多车场车辆路径问题的遗传算法

给出了多车场车辆路径问题(MDVRP)的数学模型,提出一种基于客户的编码表示方式,可以表示出各车场出动的车辆及路径,能够有效地实现MDVRP的优化,并用计算实例进行了验证。     

基于双层模糊聚类的多车场车辆路径遗传算法

对大规模多车场车辆路径问题,设计了基于双层模糊聚类的改进遗传算法求解框架,上层静态区域划分利用k-means技术将多车场到多客户的问题转化为一对多的子问题,下层模糊聚类从保证客户满意度和整合物流资源的角度出发,利用模糊聚类算法根据客户需求属性形成基于客户订单配送的动态客户群。进一步,通过改进选择算子和交叉算子来设计车辆路径优化的遗传算法。通过随机算例仿真实验,证明了提出方法和求解策略的有效性。     

泰森多边形的离散蝙蝠算法求解多车场车辆路径问题

本文提出一种泰森多边形的离散蝙蝠算法求解多车场车辆路径问题(multi-depot vehicle routing problem,MDVRP).所提出算法以离散蝙蝠算法为核心,融入了一种基于多车场多车辆问题的编解码策略.所提出算法还使用基于泰森多边形的初始化策略加快算法的前期收敛速度,采用基于向量比较机制的适应度函数来控制算法收敛的方向,引入基于近邻策略和优先配送策略的局部搜索算法来提高算法的寻优能力.实验结果表明:在合理的时间耗费内,所提出的算法能有效地求解MDVRP,尤其是带配送距离约束的MDVRP;相对于对比算法,所提出的算法表现出较强的寻优能力和稳定性.     

应急物流中的累计时间式多车场车辆路径问题

为提升应急救援的快速性和公平性,以最小化所有受灾点的累计等待时间为目标建立累计时间式多车场车辆路径问题(Cum-MDVRP)的模型。由于该问题具有NP-hard性质,设计了一种多起始点变邻域下降法对其进行快速求解。每次迭代中,多起始点方法通过改进的Split算法结合可行性修复程序生成随机的初始可行解,然后由变邻域下降法对其进一步改进。扩展的标准算例的测试结果验证了所提出模型和求解算法的有效性。     

基于深度强化学习的多配送中心车辆路径规划

多配送中心车辆路径规划(multi-depot vehicle routing problem, MDVRP)是现阶段供应链应用较为广泛的问题模型,现有算法多采用启发式方法,其求解速度慢且无法保证解的质量,因此研究快速且有效的求解算法具有重要的学术意义和应用价值.以最小化总车辆路径距离为目标,提出一种基于多智能体深度强化学习的求解模型.首先,定义多配送中心车辆路径问题的多智能体强化学习形式,包括状态、动作、回报以及状态转移函数,使模型能够利用多智能体强化学习训练;然后通过对MDVRP的节点邻居及遮掩机制的定义,基于注意力机制设计由多个智能体网络构成的策略网络模型,并利用策略梯度算法进行训练以获得能够快速求解的模型;接着,利用2-opt局部搜索策略和采样搜索策略改进解的质量;最后,通过对不同规模问题仿真实验以及与其他算法进行对比,验证所提出的多智能体深度强化学习模型及其与搜索策略的结合能够快速获得高质量的解.     

多车场多车型车辆调度问题的改进粒子群算法

多车场多车型车辆调度问题优化是物流配送中的典型NP难解问题,针对传统的粒子群算法存在收敛速度慢,易早熟收敛等问题,提出了一种改进的粒子群优化算法。该算法对种群中的粒子采用一定的概率进行柯西变异,使算法跳出局部最优解。将算法应用于多车场多车型车辆调度问题优化,算例证明该算法求解多车场多车型车辆调度问题是可行的,并且优于标准粒子群优化算法。     

带软时间窗的多车场开放式车辆调度

带软时间窗的多车场开放式车辆调度问题是在开放式车辆路径问题的基础上,考虑了多车场和客户服务时间的约束,是一类典型的NP难解问题。针对该问题,提出了一种改进的蚁群算法求解方案,并建立了相应的数学模型。首先通过设置一个虚拟车场将多车场VRP转化为单车场VRP,然后利用参数控制的改进蚁群算法与2-opt算法结合来对模型求解。算法先利用K-means与细菌觅食算法相结合的聚类技术判断蚁群状态,进而动态调整算法参数,使其快速收敛到全局最优解附近,再依据混沌理论的特点来调整参数,使其跳出局部最优。最后,再利用2-opt算法对最优解进行优化。实验结果验证了该算法求解MDOVRPSTW问题的有效性。     

一种基于图神经网络的改进邻域搜索算法

近年来图神经网络与深度强化学习的发展为组合优化问题的求解提供了新的方法。当前此类方法大多未考虑到算法参数学习问题,为解决该问题,基于图注意力网络设计了一种智能优化模型。该模型对大量问题数据进行学习,自动构建邻域搜索算子与序列破坏终止符,并使用强化学习训练模型参数。在标准算例集上测试模型并进行三组不同实验。实验结果表明,该模型学习出的邻域搜索算子具备较强的寻优能力和收敛性,同时显著降低了训练占用显存。该模型能够在较短时间内求解包含数百节点的CVRP问题,并具有一定的扩展潜力。     

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.     

战时备件配送的MDVRP问题及其遗传算法求解

战时备件配送的车辆调度是提高装备保障效率的关键因素。以装备战斗效能损失最小化为车辆调度的目标,建立了多仓库车辆路径问题MDVRP（Multi—Depot Vehicle Routing Problem）模型,并应用混合遗传算法对问题进行了求解。算法中,设计了串行、并行及半并行三种交叉算子,并应用局部搜索模块对子个体进行改进。对算例的计算实验表明,半并行交叉算子在精度方面优于另外两种交叉算子。     

Learning to Branch in Combinatorial Optimization With Graph Pointer Networks

Traditional expert-designed branching rules in branch-and-bound(B&B) are static, often failing to adapt to diverse and evolving problem instances. Crafting these rules is labor-intensive, and may not scale well with complex problems.Given the frequent need to solve varied combinatorial optimization problems, leveraging statistical learning to auto-tune B&B algorithms for specific problem classes becomes attractive. This paper proposes a graph pointer network model to learn the branch rul...     

多物流中心共同配送的车辆路径问题研究

研究多物流中心共同配送的车辆路径问题。首先考虑客户服务关系变化与客户需求的异质性情况,设计一种共享客户需求、配送车辆与物流中心的共享物流模式;再综合考虑车辆容量、油耗、碳排放、最长行驶时间、客户需求量与服务时间等因素,以总成本最小为目标构建多物流中心共同配送的车辆路径规划模型,并设计一种改进蚁群算法进行求解;最后采用多类型算例进行仿真实验,结果表明共享物流模式能有效避免交叉配送与迂回运输等不合理现象,降低物流成本,缩短车辆行驶距离,减少车辆碳排放,促进物流与环境的和谐发展。     

METAHEURISTIC APPROACH FOR THE MULTI-DEPOT VEHICLE ROUTING PROBLEM

Distribution logistics comprises all activities related to the provision of finished products and merchandise to a customer. The focal point of distribution logistics is the shipment of goods from the manufacturer to the consumer. The products can be delivered to a customer directly either from the production facility or from the trader's stock located close to the production site or, probably, via additional regional distribution warehouses. These kinds of distribution logistics are mathematically represented as a vehicle routing problem (VRP), a well-known nondeterministic polynomial time (NP)-hard problem of operations research. VRP is more suited for applications having one warehouse. In reality, however, many companies and industries possess more than one distribution warehouse. These kinds of problems can be solved with an extension of VRP called multi-depot VRP (MDVRP). MDVRP is an NP-hard and combinatorial optimization problem. MDVRP is an important and challenging problem in logistics management. It can be solved using a search algorithm or metaheuristic and can be viewed as searching for the best element in a set of discrete items. In this article, cluster first and route second methodology is adapted and metaheuristics genetic algorithms (GA) and particle swarm optimization (PSO) are used to solve MDVRP. A hybrid particle swarm optimization (HPSO) for solving MDVRP is also proposed. In HPSO, the initial particles are generated based on the k-means clustering and nearest neighbor heuristic (NNH). The particles are decoded into clusters and multiple routes are generated within the clusters. The 2-opt local search heuristic is used for optimizing the routes obtained; then the results are compared with GA and PSO for randomly generated problem instances. The home delivery pharmacy program and waste-collection problem are considered as case studies in this paper. The algorithm is implemented using MATLAB 7.0.1.     

考虑无线充电的无人机路径在线规划

近年来, 无人机在物流、通信、军事任务、灾害救援等领域中展现出了巨大的应用潜力, 然而无人机的续航 能力是制约其使用的重大因素, 在无线充电技术不断突破和发展的背景下, 本文基于深度强化学习方法, 提出了一 种考虑无线充电的无人机路径在线优化方法, 通过无线充电技术提高无人机的任务能力. 首先, 对无人机功耗模型 和无线充电模型进行了构建, 根据无人机的荷电状态约束, 设计了一种基于动态上下文向量的深度神经网络模型, 通过编码器和解码器的模型架构, 实现无人机路径的直接构造, 通过深度强化学习方法对模型进行离线训练, 从而 应用于考虑无线充电的无人机任务路径在线优化. 文本通过与传统优化方法和深度强化学习方法进行实验对比, 所提方法在CPU算力和GPU算力下分别实现了4倍以及100倍以上求解速度的提升.     

Improved Shuffled Frog Leaping Algorithm and its multi-phase model for multi-depot vehicle routing problem

In the present work, an improved Shuffled Frog Leaping Algorithm (SFLA) and its multi-phase model are presented to solve the multi-depots vehicle routing problems (MDVRPs). To further improve the local search ability of SFLA and speed up convergence, a Power Law Extremal Optimization Neighborhood Search (PLEONS) is introduced to SFLA. In the multi-phase model, firstly the proposed algorithm generates some clusters randomly to perform the clustering analyses considering the depots as the centroids of the clusters for all the customers of MDVRP. Afterward, it implements the local depth search using the SFLA for every cluster, and then globally re-adjusts the solutions, i.e., rectifies the positions of all frogs by PLEONS. In the next step, a new clustering analyses is performed to generate new clusters according to the best solution achieved by the preceding process. The improved path information is inherited to the new clusters, and the local search using SFLA for every cluster is used again. The processes continue until the convergence criterions are satisfied. The experiment results show that the proposed algorithm possesses outstanding performance to solve the MDVRP and the MDVRP with time windows.     

Hybrid ant colony optimization algorithm applied to the multi-depot vehicle routing problem

The article deals with the hybrid Ant Colony Optimization algorithm and its application to the Multi-Depot Vehicle Routing Problem (MDVRP). The algorithm combines both probabilistic and exact techniques. The former implements the bio-inspired approach based on the behaviour of ants in the nature when searching for food together with simulated annealing principles. The latter complements the former. The algorithm explores the search space in a finite number of iterations. In each iteration, the deterministic local optimization process may be used to improve the current solution. Firstly, the key parts and features of the algorithm are presented, especially in connection with the exact optimization process. Next, the article deals with the results of experiments on MDVRP problems conducted to verify the quality of the algorithm; moreover, these results are compared to other state-of-the-art methods. As experiments, Cordreau’s benchmark instances were used. The experiments showed that the proposed algorithm overcomes the other methods as it has the smallest average error (the difference between the found solution and the best known solution) on the entire set of benchmark instances.

     

基于多蚁群同步优化的多真值发现算法

为提高在多真值场景下真值发现的准确性,提出一种多蚁群同步优化的多真值发现算法（multi-ant co-lonies synchronization optimization based multi-truth discovery algorithm,MAC-SO-MTD）。以最大化各数据源提供的观测值集合与该对象真值集合之间相似度的加权和为目标,将多真值发现问题建模为求解子集问题,在此基础上设计蚁群算法进行求解：根据对象个数设置相应的蚁群,构造子集问题的有向图,利用路径概率转移公式进行同步搜索真值;将信息素更新分为本次迭代最优更新和本次迭代不更新,提高了算法的收敛速度。最后,通过算法复杂度分析和在真实数据集上的实验验证了该算法的优越性。     

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.