An Effective Hybrid Optimization Algorithm for Capacitated Vehicle Routing Problem

Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high computational complexity. A hybrid algorithm was developed to solve the problem, in which an artificial immune clonal algorithm (AICA) makes use of the global search ability to search the optimal results and simulated annealing (SA) algorithm employs certain probability to avoid becoming trapped in a local optimum. The results obtained from the computational study show that the proposed algorithm is a feasible and effective method for capacitated vehicle routing problem.

A Memetic Algorithm With Competition for the Capacitated Green Vehicle Routing Problem

In this paper, a memetic algorithm with competition(MAC) is proposed to solve the capacitated green vehicle routing problem(CGVRP). Firstly, the permutation array called traveling salesman problem(TSP) route is used to encode the solution, and an effective decoding method to construct the CGVRP route is presented accordingly. Secondly, the k-nearest neighbor(k NN) based initialization is presented to take use of the location information of the customers. Thirdly, according to the characteristics of the CGVRP, the search operators in the variable neighborhood search(VNS) framework and the simulated annealing(SA) strategy are executed on the TSP route for all solutions. Moreover, the customer adjustment operator and the alternative fuel station(AFS) adjustment operator on the CGVRP route are executed for the elite solutions after competition. In addition, the crossover operator is employed to share information among different solutions. The effect of parameter setting is investigated using the Taguchi method of design-ofexperiment to suggest suitable values. Via numerical tests, it demonstrates the effectiveness of both the competitive search and the decoding method. Moreover, extensive comparative results show that the proposed algorithm is more effective and efficient than the existing methods in solving the CGVRP.

A Survey on the Vehicle Routing Problem and Its Variants

In this paper, we have conducted a literature review on the recent developments and publications involving the vehicle routing problem and its variants, namely vehicle routing problem with time windows (VRPTW) and the capacitated vehicle routing problem (CVRP) and also their variants. The VRP is classified as an NP-hard problem. Hence, the use of exact optimization methods may be difficult to solve these problems in acceptable CPU times, when the problem involves real-world data sets that are very large. The vehicle routing problem comes under combinatorial problem. Hence, to get solutions in determining routes which are realistic and very close to the optimal solution, we use heuristics and meta-heuristics. In this paper we discuss the various exact methods and the heuristics and meta-heuristics used to solve the VRP and its variants.

A Construction Heuristic for the Split Delivery Vehicle Routing Problem

The Split Delivery Vehicle Routing Problem (SDVRP) is a relaxation of the Capacitated Vehicle Routing Problem (CVRP) where customers may be assigned to multiple routes. A new construction heuristic is developed for the SDVRP and computational results are given for thirty-two data sets from previous literature. With respect to the total travel distance, the construction heuristic compares favorably versus a column generation method and a two-phase method. In addition, the construction heuristic is computationally faster than both previous methods. This construction heuristic could be useful in developing initial solutions, very quickly, for a heuristic, algorithm, or exact procedure.

Improved ant colony optimization for multi-depot heterogeneous vehicle routing problem with soft time windows

Considering that the vehicle routing problem （VRP） with many extended features is widely used in actual life, such as multi-depot, heterogeneous types of vehicles, customer service priority and time windows etc., a mathematical model for multi-depot heterogeneous vehicle routing problem with soft time windows （MDHVRPSTW） is established. An improved ant colony optimization （IACO） is proposed for solving this model. First, MDHVRPSTW is transferred into different groups according to the nearest principle, and then the initial route is constructed by the scanning algorithm （SA）. Secondly, genetic operators are introduced, and crossover probability and mutation probability are adaptively adjusted in order to improve the global search ability of the algorithm. Moreover, the smooth mechanism is used to improve the performance of the ant colony optimization （ACO）. Finally, the 3-opt strategy is used to improve the local search ability. The proposed IACO was tested on three new instances that were generated randomly. The experimental results show that IACO is superior to the other three existing algorithms in terms of convergence speed and solution quality. Thus, the proposed method is effective and feasible, and the proposed model is meaningful.

Multi-type ant system algorithm for the time dependent vehicle routing problem with time windows

The time dependent vehicle routing problem with time windows（TDVRPTW） is considered. A multi-type ant system（MTAS） algorithm hybridized with the ant colony system（ACS）and the max-min ant system（MMAS） algorithms is proposed. This combination absorbs the merits of the two algorithms in solutions construction and optimization separately. In order to improve the efficiency of the insertion procedure, a nearest neighbor selection（NNS） mechanism, an insertion local search procedure and a local optimization procedure are specified in detail. And in order to find a balance between good scouting performance and fast convergence rate, an adaptive pheromone updating strategy is proposed in the MTAS. Computational results confirm the MTAS algorithm＇s good performance with all these strategies on classic vehicle routing problem with time windows（VRPTW） benchmark instances and the TDVRPTW instances, and some better results especially for the number of vehicles and travel times of the best solutions are obtained in comparison with the previous research.

A Time-Dependent Vehicle Routing Problem with Time Windows for E-Commerce Supplier Site Pickups Using Genetic Algorithm

The VRP is classified as an NP-hard problem. Hence exact optimization methods may be difficult to solve these problems in acceptable CPU times, when the problem involves real-world data sets that are very large. To get solutions in determining routes which are realistic and very close to the actual solution, we use heuristics and metaheuristics which are of the combinatorial optimization type. A literature review of VRPTW, TDVRP, and a metaheuristic such as the genetic algorithm was conducted. In this paper, the implementation of the VRPTW and its extension, the time-dependent VRPTW (TDVRPTW) has been carried out using the model as well as metaheuristics such as the genetic algorithm (GA). The algorithms were implemented, using Matlab and HeuristicLab optimization software. A plugin was developed using Visual C# and DOT NET framework 4.5. Results were tested using Solomon’s 56 benchmark instances classified into groups such as C1, C2, R1, R2, RC1, RC2, with 100 customer nodes, 25 vehicles and each vehicle capacity of 200. The results were comparable to the earlier algorithms developed and in some cases the current algorithm yielded better results in terms of total distance travelled and the average number of vehicles used.

A hybrid optimization approach for the heterogeneous vehicle routing problem with multiple depots cooperative operation

With the challenge of great growing of transport diversity for the automobile enterprises, the heterogeneous vehicle routing problem with multiple depots, multiple types of finished vehicles and multiple types of transport vehicles in finished vehicle logistics(HVRPMD) is modelled and solved. A multi-objective optimization model for HVRPMD is presented considering loading constraints to minimize the total cost and minimize the number of transport vehicles. Then a hybrid heuristic algorithm based on genetic algorithm and particle swarm optimization(GA-PSO) is developed. Moreover, a case study is used to evaluate the effectiveness of this algorithm. By comparing the GA-PSO algorithm with the traditional GA algorithm, the simulation results demonstrate the proposed GA-PSO algorithm is able to better support the HVRPMD problem in practice. Contributions of the paper are the modelling and solving of a complex HVRPMD in logistics industry.

New Hybrid Algorithm Based on BicriterionAnt for Solving Multiobjective Green Vehicle Routing Problem

The main objective of this paper is to propose a new hybrid algorithm for solving the Bi objective green vehicle routing problem (BGVRP) from the BicriterionAnt metaheuristic. The methodology used is subdivided as follows: first, we introduce data from the GVRP or instances from the literature. Second, we use the first cluster route second technique using the k-means algorithm, then we apply the BicriterionAntAPE (BicriterionAnt Adjacent Pairwise Exchange) algorithm to each cluster obtained. And finally, we make a comparative analysis of the results obtained by the case study as well as instances from the literature with some existing metaheuristics NSGA, SPEA, BicriterionAnt in order to see the performance of the new hybrid algorithm. The results show that the routes which minimize the total distance traveled by the vehicles are different from those which minimize the CO2 pollution, which can be understood by the fact that the objectives are conflicting. In this study, we also find that the optimal route reduces product CO2 by almost 7.2% compared to the worst route.

A Bi-Objective Green Vehicle Routing Problem: A New Hybrid Optimization Algorithm Applied to a Newspaper Distribution

The purpose of this work is to present a methodology to provide a solution to a Bi-objective Green Vehicle Routing Problem (BGVRP). The methodology, illustrated using a case study (newspaper distribution problem) and literature Instances, was divided into three stages: Stage 1, data treatment;Stage 2, “metaheuristic approaches” (hybrid or non-hybrid), used comparatively, more specifically: NSGA-II (Non-dominated Sorting Genetic Algorithm II), MOPSO (Multi-Objective Particle Swarm Optimization), which were compared with the new approaches proposed by the authors, CWNSGA-II (Clarke and Wright’s Savings with the Non-dominated Sorting Genetic Algorithm II) and CWTSNSGA-II (Clarke and Wright’s Savings, Tabu Search and Non-dominated Sorting Genetic Algorithm II);Stage 3, analysis of the results, with a comparison of the algorithms. An optimization of 19.9% was achieved for Objective Function 1 (OF1;minimization of CO2 emissions) and consequently the same percentage for the minimization of total distance, and 87.5% for Objective Function 2 (OF2;minimization of the difference in demand). Metaheuristic approaches hybrid achieved superior results for case study and instances. In this way, the procedure presented here can bring benefits to society as it considers environmental issues and also balancing work between the routes, ensuring savings and satisfaction for the users.

Efficient Network Selection Using Multi-Depot Routing Problem for Smart Cities

Smart cities make use of a variety of smart technology to improve societies in better ways.Such intelligent technologies,on the other hand,pose sig-nificant concerns in terms of power usage and emission of carbons.The suggested study is focused on technological networks for big data-driven systems.With the support of software-defined technologies,a transportation-aided multicast routing system is suggested.By using public transportation as another communication platform in a smart city,network communication is enhanced.The primary objec-tive is to use as little energy as possible while delivering as much data as possible.The Attribute Decision Making with Capacitated Vehicle(CV)Routing Problem(RP)and Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used in the proposed research.For the optimum network selection,a Multi-Attribute Decision Making(MADM)method is utilized.For the sake of reducing energy usage,the Capacitated Vehicle Routing Problem(CVRP)is employed.To reduce the transportation cost and risk,Half Open Multi-Depot Heterogeneous Vehicle Routing Problem is used.Moreover,a mixed-integer programming approach is used to deal with the problem.To produce Pareto optimal solutions,an intelligent algorithm based on the epsilon constraint approach and genetic algorithm is cre-ated.A scenario of Auckland Transport is being used to validate the concept of offloading the information onto the buses for energy-efficient and delay-tolerant data transfer.Therefore the experiments have demonstrated that the buses may be used effectively to carry out the data by customer requests while using 30%of less energy than the other systems.

A two-stage heuristic method for vehicle routing problem with split deliveries and pickups

The vehicle routing problem(VRP) is a well-known combinatorial optimization issue in transportation and logistics network systems. There exist several limitations associated with the traditional VRP. Releasing the restricted conditions of traditional VRP has become a research focus in the past few decades. The vehicle routing problem with split deliveries and pickups(VRPSPDP) is particularly proposed to release the constraints on the visiting times per customer and vehicle capacity, that is, to allow the deliveries and pickups for each customer to be simultaneously split more than once. Few studies have focused on the VRPSPDP problem. In this paper we propose a two-stage heuristic method integrating the initial heuristic algorithm and hybrid heuristic algorithm to study the VRPSPDP problem. To validate the proposed algorithm, Solomon benchmark datasets and extended Solomon benchmark datasets were modified to compare with three other popular algorithms. A total of 18 datasets were used to evaluate the effectiveness of the proposed method. The computational results indicated that the proposed algorithm is superior to these three algorithms for VRPSPDP in terms of total travel cost and average loading rate.

A two-stage metaheuristic algorithm for the dynamic vehicle routing problem in Industry 4.0 approach

Industry 4.0 is a concept that assists companies in developing a modern supply chain(MSC)system when they are faced with a dynamic process.Because Industry 4.0 focuses on mobility and real-time integration,it is a good framework for a dynamic vehicle routing problem(DVRP).This research works on DVRP.The aim of this research is to minimize transportation cost without exceeding the capacity constraint of each vehicle while serving customer demands from a common depot.Meanwhile,new orders arrive at a specific time into the system while the vehicles are executing the delivery of existing orders.This paper presents a two-stage hybrid algorithm for solving the DVRP.In the first stage,construction algorithms are applied to develop the initial route.In the second stage,improvement algorithms are applied.Experimental results were designed for different sizes of problems.Analysis results show the effectiveness of the proposed algorithm.

考虑车辆绕行的低碳校车路径优化模型

为了合理规划校车路径以降低碳排放,建立以考虑行驶距离和载重的碳排放最小化为优化目标,及以车辆绕行和容量为约束的低碳校车路径优化模型(GCSBRPTW).针对绕行问题,引入绕行因子并转化为单侧时间窗约束;设计了一种基于Lin-Kernighan heuristic(LKH)算法和莱维飞行算子的改进蚁群算法(LKH-Levy-ACO)对模型进行求解,其中LKH算法和莱维算子分别用于提高算法寻优效率和全局搜索能力.最后利用泰兴市工业园区班车线路规划实例求解,展开绕行因子取值对比、GCSBRPTW与传统校车路径模型对比、LKH-Levy-ACO与传统蚁群算法等4种算法对比实验.结果显示,绕行因子取值越小,最优解越差,GCSBRPTW比传统校车路径模型降低了约0.70%的碳排放,且LKH-Levy-ACO算法比传统蚁群算法降低了6.19%的碳排放,证明了模型的实用性和算法的有效性.

策略梯度的超启发算法求解带容量约束车辆路径问题

有容量车辆路径问题是组合优化问题中比较热门的问题,它属于经典的NP-hard问题并且时间复杂度高.本文提出了一种基于策略梯度的超启发算法,将强化学习中的确定性策略梯度算法引入到超启发算法的高层策略中的底层算法选择策略,确定性策略梯度算法采用Actor-Critic框架,另外为了能够在后续计算和神经网络参数更新中引用历史经验数据,在确定性策略梯度算法中设计了经验池用于存储状态转移数据.在超启发算法解的接受准则方面,文中通过实验对比了3种接受准则的效果,最终选择了自适应接受准则作为高层策略中解的接受准则.通过对有容量车辆路径问题标准算例的计算,并将求解结果与其他算法对比,验证了所提算法在该问题求解上的有效性和稳定性.

双重信息引导的蚁群算法求解绿色多舱车辆路径问题

针对当前实际运输中广泛存在的绿色多舱车辆路径问题(GMCVRP),文章提出一种双重信息引导的蚁群优化算法(DIACO)进行求解.首先,在DIACO的全局搜索阶段,重新构建传统蚁群优化算法(TACO)中的信息素浓度矩阵(PCM),使其同时包含客户块信息和客户序列信息,即建立具有双重信息的PCM(DIPCM),从而更全面学习和累积优质解的信息;采用3种启发式方法生成较高质量个体,用于初始化DIPCM,可快速引导算法朝向解空间中优质区域进行搜索.其次,在DIACO的局部搜索阶段,设计结合自适应策略的多种变邻域操作,用于对解空间的优质区域执行深入搜索.再次,提出信息素浓度平衡机制,以防止搜索陷入停滞.最后,使用不同规模的算例进行仿真测试和算法对比,结果验证了DIACO是求解GMCVRP的有效算法.

软时间窗下考虑冷链物流多温共配的电动汽车路径优化

为了解决冷链物流的城市配送路径优化问题,面向物流企业低成本、高效率的需求,提出了一种新的具有软时间窗的电动汽车多温共配路径优化模型.该模型基于蓄冷器与保温箱,使不同温层货物可以在普通电动汽车上同时配送,提高车辆利用率.提出一种改进的蚁群算法来求解,将两元素优化(2-optimization,2-opt)算法与蚁群算法相结合,提高算法的局部搜索能力.基于Solomon数据集进行算例分析,验证模型与算法的有效性.结果表明:相较于单温配送模式,多温共配可以减少配送成本、提升配送效率;随着时间窗宽度扩大,车辆数随之减少,配送成本呈减少趋势,当车辆数降到最少后,由于激励成本与货损成本持续下降,带动总成本缓慢下降.

带时间窗的时间依赖型同时取送货车辆路径问题研究

针对带时间窗的时间依赖型同时取送货车辆路径问题(Time Dependent Vehicle Routing Problem with Simultaneous Pickup-Delivery and Time Windows,TDVRPSPDTW),本文建立以车辆固定成本、驾驶员成本、燃油消耗及碳排放成本之和为优化目标的数学模型;并在传统蚁群算法的基础上,利用节约启发式构造初始解初始化信息素,改进状态转移规则,引入局部搜索策略,提出一种带自适应大邻域搜索的混合蚁群算法(Ant Colony Optimization with Adaptive Large Neighborhood Search,ACO-ALNS)进行求解;最后,分别选取基准问题算例和改编生成TDVRPSPDTW算例进行实验。实验结果表明:本文提出的ACO-ALNS算法可有效解决TDVRPSPDTW的基准问题;相较于模拟退火算法和带局部搜索的蚁群算法,本文算法求解得到的总配送成本最优值平均分别改善7.56%和2.90%;另外,相比于仅考虑碳排放或配送时间的模型,本文所构建的模型综合多种因素,总配送成本平均分别降低4.38%和3.18%,可有效提高物流企业的经济效益。

智慧工地物料配送动态时间窗车辆路径优化

智慧工地物料配送是建筑业提升建造效率的重要环节。为有效解决智慧工地物料配送路径优化问题,依托运筹学理论将其转化为带时间窗的车辆路径规划问题。以总配送路径最短为目标函数,建立动态时间窗车辆路径(VRPDTW)数学模型,构建全局最优理论模型。运用改进人工势场算法分析障碍物和中间节点,再代入基础蚁群算法进行施工现场全局路径规划,对VRPDTW数学模型进行优化。并通过仿真实验对模型进行实证检验。结果表明:改进算法和VRPDTW模型可实现全局优化,能够有效解决智慧工地场景下物料连续配送问题,相较于基础算法,改进算法使路径规划的准确度提高,成本降低,效率提升,具有理论意义和行业应用价值。

改进蚁群算法优化车辆路径问题的研究

研究采用改进的蚁群算法优化带约束的车辆路径的问题。考虑的约束条件包括路径约束、时间窗约束和容量约束。主要目的是提出一种改进的蚁群算法进行车辆路径优化,构建配送车辆行驶路线,实现配送路线总成本的最小化。从三方面对蚁群算法进行了改进:对参与条件转移概率的候选节点列表进行预处理减少路线构建过程计算的时间复杂度;提出插入式节约算法用于改进蚁群初始配送路线提高寻优精度;基于蚁群系统对信息素更新策略进行改进,加快算法收敛速度。基于Solomon基准数据集,与近年来已取得的研究成果展开对比实验,证明提出的改进算法在提高求解精度和搜索效率方面的有效性,在优化带约束条件的车辆路径问题时的实用性,拓展了蚁群算法的应用领域。