粒子群算法的MDVRP仿真研究

物流配送车辆路径优化问题是近年来物流领域中的研究热点,路径优化属于NP 难题,问题规模较大,很难得到最优解和满意解.应用粒子群算法是被认为求解NP 难题的有效手段之一,为解决MDVRP(多车场车辆路径)的优化问题,在求解物流配送车辆路径优化问题时提出将粒子群算法与变异操作相结合的求解方式:通过设计一个随群体适应度方差的变化而变化的变异算子,将聚集在局部收敛点附近的粒子打散,进而增强算法跳出局部最优的能力和全局寻优的几率.针对多车场车辆路径问题构造了一种新的编码方式以减少算法的无效迭代.仿真结果表明,采用全局搜索能力有显著提高,并能有效避免早熟收敛问题.     

物流运输调度问题的混沌烟花算法——基于多车型供应链

为了满足供应链物流的不同需求，考虑多种车型、车辆容量、车辆油耗、车辆最大配送距离等约束条件，以最小油耗、最短配送距离为目标，建立多车型供应链物流运输调度模型（Multi-Type Vehicle Routing Problem in Supply Chain，MTVRPSC），并提出一种混沌烟花算法求解该模型。该算法以烟花算法为核心，提出一种编解码策略实现连续空间到MTVRPSC离散空间的映射，重新定义算法的适应度函数、适应度值和适应度的比较方法，并采用混沌初始化策略和混沌搜索策略来增强算法收敛效果。实验结果表明，所提出的算法在求解MTVRPSC时具有较强的寻优能力和稳定性。     

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。     

基于粒子群算法的满载需求可拆分车辆路径规划

为了更加合理地规划车辆配送路径,尽可能使用最少的车辆数和最短路径长度来完成整个客户点的配送任务,提出一种基于粒子群算法的满载需求可拆分车辆路径(F-SDVRP)规划策略,在配送过程中通过确保任何一辆满载的配送车辆从配送点出发后均以“最优”的配送路径进行配送来达到配送的总路径“最优”要求,并通过粒子群算法不断优化整个客户点的配送顺序.仿真结果表明,在求解相关客户点配送问题时,所提出的车辆规划策略得到的结果优于对比文献中的求解方法,在配送车辆数相同的情况下,最大的路径长度减少率达到8.21%.此外,各算例的仿真结果表明,所提出的策略的寻优结果稳定,粒子群算法可以解决满载需求可拆分车辆路径规划问题.     

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.     

求解带硬时间窗的多目标车辆路径问题的多种混合蝙蝠算法

针对多目标车辆路径问题的研究,考虑了车载量限制和硬时间窗的约束条件,以最小派车数和最小车辆行驶距离为目标建立了数学模型。在分析基本蝙蝠算法求解离散问题局限性的基础上,混合蝙蝠法加入交叉算子和重组算子,提高算法性能。利用遗传算法的特点,构建出三种混合蝙蝠算法,算例测试结果表明,混合蝙蝠算法是解决离散型问题的一种有效方法。与基本蝙蝠算法相比,混合蝙蝠算法具有较高的计算效率和持续优化能力,其中单点重组精英遗传混合蝙蝠算法解决算例寻优能力最佳。 关键词：混合蝙蝠算法;车辆路径问题;多目标;硬时间窗     

基于end-to-end深度强化学习的多车场车辆路径优化

为提高多车场车辆路径问题(multi-depot vehicle routing problem, MDVRP)的求解效率,提出了端到端的深度强化学习框架。首先,将MDVRP建模为马尔可夫决策过程(Markov decision process, MDP),包括对其状态、动作、收益的定义;同时,提出了改进图注意力网络(graph attention network, GAT)作为编码器对MDVRP的图表示进行特征嵌入编码,设计了基于Transformer的解码器;采用改进REINFORCE算法来训练该模型,该模型不受图的大小约束,即其一旦完成训练,就可用于求解任意车场和客户数量的算例问题。最后,通过随机生成的算例和公开的标准算例验证了所提出框架的可行性和有效性,即使在求解客户节点数为100的MDVRP上,经训练的模型平均仅需2 ms即可得到与现有方法相比更具优势的解。     

求解0-1背包问题的二进制蝙蝠算法

为了求解离散空间中的最优化问题,提出了一种二进制蝙蝠算法,并引入时变惯性因子来提高算法的全局收敛速度;在此基础上,为提高求解0-1背包问题时找到最优解的机率,利用贪心优化策略对无效的蝙蝠个体进行优化,从而给出了贪心二进制蝙蝠算法（GBBA）。仿真计算结果表明,GBBA算法在寻优能力和收敛性能方面比已有的GMBA算法都更优越。     

求解带容量和时间窗约束车辆路径问题的改进蝙蝠算法

带时间窗和容量约束的车辆路径问题是车辆路径问题重要的扩展之一,属于NP难题,精确算法的求解效率较低,且对于较大规模问题难以在有限时间内给出最优解.为了满足企业和客户快速有效的配送需求,使用智能优化算法可以在有限的时间内给出相对较优解.研究了求解带容量和时间窗约束车辆路径问题的改进离散蝙蝠算法,为增加扰动机制,提高搜索速度和精度,在对客户点按其所在位置进行聚类的基础上,在算法中引入了变步长搜索策略和两元素优化方法进行局部搜索.仿真实验结果表明,所设计算法具有较高寻优能力和较强的实用价值.     

易腐生鲜货品车辆路径问题的改进混合蝙蝠算法

针对配送易腐生鲜货品的车辆其配送路径的选择不仅受货品类型、制冷环境变化、车辆容量限制、交货时间等多种因素的影响,而且需要达到一定的目标（如：费用最少、客户满意度最高）,构建了易腐生鲜货品车辆路径问题（VRP）的多目标模型,并提出了求解该模型的改进混合蝙蝠算法。首先,采用时间窗模糊化处理方法定义客户满意度函数,细分易腐生鲜货品类型并定义制冷成本,建立了最优路径选择的多目标模型;然后,在分析蝙蝠算法求解离散问题易陷入局部最优、过早收敛等问题的基础上,精简经典蝙蝠算法的速度更新公式,并对混合蝙蝠算法的单多点变异设定选择机制,提高算法性能;最后,对改进混合蝙蝠算法进行性能测试。实验结果表明,与基本蝙蝠算法和已有混合蝙蝠算法相比,所提算法在求解VRP时能够提高客户满意度1.6%~4.2%,且减小平均总成本0.68%~2.91%。该算法具有计算效率高、计算性能好和较高的稳定性等优势。     

多中心半开放式送取需求可拆分的车辆路径优化

针对多中心半开放式送取需求可拆分的车辆路径问题,构建了以车辆配送距离最短为目标的多中心半开放式送取需求可拆分的数学模型。设计大变异邻域遗传算法进行求解,采用二维染色体编码及顺序交叉策略,同时运用大变异策略和邻域搜索策略提高算法全局和局部的寻优能力,通过算例对比验证了所提模型与算法的有效性。算例实验表明,大变异邻域遗传算法在求解多中心物流配送车辆路径问题上求解质量较优、求解效率较高、求解结果较为稳定,同时验证了联合配送下多中心半开放式送取需求可拆分的配送模式优于独立配送下单中心送取需求可拆分的配送模式。研究成果不仅拓展了车辆路径问题,还可为相关快递物流企业配送优化提供决策参考。     

Multi-depot vehicle routing problem: a one-stage approach

This paper introduces multi-depot vehicle routing problem with fixed distribution of vehicles (MDVRPFD) which is one important and useful variant of the traditional multi-depot vehicle routing problem (MDVRP) in the supply chain management and transportation studies. After modeling the MDVRPFD as a binary programming problem, we propose two solution methodologies: two-stage and one-stage approaches. The two-stage approach decomposes the MDVRPFD into two independent subproblems, assignment and routing, and solves them separately. In contrast, the one-stage approach integrates the assignment with the routing where there are two kinds of routing methods-draft routing and detail routing. Experimental results show that our new one-stage algorithm outperforms the published methods. Note to Practitioners-This work is based on several consultancy work that we have done for transportation companies in Hong Kong. The multi-depot vehicle routing problem (MDVRP) is one of the core optimization problems in transportation, logistics, and supply chain management, which minimizes the total travel distance (the major factor of total transportation cost) among a number of given depots. However, in real practice, the MDVRP is not reliable because of the assumption that there have unlimited number of vehicles available in each depot. In this paper, we propose a new useful variant of the MDVRP, namely multi-depot vehicle routing problem with fixed distribution of vehicles (MDVRPFD), to model the practicable cases in applications. Two-stage and one-stage solution algorithms are also proposed. The industry participators can apply our new one-stage algorithm to solve the MDVRPFD directly and efficiently. Moreover, our one-stage solution framework allows users to smoothly add new specified constraints or variants.     

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.     

Multi-phase modified shuffled frog leaping algorithm with extremal optimization for the MDVRP and the MDVRPTW

In this work, a novel multi-phase modified shuffled frog leaping algorithm (MPMSFLA) framework is presented to solve the multi-depot vehicle routing problem (MDVRP) more quickly. The presented algorithm adopts the K-means algorithm to execute the clustering analyses for all customers, generates a frog population according to the result of the clustering analyses, and then proceeds to the three-phase process. In the first phase, a cluster MSFLA local search is carried out for each cluster. In the second phase, the algorithm selects good individuals through a binary tournament to construct a new population and then performs a global optimization for all customers and depots using the global MSFLA. In the third phase, a cluster adjustment is implemented for the population to generate new clusters. These procedures continue until the convergence criterion is satisfied. The experimental results show that our algorithm can achieve a high quality solution within a short runtime for the MDVRP, the MDVRP with time windows (MDVRPTW) and the capacitated vehicle routing problem (CVRP). The proposed algorithm is suitable for solving large-scale problems.     

车辆路径问题的轻鲁棒优化模型与算法

针对不确定旅行时间下的车辆路径问题,以总变动成本最小为优化目标,建立了一种轻鲁棒优化模型,提出了一种针对问题特征的超启发式粒子群算法.在算法中,利用基于图论中深度优先搜索的初始化策略加快算法的早期收敛速度,引入基于均衡策略的启发式规则变换方式来提高算法的寻优能力,重新设计的粒子更新公式确保生成低层构造算法的有效性.实验...     

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.     

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.