Multi-objective vehicle routing problem with time windows using goal programming and genetic algorithm

This paper presents a new model and solution for multi-objective vehicle routing problem with time windows (VRPTW) using goal programming and genetic algorithm that in which decision maker specifies optimistic aspiration levels to the objectives and deviations from those aspirations are minimized. VRPTW involves the routing of a set of vehicles with limited capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. This paper uses a direct interpretation of the VRPTW as a multi-objective problem where both the total required fleet size and total traveling distance are minimized while capacity and time windows constraints are secured. The present work aims at using a goal programming approach for the formulation of the problem and an adapted efficient genetic algorithm to solve it. In the genetic algorithm various heuristics incorporate local exploitation in the evolutionary search and the concept of Pareto optimality for the multi-objective optimization. Moreover part of initial population is initialized randomly and part is initialized using Push Forward Insertion Heuristic and λ-interchange mechanism. The algorithm is applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances. Results show that the suggested approach is quiet effective, as it provides solutions that are competitive with the best known in the literature.     

An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows

The vehicle routing problem with time windows is a complex combinatorial problem with many real-world applications in transportation and distribution logistics. Its main objective is to find the lowest distance set of routes to deliver goods, using a fleet of identical vehicles with restricted capacity, to customers with service time windows. However, there are other objectives, and having a range of solutions representing the trade-offs between objectives is crucial for many applications. Although previous research has used evolutionary methods for solving this problem, it has rarely concentrated on the optimization of more than one objective, and hardly ever explicitly considered the diversity of solutions. This paper proposes and analyzes a novel multi-objective evolutionary algorithm, which incorporates methods for measuring the similarity of solutions, to solve the multi-objective problem. The algorithm is applied to a standard benchmark problem set, showing that when the similarity measure is used appropriately, the diversity and quality of solutions is higher than when it is not used, and the algorithm achieves highly competitive results compared with previously published studies and those from a popular evolutionary multi-objective optimizer.     

应急物资运输路径多目标优化模型及求解算法

针对应急前期运输商自有车辆不足的实际背景,采用自有车辆和第三方租用车辆共同配送的运输模式,对混合车辆路径的组合优化问题进行研究。首先,考虑需求点和运输商的不同利益诉求,以系统满意度最大、系统配送时间和总成本最小为优化目标,建立带软时间窗的多目标混合车辆路径优化模型。其次,考虑NSGA-Ⅱ算法在求解该类问题时收敛性差和Pareto前沿分布不均匀的缺点,将蚁群算法的启发式策略和信息素正反馈机制用于生成子代种群,非支配排序策略模型用于指导算法的多目标择优过程,并引入变邻域下降搜索以扩大搜索空间,提出求解多目标的非支配排序蚁群算法以突破原有算法瓶颈。算例表明：构建的模型可对决策者在不同的情境下依据不同的优化目标选择合理的路径提供参考,提出的算法在求解不同规模的问题和不同分布类型的问题中均表现出较好的性能。     

A New Multi-objective Competitive Open Vehicle Routing Problem Solved by Particle Swarm Optimization

This paper presents a new variant of an open vehicle routing problem (OVRP), in which competition exists between distributors. In the OVRP with competitive time windows (OVRPCTW), the reaching time to customers affects the sales amount. Therefore, distributors intend to service customers earlier than rivals, to obtain the maximum sales. Moreover, a part of a driver??s benefit is related to the amount of sales; thus, the balance of goods carried in each vehicle is important in view of the limited vehicle capacities. In this paper, a new, multi-objective mathematical model of the homogeneous and competitive OVRP is presented, to minimize the travel cost of routes and to maximize the obtained sales while concurrently balancing the goods distributed among vehicles. This model is solved by the use of a multi-objective particle swarm optimization (MOPSO) algorithm, and the related results are compared with the results of NSGA-II, which is a well-known multi-objective evolutionary algorithm. A comparison of our results with three performance metrics confirms that the proposed MOPSO is an efficient algorithm for solving the competitive OVRP with a reasonable computational time and cost.     

An arc flow formulation to the multitrip production,inventory, distribution,and routing problem with time windows

The multitrip production, inventory, distribution, and routing problem with time windows (MPIDRPTW) is an integrated problem that combines a production and distribution problem, a multitrip vehicle routing problem, and an inventory routing problem. In the MPIDRPTW, a set of customers, which have a time-varying demand during a finite planning horizon, is served by a single production facility. The distribution is accomplished by a fleet of homogeneous vehicles that deliver the customer orders within their specific time windows. Production management has to be done according to the inventories at the facility and at the customers. An exact arc flow model based on a graph is proposed to solve the MPIDRPTW, where the nodes represent instants of time. The main goal of the problem is to minimize the costs associated with the entire system. The proposed approach was implemented and a set of experimental tests were conducted based on a set of adapted instances from the literature.     

A multilevel approach for modelling vehicle routing problem with uncertain travelling time

Vehicle routing problem is concerned with finding optimal collection or delivery routes in a transportation network, beginning and ending at a central depot, for a fleet of vehicles to serve a set of customers under some constraints. Assuming the travel times between two customers are uncertain variables, this paper proposes an uncertain multilevel programming model for a vehicle routing problem, of which the leader’s object is to minimize the total waiting times of the customers, and the followers’ objects are to minimize the waiting times of the vehicles for the beginning moments of the customers’ time windows. The uncertain multilevel programming model is transformed into a determinacy programming model, and an intelligent algorithm is designed for solving the crisp model.     

An ACO hybrid metaheuristic for close–open vehicle routing problems with time windows and fuzzy constraints

The close–open vehicle routing problem is a realistic variant of the “classical” vehicle routing problem where the routes can be opened and closed, i.e. all the vehicles are not required to return to the depot after completing their service. This variant is a planning model that is a standard practice in business nowadays. Companies are contracting their deliveries to other companies that hire vehicles, and payment is made based on the distance covered by the vehicles. Available information on parameters in real world situations is also imprecise, and must be included in the optimization model and method. The aims of this paper are to formulate a model of this novel variant with time windows and imprecise constraints and to propose a fuzzy optimization approach and a hybrid metaheuristic for its solutions. The full proposal is applied to a real route planning problem with outsourcing, obtaining promising practical results. Customer demands and travel times are imprecise, thus capacity and time windows constraints are considered flexible and modelled as fuzzy constraints.     

Multi-Objective Genetic Algorithms for Vehicle Routing Problem with Time Windows

The Vehicle Routing Problem with Time windows (VRPTW) is an extension of the capacity constrained Vehicle Routing Problem (VRP). The VRPTW is NP-Complete and instances with 100 customers or more are very hard to solve optimally. We represent the VRPTW as a multi-objective problem and present a genetic algorithm solution using the Pareto ranking technique. We use a direct interpretation of the VRPTW as a multi-objective problem, in which the two objective dimensions are number of vehicles and total cost (distance). An advantage of this approach is that it is unnecessary to derive weights for a weighted sum scoring formula. This prevents the introduction of solution bias towards either of the problem dimensions. We argue that the VRPTW is most naturally viewed as a multi-objective problem, in which both vehicles and cost are of equal value, depending on the needs of the user. A result of our research is that the multi-objective optimization genetic algorithm returns a set of solutions that fairly consider both of these dimensions. Our approach is quite effective, as it provides solutions competitive with the best known in the literature, as well as new solutions that are not biased toward the number of vehicles. A set of well-known benchmark data are used to compare the effectiveness of the proposed method for solving the VRPTW.     

MDVRPTW问题多阶段迭代启发式算法

提出一个求解多车库VRPTW问题的聚类和迭代混合遗传算法。该算法采用三阶段过程：客户聚类分配、路径规划和路径改进,与以往两阶段算法不同,该算法采用混合遗传算法进行路径规划,采用竞争-插入进行路径改进,且路径规划与路径改进有机结合形成迭代路径规划过程。用Cordeau等人提出的算例实验表明该算法能够在可以接受的计算时间内得到可接受的好解。     

Time Windows Based Dynamic Routing in Multi-AGV Systems

This paper presents a dynamic routing method for supervisory control of multiple automated guided vehicles (AGVs) that are traveling within a layout of a given warehouse. In dynamic routing a calculated path particularly depends on the number of currently active AGVs' missions and their priorities. In order to solve the shortest path problem dynamically, the proposed routing method uses time windows in a vector form. For each mission requested by the supervisor, predefined candidate paths are checked if they are feasible. The feasibility of a particular path is evaluated by insertion of appropriate time windows and by performing the windows overlapping tests. The use of time windows makes the algorithm apt for other scheduling and routing problems. Presented simulation results demonstrate efficiency of the proposed dynamic routing. The proposed method has been successfully implemented in the industrial environment in a form of a multiple AGV control system.     

The vehicle routing problem with multiple prioritized time windows: A case study

This paper addresses Multi-objective Vehicle Routing Problem with Multiple Prioritized Time Windows (VRPMPTW) in which the distributer proposes a set of all non-overlapping time windows with equal or different lengths and the customers prioritize these delivery time windows. VRPMPTW aims to find a set of routes of minimal total traveling cost and maximal customer satisfaction (with regard to the prioritized time windows), starting and ending at the depot, in such a way that each customer is visited by one vehicle given the capacity of the vehicle to satisfy a specific demand. This problem is inspired from a real life application. The contribution of this paper lies in its addressing the VRPMPTW from a problem definition, modeling and methodological point of view. We developed a mathematical model for this problem. This model can simply be used for a wide range of applications where the customers have multiple flexible time windows and violation of time windows may drop the satisfaction levels of customers and lead to profit loss in the long term. A Cooperative Coevolutionary Multi-objective Quantum-Genetic Algorithm (CCMQGA) is also proposed to solve this problem. A new local search is designed and used in CCMQGA to reach an appropriate pareto front. Finally, the proposed approach is employed in a real case study and the results of the proposed CCMQGA are compared with the current solution obtained from managerial experience, the results of NSGA-II and the multi-objective quantum-inspired evolutionary algorithm.     

基于配送收益均衡的多目标绿色车辆路径优化算法

针对电商平台物流中的碳排放成本较大以及配送过程中配送员收益不均衡的情况,为满足平台减少物流成本和人力成本的需求,提高车辆配送效率,降低碳排放量,实现低碳绿色出行,研究带有时间窗、配送收益均衡的多目标绿色车辆路径规划问题,并设计混合智能求解算法.首先,建立基于行驶速度的燃油消耗、基于模糊客户满意度的惩罚成本和配送收益均衡函数,构建以最小化燃油消耗量、惩罚成本和配送收益方差为目标的多目标绿色车辆路径模型;然后,将变邻域搜索算子融入NSGA-II算法,设计求解上述模型的多目标进化优化算法,以提高算法的寻优性能;最后,选择Solomon中的18个测试数据集进行实验,通过与2个模型和3种算法的超体积值和knee点值进行对比,验证所提出模型的可行性和算法的有效性,为降低碳排放量、实现低碳绿色出行提供新方案.     

基于时空聚类求解带容积约束的选址-路径问题

选址-路径问题是供应链管理和物流系统规划中的一个重要问题,对总成本具有十分重要的影响.对考虑配送中心容积约束的带时间窗的选址-路径问题进行研究,建立以总成本最小和客户满意度最大为目标的多目标规划模型,提出两阶段算法对其进行求解.首先,利用k-means聚类算法确定配送中心选址;然后,提出一种基于时间-空间双因素的客户划分方法以确定配送中心所服务客户;最后,利用粒子群算法对各配送中心的配送路径进行规划.数值算例表明,所提出的算法较其他已有算法,均能有效地降低物流运作总成本及总配送路径长度,为解决带容积约束及时间窗的选址-路径问题提供了一种新的解决思路.     

A genetic algorithm based approach to vehicle routing problem with simultaneous pick-up and deliveries

The vehicle routing problem with simultaneous pick-up and deliveries, which considers simultaneous distribution and collection of goods to/from customers, is an extension of the capacitated vehicle routing problem. There are various real cases, where fleet of vehicles originated in a depot serves customers with pick-up and deliveries from/to their locations. Increasing importance of reverse logistics activities make it necessary to determine efficient and effective vehicle routes for simultaneous pick-up and delivery activities. The vehicle routing problem with simultaneous pick-up and deliveries is also NP-hard as a capacitated vehicle routing problem and this study proposes a genetic algorithm based approach to this problem. Computational example is presented with parameter settings in order to illustrate the proposed approach. Moreover, performance of the proposed approach is evaluated by solving several test problems.     

A new mathematical model for a competitive vehicle routing problem with time windows solved by simulated annealing

This paper presents an extension of a competitive vehicle routing problem with time windows (VRPTW) to find short routes with the minimum travel cost and maximum sale by providing good services to customers before delivering the products by other rival distributors. In distribution of the products with short life time that customers need special device for keeping them, reaching time to customers influences on the sales amount which the classical VRPs are unable to handle these kinds of assumptions. Hence, a new mathematical model is developed for the proposed problem and for solving the problem, a simulated annealing (SA) approach is used. Then some small test problems are solved by the SA and the results are compared with obtained results from Lingo 8.0. For large-scale problems, the, Solomon's benchmark instances with additional assumption are used. The results show that the proposed SA algorithm can find good solutions in reasonable time.     

Adaptive granular local search heuristic for a dynamic vehicle routing problem

The advance of communication and information technologies based on satellite and wireless networks have allowed transportation companies to benefit from real-time information for dynamic vehicle routing with time windows. During daily operations, we consider the case in which customers can place requests such that their demand and location are stochastic variables. The time windows at customer locations can be violated although lateness costs are incurred. The objective is to define a set of vehicle routes which are dynamically updated to accommodate new customers in order to maximize the expected profit. This is the difference between the total revenue and the sum of lateness costs and costs associated with the total distance traveled. The solution approach makes use of a new constructive heuristic that scatters vehicles in the service area and an adaptive granular local search procedure. The strategies of letting a vehicle wait, positioning a vehicle in a region where customers are likely to appear, and diverting a vehicle away from its current destination are integrated within a granular local search heuristic. The performance of the proposed approach is assessed in test problems based on real-life Brazilian transportation companies.     

应急物流车辆调度多目标鲁棒优化研究

针对应急物流车辆调度问题中对于经济性、时效性、可靠性和鲁棒性的多种要求，考虑了含有时间窗、不确定需求、不确定行驶时间，以及路段含有失效风险的多目标鲁棒车辆路径优化问题，通过定义新的成本函数、满意度函数、风险度函数和鲁棒度函数作为四个优化目标来构建模型，并基于鲁棒优化理论将不确定模型转化为确定性鲁棒对应模型求解，为解决不确定环境下优化问题提供了新的思路。算法方面，主要基于SPEA2算法框架求解该多目标模型，针对算法缺陷提出多种改进策略，并通过对比实验证明了改进策略的有效性。     

模糊时间窗VRP的动态规划和禁忌搜索混合算法

为优化具有模糊时间窗的车辆路径问题,以物流配送成本和顾客平均满意度为目标,建立了多目标数学规划模型。基于Pareto占优的理论给出了求解多目标优化问题的并行多目标禁忌搜索算法,算法中嵌入同时优化顾客满意度的动态规划方法,运用阶段划分,把原问题分解为关于紧路径的优化子问题。对模糊时间窗为线性分段函数形式和非线性凹函数形式的隶属度函数,分别提出了次梯度有限迭代算法和次梯度中值迭代算法来优化顾客的最优开始服务时间。通过Solomon的标准算例,与次梯度投影算法的比较验证了动态规划方法优化服务水平的有效性,与主流的NSGA-II算法的对比实验表明了该研究提出的多目标禁忌搜索算法的优越性。     

The use of a fuzzy multi-objective linear programming for solving a multi-objective single-machine scheduling problem

This paper develops a fuzzy multi-objective linear programming (FMOLP) model for solving a multi-objective single-machine scheduling problem. The proposed model attempts to minimize the total weighted tardiness and makespan simultaneously. In this problem, a proposed FMOLP method is applied with respect to the overall acceptable degree of the decision maker (DM) satisfaction. A number of numerical examples are solved to show the effectiveness of the proposed approach. The related results are compared with the Wang and Liang's approach. These computational results show that the proposed FMOLP model achieves lower objective functions and higher satisfaction degrees.     

An evolutionary approach for multi-objective vehicle routing problems with backhauls

The vehicle routing problem (VRP) is an important aspect of transportation logistics with many variants. This paper studies the VRP with backhauls (VRPB) in which the set of customers is partitioned into two subsets: linehaul customers requiring a quantity of product to be delivered, and backhaul customers with a quantity to be picked up. The basic VRPB involves finding a collection of routes with minimum cost, such that all linehaul and backhaul customers are serviced. A common variant is the VRP with selective backhauls (VRPSB), where the collection from backhaul customers is optional. For most real world applications, the number of vehicles, the total travel cost, and the uncollected backhauls are all important objectives to be minimized, so the VRPB needs to be tackled as a multi-objective problem. In this paper, a similarity-based selection evolutionary algorithm approach is proposed for finding improved multi-objective solutions for VRPB, VRPSB, and two further generalizations of them, with fully multi-objective performance evaluation.