Solving the heterogeneous fixed fleet open vehicle routing problem by a combined metaheuristic algorithm

The vehicle routing problem (VRP) is a well-known combinatorial optimisation problem and holds a central place in logistics management. Many exact, heuristic and metaheuristic approaches have been proposed to solve VRP. An important variant of the VRP arises when a ?eet of vehicles is fixed and characterised by different capacities for distribution activities. The problem is known as the heterogeneous fixed fleet VRP (HFFVRP). The HFFVRP is a natural generalisation of the VRP with several vehicle types, each type being defined by a capacity, a fixed cost and a cost per distance unit, and can cover more practical situations in transportation. This problem consists of determining a set of vehicle trips of minimum total length in which a set of customers is to be satisfied in the demand constraints using identical vehicles with limited capacity. If open routes instead of closed ones are considered in the HFFVRP, the problem becomes a heterogeneous fixed fleet Open VRP (HFFOVRP) which has numerous applications in industrial and service problems. In this paper, a bone route algorithm which uses the tabu search as an improved procedure is utilised to solve the HFFOVRP. The proposed algorithm was tested empirically on a 24 of generated VRPs, and compared with elite ant system and ant colony system. In all cases, the proposed algorithm finds the best-known solutions within a reasonable time.     

A branch and cut algorithm for the VRP with satellite facilities

An important aspect of the vehicle routing problem (VRP) that has been largely overlooked is the use of satellite facilities to replenish vehicles during a route. When possible, satellite replenishment allows the drivers to continue making deliveries until the close of their shift without necessarily returning to the central depot. This situation arises primarily in the distribution of fuels and certain retail items. When demand is random, optimizing customer routes a priori may result in significant additional costs for a particular realization of demand. Satellite facilities are one way of safeguarding against unexpected demand. This paper presents a branch and cut methodology for solving the VRP with satellite facilities subject to capacity and route time constraints. We begin with a mixed-integer linear programming formulation and then describe a series of valid inequalities that can be used to cut off solutions to the linear programming relaxation. Several separation heuristics are then outlined that are used to generate the cuts. Embedded in the methodology is a VRP heuristic for finding good feasible solutions at each stage of the computations. Results are presented for a set of problems derived from our experience with a leading propane distributor.     

A hybrid genetic algorithm for the multi-depot open vehicle routing problem

This paper studies the multi-depot open vehicle routing problem (MDOVRP), a variant of the vehicle routing problem (VRP), in which vehicles start from several depots and are not required to return to the depot. Despite the vast amount of literature about VRPs, the MDOVRP has received very little attention from researchers. In this paper, a new hybrid genetic algorithm is presented for finding the routes that minimize the traveling cost of the vehicles. Computational results on a number of test instances indicate the proposed algorithm dominates the CPLEX solver and the existing approach in the literature. Meanwhile, experiments are conducted on multi-depot VRP benchmarks, and the results are compared with a sophisticated tabu search approach and an exact method.     

Optimisation of the multi-depots pick-up and delivery problems with time windows and multi-vehicles using PSO algorithm

Many sectors in the transport industry are concerned about the vehicle routing problem (VRP), hence the growing interest of researchers for this type of problem and its variants. This is due essentially to its many real applications in logistics for the transport of goods. The originality and contribution of our work is that we have dealt a problem that combines several variants: multiple vehicles (m), multiple depots (MD), pickup and delivery problem (PDP) with time windows (TW). Hence the notation of our problem: m-MDPDPTW. In this paper, we present the m-MDPDPTW, which is an optimisation problem belonging to the category of NP Hard problems. This problem must meet requests for transport between customers and suppliers satisfying precedence, capacity and time constraints. The goal is to find the best solution, which is the best route minimising the total travelled distance. To solve and optimise our m-MDPDPTW, we have developed a new algorithm based on the particle swarm optimisation (PSO) method. The performance of this new approach is tested on data set instances of Li and Lim's benchmark problems in which we have added multiple depot locations. Comparing with prior works, our proposed approach gave better results by decreasing the distance for several studied instances.     

供应链中随机需求车辆选径问题的研究

结合供应链的需要给出了允许两次服务失败的数学模型,提出了一种混沌神经网络求解算法,对该问题进行了求解,并与SA算法进行了比较.结果表明该算法具有很强的避免陷入局部极小点的能力,较大地提高了优化的性能和搜索效率,适用于求解车辆选径问题.     

应用蜜蜂繁殖进化型粒子群算法求解车辆路径问题

为了提高粒子群算法求解车辆路径问题时收敛速度和全局搜索能力,将蜜蜂繁殖进化机制与粒子群算法相结合,应用到CVRP问题的求解。该算法中,最优的个体作为蜂王与通过选择机制选择的雄蜂以随机概率进行交叉,增强了最优个体信息的应用能力;同时,随机产生一部分雄蜂种群,并将其与蜂王交叉增加了算法的多样性。实例分析表明该算法具有较好的全局搜索能力,验证了该算法的可行性。     

Study on the vehicle routing problem considering congestion and emission factors

To meet the requirement of greening transportation in poor traffic condition, vehicle routing problem (VRP) with consideration of fuel consumption and congestion is studied. We formulated a time-dependent green vehicle routing problem (TD-GVRP) model with minimised total cost as the objective function which includes fuel consumption cost, and the measurement of fuel consumption is based on the Comprehensive Modal Emissions Model (CMEM). In the model, the situation of waiting at customer nodes to avoid bad traffic is defined. To solve this model, a Response Surface Method (RSM)-based hybrid algorithm (HA) that combines genetic algorithm (GA) and particle swarm optimisation (PSO) is constructed. Finally, using instances from PRPLIB database, the following experiments are carried out and the corresponding conclusions are drawn. (i) Comparison of the proposed objective and traditional VRP objectives shows that fuel consumption can be greatly reduced by introducing fuel consumption factor into the objective function. (ii) Sensitivity analysis of congestion duration provides the influence of congestion duration on fuel consumption and travel time. (iii) Experiments based on different waiting time reveal that the optimisation of departure time can reduce fuel consumption and total cost to some extent.     

An optimization algorithm for a capacitated vehicle routing problem with time windows

In this paper, vehicle routing problem (VRP) with time windows and real world constraints are considered as a real-world application on google maps. Also, tabu search is used and Hopfield neural networks is utilized. Basic constraints consist of customer demands, time windows, vehicle speed, vehicle capacity and working hours. Recently, cost and on-time delivery are the most important factors in logistics. Thus, the logistic applications attract attention of companies. In logistic management, determining the locations of delivery points and deciding the path are the vital components that should be considered. Deciding the paths of vehicles provides companies to use their vehicles efficiently. And with utilizing optimized paths, big amounts of cost and time savings will be gained. The main aim of the work is providing the best path according to the needs of the customers, minimizing the costs with utilizing the VRP and presenting an application for companies that need logistic management. To compare the results, simulated annealing is used on special scenarios. And t-test is performed in the study for the visited path in km with p-value of 0.05.     

基于离散差分进化算法的随机车辆路径问题

针对差分进化算法求解组合优化问题存在的局限性,引入计算机语言中的2种按位运算符,对差分进化算法的变异算子进行重新设计,用来求解不确定需求和旅行时间下同时取货和送货的随机车辆路径问题（SVRPSPD）。通过对车辆路径问题的benchmark问题和SVRPSPD问题进行路径优化,并同差分进化算法和遗传算法的计算结果进行比较,验证了离散差分进化算法的性能。结果表明,离散差分进化算法在解决复杂的SVRPSPD问题时,具有较好的优化性能,不仅能得到更好的优化结果,而且具有更快的收敛速度。     

面向快递同城运输的车辆路径问题研究

为降低运输成本,研究了快递同城运输中的车辆路径问题。建立多车型,含时间窗约束、容量约束、车辆限行约束,并考虑错峰交货的,以最小化运输成本为目标的混合整数规划模型。提出以点到点集的距离之和作为邻域搜索优先指标的构造性启发式算法,设计了基于“路径−车型对”的列生成算法,初始列由启发式算法求得。实验结果显示,对于120个点的大规模问题,列生成算法只需175秒就能得到近似最优解,验证了该算法的有效性及对一定规模内快递同城运输问题的适用性。     

带软时间窗的同时取送货车辆路径问题研究

考虑软时间窗下的车辆路径问题,客户点常伴有同时取送货的双重需求。针对此类问题,通过对软时间窗、车辆在途前后时间关系及二者融合问题进行刻画,同时将车辆行驶距离、车辆使用数、违反软时间窗总时间、客户满意度等纳入综合考量,构建相应混合整数非线性规划(mixed integer nonlinear programming, MINLP)模型。设计相应多目标优化求解算法,运用理想点法对目标函数进行转化,将多目标优化问题转化为单目标优化问题。结合相应算例集,运用LINGO 17.0全局求解程序求得每组算例的全局最优解。结果表明,针对带软时间窗的同时取送货车辆路径问题(vehicle routing problem with simultaneous pick-up and delivery and soft time windows, VRPSPDSTW),所建模型及算法是有效且可行的。     

An integrated approach to the vehicle routing and container loading problems

Real-world distribution problems raise some practical considerations that usually are not considered in a realistic way in more theoretical studies. One of these considerations is related to the vehicle capacity, not only in terms of cubic meters or weight capacity but also in terms of the cargo physical arrangements. In a distribution scene, two combinatorial optimization problems, the vehicle routing problem with time windows and the container loading problem, are inherently related to each other. This work presents a framework to integrate these two problems using two different resolution methods. The first one treats the problem in a sequential approach, while the second uses a hierarchical approach. To test the quality and efficiency of the proposed approaches, some test problems were created based on the well-known Solomon, Bischoff and Ratcliff test problems. The results of the integrated approaches are presented and compared with results of the vehicle routing problem with time windows and the container loading problem applied separately.     

混合蝙蝠算法在包装件配送中的应用研究

目的使蝙蝠算法(BA)适应包装件配送车辆路径问题(VRP)的求解,并提高该算法的求解性能。方法在标准BA算法的基础上提出混合蝙蝠算法(HBA)。首先,设计改进的蝙蝠算法(IBA),使其能够适用于包装件配送VRP问题的求解。其次,引入混沌系统,对IBA算法进行混沌初始化。然后,设计裂变算子和变异算子。在IBA算法迭代前半段,将蝙蝠种群中较差的一半蝙蝠重新混沌初始化,以提高种群多样性。在IBA算法迭代后半段,对陷入局部最优解的蝙蝠进行鲶鱼扰动。最后,提出HBA算法并对企业实例进行仿真测试。结果 HBA算法求得的最优配送距离为773.01 km,相对于GA算法(781.25 km)和IBA算法(786.04 km)分别节约了8.24 km和13.03 km。结论与IBA算法和GA算法相比,HBA算法求解包装件配送VRP问题的全局优化能力更强、收敛速度更快。     

包装废弃物回收车辆路径问题的改进遗传算法

目的采用优化传统遗传算法(GA)研究包装废弃物回收车辆路径问题(VRP)的性能。方法提出改进遗传算法(IGA)。首先,设计基于贪婪算法的初始种群生成算子,提高初始种群质量;其次,设计根据适应度值大小、进化代数等自适应调整的交叉和变异概率;然后,设计最大保留交叉算子,保证种群的多样性;最后,对企业实例和标准算例进行仿真测试。结果采用IGA算法、蚁群算法(ACO)能求得算例最优解,且IGA算法运行速度快于ACO算法,分支界定算法(BBM)、传统GA算法无法求得算例最优解。结论与BBM算法、传统GA算法和ACO算法相比,IGA算法求解包装废弃物回收VRP问题的整体性能更优。     

Production scheduling optimization algorithm for the hot rolling processes

The hot rolling production scheduling problem is an extremely difficult and time-consuming process, so it is quite difficult to achieve an optimal solution with traditional optimization methods owing to the high computational complexity. To ensure the feasibility of solutions and improve the efficiency of the scheduling, this paper proposes a vehicle routing problem (VRP) to model the problem and develops an easily implemented hybrid approach (QPSO-SA) to solve the problem. In the hybrid approach, quantum particle swarm optimization (QPSO) combines local search and global search to search the optimal results and simulated annealing (SA) employs certain probability to avoid getting into a local optimum. The computational results from actual production data have shown that the proposed model and algorithm are feasible and effective for the hot rolling scheduling problem.     

A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty

In this paper we introduce a robust optimization approach to solve the Vehicle Routing Problem (VRP) with demand uncertainty. This approach yields routes that minimize transportation costs while satisfying all demands in a given bounded uncertainty set. We show that for the Miller-Tucker-Zemlin formulation of the VRP and specific uncertainty sets, solving for the robust solution is no more difficult than solving a single deterministic VRP. Our computational results on benchmark instances and on families of clustered instances show that the robust solution can protect from unmet demand while incurring a small additional cost over deterministic optimal routes. This is most pronounced for clustered instances under moderate uncertainty, where remaining vehicle capacity is used to protect against variations within each cluster at a small additional cost. We compare the robust optimization model with classic stochastic VRP models for this problem to illustrate the differences and similarities between them. We also observe that the robust solution amounts to a clever management of the remaining vehicle capacity compared to uniformly and non-uniformly distributing this slack over the vehicles.     

Simulation-based optimisation approach for the stochastic two-echelon logistics problem

This work proposes a simulation-based optimisation approach for the two-echelon vehicle routing problem with stochastic demands (2E-VRPSD). In the proposed 2E-VRPSD, freight delivery from the depot to the customers is managed by shipping the freight through intermediate satellites, while each customer has a stochastic demand. The 2E-VRPSD is an extension of the famous capacitated vehicle routing problem with stochastic demands and the two-echelon vehicle routing problem (2E-VRP). A tabu search algorithm is designed to solve the 2E-VRPSD, in which Monte Carlo sampling is adopted to tackle the issue of stochastic demands. Modified two-echelon vehicle routing problem benchmark instances are used in the numerical experiments. The computational results show the advantage of the proposed simulation-based approach.     

基于密度峰值聚类的VRPTW问题研究

提出一种密度峰值聚类 (density peak clustering, DPC)与遗传算法(genetic algorithm, GA)相结合的新型混合算法(density peak clustering with genetic algorithm, DGA),求解带时间窗的车辆路径问题。首先应用DPC对客户进行聚类以缩减问题规模,再将聚类后的客户用GA进行线路优化。结果表明：DGA在9个数据集上的平均值比模拟退火(simulated annealing, SA)和禁忌搜索(Tabu)分别提高了13.41%和4.7%,单个数据集最大提高了26.4%。这证明了该算法是求解车辆调度问题的高效算法。     

Research on Vehicle Routing Problem with Soft Time Windows Based on Hybrid Tabu Search and Scatter Search Algorithm

With the expansion of the application scope of social computing problems, many path problems in real life have evolved from pure path optimization problems to social computing problems that take into account various social attributes, cultures, and the emotional needs of customers. The actual soft time window vehicle routing problem, speeding up the response of customer needs, improving distribution efficiency, and reducing operating costs is the focus of current social computing problems. Therefore, designing fast and effective algorithms to solve this problem has certain theoretical and practical significance. In this paper, considering the time delay problem of customer demand, the compensation problem is given, and the mathematical model of vehicle path problem with soft time window is given. This paper proposes a hybrid tabu search (TS) & scatter search (SS) algorithm for vehicle routing problem with soft time windows (VRPSTW), which mainly embeds the TS dynamic tabu mechanism into the SS algorithm framework. TS uses the scattering of SS to avoid the dependence on the quality of the initial solution, and SS uses the climbing ability of TS improves the ability of optimizing, so that the quality of search for the optimal solution can be significantly improved. The hybrid algorithm is still based on the basic framework of SS. In particular, TS is mainly used for solution improvement and combination to generate new solutions. In the solution process, both the quality and the dispersion of the solution are considered. A simulation experiments verify the influence of the number of vehicles and maximum value of tabu length on solution, parameters’ control over the degree of convergence, and the influence of the number of diverse solutions on algorithm performance. Based on the determined parameters, simulation experiment is carried out in this paper to further prove the algorithm feasibility and effectiveness. The results of this paper provide further ideas for solving vehicle routing problems with time windows and improving the efficiency of vehicle routing problems and have strong applicability.     

求解VRP问题的混沌模拟退火萤火虫算法

目的使萤火虫优化算法(GSO)能够适用于车辆路径问题(VRP)的求解,同时提高该算法的求解性能。方法通过对GSO算法的改进,提出求解VRP问题的混沌模拟退火萤火虫优化算法(CSAGSO)。首先,设计改进的GSO算法(IGSO)使IGSO算法能够适应VRP问题的求解;其次,在IGSO算法中引入模拟退火机制,提出模拟退火萤火虫优化算法(SAGSO),使IGSO算法可有效避免陷入局部极小并最终趋于全局最优。然后,在SAGSO算法中引入混沌机制,提出CSAGSO算法,对SAGSO算法的荧光素浓度值进行混沌初始化和混沌扰动;最后,对标准算例集进行仿真测试。结果与遗传算法、蚁群算法和粒子群算法相比,CSAGSO算法的全局寻优能力、收敛速度及稳定性均改善了50%以上。结论对GSO算法的改进是合理的,且CSAGSO算法的全局优化能力、收敛速度和稳定性均优于遗传算法、蚁群算法和粒子群算法。