Exact and heuristic algorithms for the vehicle routing problem with multiple interdependent time windows

In this paper a model and several solution procedures for a novel type of vehicle routing problems where time windows for the pickup of perishable goods depend on the dispatching policy used in the solution process are presented. This problem is referred to as Vehicle Routing Problem with multiple interdependent time windows (VRPmiTW) and is motivated by a project carried out with the Austrian Red Cross blood program to assist their logistics department. Several variants of a heuristic constructive procedure as well as a branch-and-bound based algorithm for this problem were developed and implemented. Besides finding the expected reduction in costs when compared with the current procedures of the Austrian Red Cross, the results show that the heuristic algorithms find solutions reasonably close to the optimum in fractions of a second. Another important finding is that increasing the number of pickups at selected customers beyond the theoretical minimum number of pickups yields significantly greater potential for cost reductions.     

有时间窗车辆路径问题的捕食搜索算法

有时间窗车辆路径问题是当前物流配送系统研究中的热点问题,该问题具有NP难性质。难以求得最优解或满意解,在建立有时间窗车辆路径问题数学模型的基础上。设计了一种模仿动物捕食策略的捕食搜索算法．该算法利用控制搜索空间的限制大小来实现算法的局域搜索和全局搜索,具有良好的局部集中搜索和跳出局部最优的能力．通过实例计算,并与相关启发式算法比较．取得了满意的结果．     

A genetic and set partitioning two-phase approach for the vehicle routing problem with time windows

The Vehicle Routing Problem with Time Windows (VRPTW) is a well-known and complex combinatorial problem, which has received considerable attention in recent years. This problem has been addressed using many different techniques including both exact and heuristic methods. The VRPTW benchmark problems of Solomon [Algorithms for the vehicle routing and scheduling problems with time window constraints, Operations Research 1987; 35(2): 254–65] have been most commonly chosen to evaluate and compare all algorithms. Results from exact methods have been improved considerably because of parallel implementations and modern branch-and-cut techniques. However, 24 out of the 56 high order instances from Solomon's original test set still remain unsolved. Additionally, in many cases a prohibitive time is needed to find the exact solution. Many of the heuristic methods developed have proved to be efficient in identifying good solutions in reasonable amounts of time. Unfortunately, whilst the research efforts based on exact methods have been focused on the total travel distance, the focus of almost all heuristic attempts has been on the number of vehicles. Consequently, it is more difficult to compare and take advantage of the strong points from each approach. This paper proposes a robust heuristic approach for the VRPTW using travel distance as the main objective through an efficient genetic algorithm and a set partitioning formulation. The tests were produced using real numbers and truncated data type, allowing a direct comparison of its results against previously published heuristic and exact methods. Furthermore, computational results show that the proposed heuristic approach outperforms all previously known and published heuristic methods in terms of the minimal travel distance.     

求解带软时间窗车辆路径问题的融合算法

设计了遗传算法与变异蚂蚁算法的一个融合算法,该算法采用优良基因保护策略,引入蚂蚁寻径变异机制,并改进了信息素的更新方式,提高了寻径速度以及寻径的全局性。经过对比实验,验证了本融合算法可以有效而快速地获得问题模型的最优解或近似最优解。     

Solving a vehicle routing problem with time windows by a decomposition technique and a genetic algorithm

The present study investigates the cost concerns of distribution centers and formulates a vehicle routing problem with time window constraints accordingly. Based on the embedded structure of the original problem, a decomposition technique is employed to decompose the original problems to a clustering problem (main problem) and a set of traveling salesman problems (sub-problems) with time window constraints. This decomposition not only reduces the problem size but also enable the use of simpler solution procedures. A genetic algorithm is developed to solve the clustering problem, while a simple heuristic algorithm is formulated to solve the set of traveling salesman problems. The solution of the original problem is obtained through iterative interactions between the main problem and the set of sub-problems. The performance of the proposed approach is compared with the well-known insertion method and a manual scheduling of a distribution center.     

时间窗约束下的配送车辆调度问题研究

为解决时间窗约束下的物流配送车辆的多目标调度优化问题,给出了一种基于免疫计算的配送车辆调度优化方案。设计了配送车辆调度问题的数学模型和一种基于非劣邻域支配的多目标调度优化算法,在仿真环境下进行了实验。实验结果表明,算法能够有效地解决物流配送车辆调度问题,具有较好的应用价值。     

Formulations and exact algorithms for the vehicle routing problem with time windows

In this paper we review the exact algorithms proposed in the last three decades for the solution of the vehicle routing problem with time windows (VRPTW). The exact algorithms for the VRPTW are in many aspects inherited from work on the traveling salesman problem (TSP). In recognition of this fact this paper is structured relative to four seminal papers concerning the formulation and exact solution of the TSP, i.e. the arc formulation, the arc-node formulation, the spanning tree formulation, and the path formulation. We give a detailed analysis of the formulations of the VRPTW and a review of the literature related to the different formulations. There are two main lines of development in relation to the exact algorithms for the VRPTW. One is concerned with the general decomposition approach and the solution to certain dual problems associated with the VRPTW. Another more recent direction is concerned with the analysis of the polyhedral structure of the VRPTW. We conclude by examining possible future lines of research in the area of the VRPTW.     

超启发式分布估计算法求解带软时间窗的同时取送货车辆路径问题

本文针对带软时间窗的同时取送货车辆路径问题(VRPSPDSTW),以最小化车辆行驶总里程和最大化服务准时率为优化目标,提出一种超启发式分布估计算法(HHEDA)进行求解.全局搜索阶段,首先,提出3种启发式规则生成初始个体,以确保初始种群的质量和分散性;其次,根据问题特点,构造3个概率矩阵分别学习和积累优质解的排序信息、...     

A decomposition based memetic algorithm for multi-objective vehicle routing problem with time windows

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) provides an excellent algorithmic framework for solving multi-objective optimization problems. It decomposes a target problem into a set of scalar sub-problems and optimizes them simultaneously. Due to its simplicity and outstanding performance, MOEA/D has been widely studied and applied. However, for solving the multi-objective vehicle routing problem with time windows (MO-VRPTW), MOEA/D faces a difficulty that many sub-problems have duplicated best solutions. It is well-known that MO-VRPTW is a challenging problem and has very few Pareto optimal solutions. To address this problem, a novel selection operator is designed in this work to enhance the original MOEA/D for dealing with MO-VRPTW. Moreover, three local search methods are introduced into the enhanced algorithm. Experimental results indicate that the proposed algorithm can obtain highly competitive results on Solomon׳s benchmark problems. Especially for instances with long time windows, the proposed algorithm can obtain more diverse set of non-dominated solutions than the other algorithms. The effectiveness of the proposed selection operator is also demonstrated by further analysis.     

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。     

Waste collection vehicle routing problem with time windows

In this paper, we address a real life waste collection vehicle routing problem with time windows (VRPTW) with consideration of multiple disposal trips and drivers’ lunch breaks. Solomon's well-known insertion algorithm is extended for the problem. While minimizing the number of vehicles and total traveling time is the major objective of vehicle routing problems in the literature, here we also consider the route compactness and workload balancing of a solution since they are very important aspects in practical applications. In order to improve the route compactness and workload balancing, a capacitated clustering-based waste collection VRPTW algorithm is developed. The proposed algorithms have been successfully implemented and deployed for the real life waste collection problems at Waste Management, Inc. A set of waste collection VRPTW benchmark problems is also presented in this paper.Waste collection problems are frequently considered as arc routing problems without time windows. However, that point of view can be applied only to residential waste collection problems. In the waste collection industry, there are three major areas: commercial waste collection, residential waste collection and roll-on-roll-off. In this paper, we mainly focus on the commercial waste collection problem. The problem can be characterized as a variant of VRPTW since commercial waste collection stops may have time windows. The major variation from a standard VRPTW is due to disposal operations and driver's lunch break. When a vehicle is full, it needs to go to one of the disposal facilities (landfill or transfer station). Each vehicle can, and typically does, make multiple disposal trips per day. The purpose of this paper is to introduce the waste collection VRPTW, benchmark problem sets, and a solution approach for the problem. The proposed algorithms have been successfully implemented and deployed for the real life waste collection problems of Waste Management, the leading provider of comprehensive waste management services in North America with nearly 26,000 collection and transfer vehicles.     

A knowledge-based evolutionary algorithm for the multiobjective vehicle routing problem with time windows

This paper addresses the multiobjective vehicle routing problem with time windows (MOVRPTW). The objectives are to minimize the number of vehicles and the total distance simultaneously. Our approach is based on an evolutionary algorithm and aims to find the set of Pareto optimal solutions. We incorporate problem-specific knowledge into the genetic operators. The crossover operator exchanges one of the best routes, which has the shortest average distance, the relocation mutation operator relocates a large number of customers in non-decreasing order of the length of the time window, and the split mutation operator breaks the longest-distance link in the routes. Our algorithm is compared with 10 existing algorithms by standard 100-customer and 200-customer problem instances. It shows competitive performance and updates more than 1/3 of the net set of the non-dominated solutions.     

An improved model for vehicle routing problem with time constraint based on genetic algorithm

A vehicle routing problem (VRP) with time constraint is one of the important problems in distribution and transportation. Thus the generic VRP and its practical extensions are discussed in great detail in the literatures. In the VRP, the service of a customer must start and finish within a given time interval. The objective of this problem is to minimize the cost of servicing the set of customers without being tardy or exceeding the capacity or travel time of the vehicles. In this research we concentrated on developing a GA–TSP model by improving the genetic algorithm (GA) operators and the initial population. For the computational purpose, we developed a GUI (graphic user interface)-type computer program according to the proposed method. The computational results show that the proposed method is very effective on a set of standard test problems and it can be potentially useful in solving the VRPs.     

The robust vehicle routing problem with time windows

This paper addresses the robust vehicle routing problem with time windows. We are motivated by a problem that arises in maritime transportation where delays are frequent and should be taken into account. Our model only allows routes that are feasible for all values of the travel times in a predetermined uncertainty polytope, which yields a robust optimization problem. We propose two new formulations for the robust problem, each based on a different robust approach. The first formulation extends the well-known resource inequalities formulation by employing adjustable robust optimization. We propose two techniques, which, using the structure of the problem, allow to reduce significantly the number of extreme points of the uncertainty polytope. The second formulation generalizes a path inequalities formulation to the uncertain context. The uncertainty appears implicitly in this formulation, so that we develop a new cutting plane technique for robust combinatorial optimization problems with complicated constraints. In particular, efficient separation procedures are discussed. We compare the two formulations on a test bed composed of maritime transportation instances. These results show that the solution times are similar for both formulations while being significantly faster than the solutions times of a layered formulation recently proposed for the problem.     

A survey of genetic algorithms for solving multi depot vehicle routing problem

This article presents a survey of genetic algorithms that are designed for solving multi depot vehicle routing problem. In this context, most of the articles focus on different genetic approaches, methods and operators, commonly used in practical applications to solve this well-known and researched problem. Besides providing an up-to-date overview of the research in the field, the results of a thorough experiment are presented and discussed, which evaluated the efficiency of different existing genetic methods on standard benchmark problems in detail. In this manner, the insights into strengths and weaknesses of specific methods, operators and settings are presented, which should help researchers and practitioners to optimize their solutions in further studies done with the similar type of the problem in mind. Finally, genetic algorithm based solutions are compared with other existing approaches, both exact and heuristic, for solving this same problem.     

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.     

带时间窗车辆路径问题的多目标文化基因算法

针对物流配送中带时间窗的车辆路径问题,以最小化车辆使用数和行驶距离为目标,建立了多目标数学模型,提出了一种求解该问题的多目标文化基因算法。种群搜索采用遗传算法的进化模式和Pareto排序的选择方式,局部搜索采用禁忌搜索机制和存储池的结构,协调两者得到的Pareto非占优解的关系。与不带局部搜索的多目标遗传算法和单目标文化基因算法的对比实验表明,本文算法的求解质量较高。     

有时间窗车辆路径问题的混合智能算法

有时间窗的车辆路径问题属于组合优化领域中的NP-hard问题。在对该问题进行分析的基础上,为之建立了数学模型,提出了一种求解该问题的混合智能算法。该算法通过使用蚁群算法和遗传算法交替优化,并且及时交换信息,弥补了蚁群算法和遗传算法各自的不足,达到了优势互补的效果,增强了算法的寻优能力,避免了停滞现象。实验结果表明,该算法能有效解决有时间窗的车辆路径问题。     

Vehicle routing problem with a heterogeneous fleet and time windows

In this paper, a problem variant of the vehicle routing problem with time windows is introduced to consider vehicle routing with a heterogeneous fleet, a limited number of vehicles and time windows. A method that extends an existing tabu search procedure to solve the problem is then proposed. To evaluate the performance of the proposed method, experiments are conducted on a large set of test cases, which comprises several benchmark problems from numerous problem variants of the vehicle routing problem with a heterogeneous fleet. It is observed that the proposed method can be used to give reasonably good results for these problem variants. In addition, some ideas are presented to advance the research in heuristics, such as fair reporting standards, publication of benchmark problems and executable routines developed for algorithmic comparison.     

A tabu search heuristic for the single vehicle pickup and delivery problem with time windows

The single vehicle pickup and delivery problem with time windows is a generalization of the traveling salesman problem. In such a problem, a number of transportation requests have to be satisfied by one vehicle, each request having constraints to respect: a pickup at its origin and a delivery at its destination, and a time window at each location. The capacity of the vehicle has to be respected. The aim is to minimize the total distance traveled by the vehicle. A number of exact and approximate solution methods exists in the literature, but to the authors knowledge none of them make use of metaheuristics, still promising with other vehicle routing problems. In this paper we present tabu search and probabilistic tabu search. Results obtained on classical traveling salesman problems and a class of randomly generated instances indicate that our approach often produces optimal solutions in a relatively short execution time.