants appear to be competitive and produce new best results when tested on the data sets from the literature. We also constructed larger data sets for which benchmarking results are provided for future comparison.     

A variable neighborhood search based algorithm for finite-horizon Markov Decision Processes

This paper considers the application of a variable neighborhood search (VNS) algorithm for finite-horizon (H stages) Markov Decision Processes (MDPs), for the purpose of alleviating the “curse of dimensionality” phenomenon in searching for the global optimum. The main idea behind the VNSMDP algorithm is that, based on the result of the stage just considered, the search for the optimal solution (action) of state x in stage t is conducted systematically in variable neighborhood sets of the current action. Thus, the VNSMDP algorithm is capable of searching for the optimum within some subsets of the action space, rather than over the whole action set. Analysis on complexity and convergence attributes of the VNSMDP algorithm are conducted in the paper. It is shown by theoretical and computational analysis that, the VNSMDP algorithm succeeds in searching for the global optimum in an efficient way.     

Creating very large scale neighborhoods out of smaller ones by compounding moves

This paper discusses neighborhood search algorithms where the size of the neighborhood is “very large” with respect to the size of the input data. We concentrate on such a very large scale neighborhood (VLSN) search technique based on compounding independent moves (CIM) such as 2-opts, swaps, and insertions. We present a systematic way of creating and searching CIM neighborhoods for routing problems with side constraints. For such problems, the exact search of the CIM neighborhood becomes NP-hard. We introduce a multi-label shortest path algorithm for searching these neighborhoods heuristically. Results of a computational study on the vehicle routing problem with capacity and distance restrictions shows that CIM algorithms are very competitive approaches for solving vehicle routing problems. Overall, the solutions generated by the CIM algorithm have the best performance among the current solution methodologies in terms of percentage deviation from the best-known solutions for large-scale capacitated VRP instances.     

带时间窗偏好的同时配集货且需求可拆分车辆路径问题

针对带时间窗偏好的同时配集货且需求可拆分车辆路径问题,最小化派遣成本、理货成本、时间窗惩罚成本以及油耗成本之和,建立数学模型。设计混合遗传变邻域搜索算法求解问题,在算法中引入时空距离的理念,首先用最近邻插入法和Logistic映射方程生成初始种群;然后利用变邻域搜索算法的深度搜索能力优化算法;提出自适应搜索策略,平衡种群进化所需的广度和深度;设计拆分准则,为各客户设置不同的拆分服务量;提出确定车辆最优出发时间的时差推移法,减少车辆在客户处的等待时间;最后通过多组算例验证本文模型和算法的有效性。     

带投资约束且p不确定的推广p-中位问题

p-中位问题是设施选址中的一个经典模型,在交通、物流等领域有着广泛应用．在经典p-中位问题的基础上提出一种p不确定的推广p-中位问题,并且加上总投资约束,使得此推广模型更加实用．针对此推广模型,提出三种启发式算法：简单启发式算法、变邻域搜索算法和改进的遗传算法．数值实验结果表明变邻域搜索算法和改进的遗传算法在求解此推广模型时是有效的．     

A variable neighborhood search with an effective local search for uncapacitated multilevel lot-sizing problems

In this study, we improved the variable neighborhood search (VNS) algorithm for solving uncapacitated multilevel lot-sizing (MLLS) problems. The improvement is twofold. First, we developed an effective local search method known as the Ancestors Depth-first Traversal Search (ADTS), which can be embedded in the VNS to significantly improve the solution quality. Second, we proposed a common and efficient approach for the rapid calculation of the cost change for the VNS and other generate-and-test algorithms. The new VNS algorithm was tested against 176 benchmark problems of different scales (small, medium, and large). The experimental results show that the new VNS algorithm outperforms all of the existing algorithms in the literature for solving uncapacitated MLLS problems because it was able to find all optimal solutions (100%) for 96 small-sized problems and new best-known solutions for 5 of 40 medium-sized problems and for 30 of 40 large-sized problems.     

A general variable neighborhood search for the one-commodity pickup-and-delivery travelling salesman problem

We present a variable neighborhood search approach for solving the one-commodity pickup-and-delivery travelling salesman problem. It is characterized by a set of customers such that each of the customers either supplies (pickup customers) or demands (delivery customers) a given amount of a single product, and by a vehicle, whose given capacity must not be exceeded, that starts at the depot and must visit each customer only once. The objective is to minimize the total length of the tour. Thus, the considered problem includes checking the existence of a feasible travelling salesman’s tour and designing the optimal travelling salesman’s tour, which are both NP-hard problems. We adapt a collection of neighborhood structures, k-opt, double-bridge and insertion operators mainly used for solving the classical travelling salesman problem. A binary indexed tree data structure is used, which enables efficient feasibility checking and updating of solutions in these neighborhoods. Our extensive computational analysis shows that the proposed variable neighborhood search based heuristics outperforms the best-known algorithms in terms of both the solution quality and computational efforts. Moreover, we improve the best-known solutions of all benchmark instances from the literature (with 200 to 500 customers). We are also able to solve instances with up to 1000 customers.     

顺序相依拆卸线平衡多目标优化模型及算法研究

拆卸是产品回收过程最关键环节之一,拆卸效率直接影响再制造成本。本文在分析现有模型不足基础上,考虑最小化总拆卸时间,建立多目标顺序相依拆卸线平衡问题优化模型,并提出了一种自适应进化变邻域搜索算法。所提算法引入种群进化机制,并采用一种组合策略构建初始种群,通过锦标赛法选择个体进化;在局部搜索时,设计了邻域结构自适应选择策略,并采用基于交叉的全局学习机制加速跳出局部最优,以提高算法寻优能力。对比实验结果,证实了所提模型的合理性以及算法的高效性。     

An adaptive large neighborhood search algorithm for a selective and periodic inventory routing problem

We study a selective and periodic inventory routing problem (SPIRP) and develop an Adaptive Large Neighborhood Search (ALNS) algorithm for its solution. The problem concerns a biodiesel production facility collecting used vegetable oil from sources, such as restaurants, catering companies and hotels that produce waste vegetable oil in considerable amounts. The facility reuses the collected waste oil as raw material to produce biodiesel. It has to meet certain raw material requirements either from daily collection, or from its inventory, or by purchasing virgin oil. SPIRP involves decisions about which of the present source nodes to include in the collection program, and which periodic (weekly) routing schedule to repeat over an infinite planning horizon. The objective is to minimize the total collection, inventory and purchasing costs while meeting the raw material requirements and operational constraints. A single-commodity flow-based mixed integer linear programming (MILP) model was proposed for this problem in an earlier study. The model was solved with 25 source nodes on a 7-day cyclic planning horizon. In order to tackle larger instances, we develop an ALNS algorithm that is based on a rich neighborhood structure with 11 distinct moves tailored to this problem. We demonstrate the performance of the ALNS, and compare it with the MILP model on test instances containing up to 100 source nodes.     

第三方库存-路线问题的模型及混合遗传算法设计

根据第三方库存-路线问题的特点,以车辆租赁费用和运行费用之和为目标函数,不限制客户每次的配送量小于车辆容量,建立了满载运输和非满载运输混合的整数规划模型.针对第三方库存-路线问题的复杂性,本文设计嵌入禁忌搜索的遗传算法来同时决策库存和路线问题.首先对配送间隔进行编码,然后用禁忌搜索法计算每天需要配送的车辆路线问题.最后与其下界值进行比较,结果表明该算法是一个有效的算法,不但第三方能取得较低的运营总成本和较高的车辆利用率,而且也能为客户节约库存空间.     

Scheduling periodic customer visits for a traveling salesperson

The problem considered in this paper deals with determining daily routes for a traveling salesperson who provides customers in Upper Austria with product range information of a large, global food wholesaler. Each customer has to be visited at least once a year, with some customers requiring up to one visit per month. Further, some customers may not be visited each day of the week. Our decision support system uses a commercial GIS software to extract customer data for input into the optimization procedure and to visualize the results obtained by the algorithm. The optimization approach is based on the variable neighborhood search algorithm which assigns customers to days and determines routes for the salesperson for each day with the primary objective to minimize the total travel time of the salesperson. Another objective studied is to minimize the number of days needed by the salesperson to visit all customers in a given month. Further we analyze the effects of changes in the business environment like increases in the amount or flexibility of the salesperson’s working time and variations in the possible days for customer visits. Finally, we enrich the objective function by considering periodicity requirements for customer visits. Specifically, we penalize irregular schedules, where the time between two successive customer visits varies.     

求解带时间窗车辆路径问题的混合Memetic算法

为提高带时间窗车辆路径问题的求解精度和求解效率,设计了一种混合Memetic算法。采用基于时间窗升序排列的混合插入法构造初始种群,提高解质量的同时兼顾多样性,扩大搜索空间;任意选择组成父代种群,以维持搜索空间;运用简化的变邻域搜索进行局部开发,引入邻域半径减少策略提高开发效率,约束放松机制开放局部空间;以弧为对象,增加种群向当前最优解和全局最优解的后学习过程。实验结果表明,所提出的算法具有较好的寻优精度和稳定性,能搜索到更好的路径长度结果,更新了现有研究在最短路径长度的目标函数上的下限。     

Skewed VNS enclosing second order algorithm for the degree constrained minimum spanning tree problem

We develop ideas to enhance the performance of the variable neighborhood search (VNS) by guiding the search in the shaking phase, and by employing the Skewed strategy. For this purpose, Second Order algorithms and Skewed functions expressing structural differences are embedded in an efficient VNS proposed in the literature for the degree constrained minimum spanning tree problem. Given an undirected graph with weights associated with its edges, the degree constrained minimum spanning tree problem consists in finding a minimum spanning tree of the given graph, subject to constraints on node degrees. Computational experiments are conducted on the largest and hardest benchmark instances found in the literature to date. We report results showing that the VNS with the proposed strategies improved the best known solutions for all the hardest benchmark instances. Moreover, these new best solutions significantly reduced the gaps with respect to tight lower bounds reported in the literature.