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.     

Artificial intelligence heuristics in solving vehicle routing problems with time window constraints

This paper describes the authors’ research on various heuristics in solving vehicle routing problem with time window constraints (VRPTW) to near optimal solutions. VRPTW is NP-hard problem and best solved to near optimum by heuristics. In the vehicle routing problem, a set of geographically dispersed customers with known demands and predefined time windows are to be served by a fleet of vehicles with limited capacity. The optimized routines for each vehicle are scheduled as to achieve the minimal total cost without violating the capacity and time window constraints. In this paper, we explore different hybridizations of artificial intelligence based techniques including simulated annealing, tabu search and genetic algorithm for better performance in VRPTW. All the implemented hybrid heuristics are applied to solve the Solomon's 56 VRPTW with 100-customer instances, and yield 23 solutions competitive to the best solutions published in literature according to the authors’ best knowledge.     

A hybrid genetic algorithm for multi-depot homogenous locomotive assignment with time windows

This paper presents a hybrid genetic algorithm to solve a multi-depot homogenous locomotive assignment problem with time windows. The locomotive assignment problem is to assign a set of homogeneous locomotives locating in a set of dispersed depots to a set of pre-schedules trains that are supposed to be serviced in pre-specified hard/soft time windows. A mathematical model is presented, using vehicle routing problem with time windows (VRPTW) for formulation of the problem. A cluster-first, route-second approach is used to inform the multi-depot locomotive assignment to a set of single depot problems and after that we solve each problem independently. Each single depot problem is solved heuristically by a hybrid genetic algorithm that in which Push Forward Insertion Heuristic (PFIH) is used to determine the initial solution and λ-interchange mechanism is used for neighborhood search and improving method. A medium sized numerical example with different scenarios is presented and examined to more clarification of the approach as well as to check capabilities of the model and algorithm. Also some of the results are compared with the solutions produced by branch & bound technique to determine validity and quality of the model. The experiments with a set of 15 completely random generated instance problems indicate that this algorithm is efficient and solves the problem in a polynomial time.     

A hybrid algorithm for vehicle routing problem with time windows

Vehicle routing problem with time windows (VRPTW) is a well-known combinatorial problem. Many researches have presented meta-heuristics are effective approaches for VRPTW. This paper proposes a hybrid approach, which consists of ant colony optimization (ACO) and Tabu search, to solve the problem. To improve the performance of ACO, a neighborhood search is introduced. Furthermore, when ACO is close to the convergence Tabu search is used to maintain the diversity of ACO and explore new solutions. Computational experiments are reported for a set of the Solomon’s 56 VRPTW and the approach is compared with some meta-heuristic published in literature. Results show that considering the tradeoff of quality and computation time, the hybrid algorithm is a competitive approach for VRPTW.     

基于带时间窗口车辆路径问题的蚁群算法

带时间窗口的车辆路径问题（VRPTW）是一个NP-Complete优化问题。VRPTW的主要目标在于利用最少的车辆数以及最短的行程来服务客户，客户有固定的需求和被服务的时间限制。基于该问题提出了一种并行多蚁群算（PMACS-VRFTW）：首先利用QUICK-ACS生成初始解，然后利用ACS-VEI和ACS-TIME分别优化车辆数和行程距离。试验表明，所提出的算法基于Solomon的VRPTW基准实例获得了很好的结果。     

基于多态蚁群算法的多目标邮政物流车辆路径问题研究*

针对在现有邮路运输的基础上加载一体化物流项目后的邮政物流车辆调度与路径选择优化问题,建立了基于硬时间窗、车辆混合搭载、往返归集的多目标邮政物流车辆路径问题数学模型,以四川邮政雅芳一体化混合物流2008年5月的数据为例,利用自适应的多态蚁群算法对带时间约束多目标混合邮政物流VRP进行了求解。结果表明多态蚁群算法可以求解多目标邮政物流VRP,能提高收敛速度和寻优性能。     

基于Memetic算法的带时间窗车辆路径问题研究*

提出一种模拟文化进化的Memetic算法求解带时间窗的车辆路径问题。设计了一种实数编码方案,将离散的问题转为连续优化问题。采用邻域搜索帮助具备一定学习能力的个体提高寻优速度;采用禁忌搜索帮助部分个体跳出局部最优点,增强全局寻优性能。实验结果表明,该算法可以更有效地求出优化解,是带时间窗车辆路径问题的一种有效求解算法。     

A multi-objective dynamic vehicle routing problem with fuzzy time windows: Model,solution and application

In this paper, a multi-objective dynamic vehicle routing problem with fuzzy time windows (DVRPFTW) is presented. In this problem, unlike most of the work where all the data are known in advance, a set of real time requests arrives randomly over time and the dispatcher does not have any deterministic or probabilistic information on the location and size of them until they arrive. Moreover, this model involves routing vehicles according to customer-specific time windows, which are highly relevant to the customers’ satisfaction level. This preference information of customers can be represented as a convex fuzzy number with respect to the satisfaction for a service time. This paper uses a direct interpretation of the DVRPFTW as a multi-objective problem where the total required fleet size, overall total traveling distance and waiting time imposed on vehicles are minimized and the overall customers’ preferences for service is maximized. A solving strategy based on the genetic algorithm (GA) and three basic modules are proposed, in which the state of the system including information of vehicles and customers is checked in a management module each time. The strategy module tries to organize the information reported by the management module and construct an efficient structure for solving in the subsequent module. The performance of the proposed approach is evaluated in different steps on various test problems generalized from a set of static instances in the literature. In the first step, the performance of the proposed approach is checked in static conditions and then the other assumptions and developments are added gradually and changes are examined. The computational experiments on data sets illustrate the efficiency and effectiveness of the proposed approach.     

求解带时间窗车辆路径问题的混沌遗传算法

针对遗传算法随机性大、末成熟收敛等缺点,提出了将混沌搜索技术和遗传算法相耦合的混沌遗传算法来求解带时间窗的物流配送车辆路径问题(VRPTW)。该算法将混沌变量映射到优化变量的取值范围中,把得到的混沌变量进行编码生成初始种群,然后在遗传操作进行之后对优秀个体增加混沌扰动,促进种群的进化收敛速度,得到最优解。实例计算结果与其他算法比较表明,该算法在求解VRPTW问题时,搜索效率高,能以较快的速度收敛于全局最优解,为求解VRPTW问题提供了一种新方法。     

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.     

Modeling rolling batch planning as vehicle routing problem with time windows

This paper considers the rolling batch planning problem of grouping and sequencing a given set of slabs into several rolling units in iron and steel industry. The existing mathematical methods often used for the problem are traveling salesman problem (TSP) and vehicle routing problem (VRP), but these methods are not precise, because the position limitation of some slabs in a rolling unit scheduling is not considered. Therefore we suggest a new model, vehicle routing problem with time window (VRPTW) to describe the rolling batch planning problem, in which the position limitation of slabs are quantified as the time constraints. Several solution methods including the genetic algorithm are presented for solving the problem and the computational results show that the genetic algorithm is superior to other methods.In this paper, the vehicle routing problem with time window (VRPTW) of combinational optimization is used to analyze and model the rolling batch planning problem. Genetic algorithm and heuristic are used to solve the problem. Simulation results based on the actual production data show that this model is precise and the genetic algorithm based method is very promising.     

Sequencing material handling equipment in production facilities

In this article we consider the problem of sequencing material handling equipment in manufacturing systems, subject to constraints that restrict the start and end time of each production activity, according to pre‐specified daily resource operational schedules and process planning information. The underlying decision problem is modeled using an integer programming formulation similar to vehicle routing with time windows (VRPTW). To take advantage of standard approaches for the VRPTW, we develop a transformation schema that allows a one‐to‐one mapping between the manufacturing problem and VRPTW. An efficient heuristic to solve the resulting transformed problem is proposed. The method, which is a penalty‐based sequential insertion heuristic, allows routes to be constructed by exploiting the tradeoff between material handling and resource starvation costs. The steps of the method are illustrated via a comprehensive example and results on benchmark problems are reported.     

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.     

Heuristic methods for vehicle routing problem with time windows

This paper documents our investigation into various heuristic methods to solve the vehicle routing problem with time windows (VRPTW) to near optimal solutions. The objective of the VRPTW is to serve a number of customers within predefined time windows at minimum cost (in terms of distance travelled), without violating the capacity and total trip time constraints for each vehicle. Combinatorial optimisation problems of this kind are non-polynomial-hard (NP-hard) and are best solved by heuristics. The heuristics we are exploring here are mainly third-generation artificial intelligent (AI) algorithms, namely simulated annealing (SA), Tabu search (TS) and genetic algorithm (GA). Based on the original SA theory proposed by Kirkpatrick and the work by Thangiah, we update the cooling scheme and develop a fast and efficient SA heuristic. One of the variants of Glover's TS, strict Tabu, is evaluated and first used for VRPTW, with the help of both recency and frequency measures. Our GA implementation, unlike Thangiah's genetic sectoring heuristic, uses intuitive integer string representation and incorporates several new crossover operations and other advanced techniques such as hybrid hill-climbing and adaptive mutation scheme. We applied each of the heuristics developed to Solomon's 56 VRPTW 100-customer instances, and yielded 18 solutions better than or equivalent to the best solution ever published for these problems. This paper is also among the first to document the implementation of all the three advanced AI methods for VRPTW, together with their comprehensive results.     

基于多目标遗传算法求解时间窗车辆路径问题

有别于传统的单目标方法,将带时间窗约束的车辆路径问题描述成为一个多目标最优化问题,并为之提出了一种多目标遗传算法。在算法中设计了擂台法则作为构造非支配集的方法,提出了可变爬山率的局部爬山法,并通过将组合种群分成多层非支配集来实现精英保留策略。实验结果表明,该算法能有效地求解车辆路径问题并且为决策者提供了强有力的决策支持。     

蚂蚁算法在带时间窗车辆路径问题中的应用及参数分析

带时间窗的车辆路径问题是一个典型的NP-Hard问题,本文将蚂蚁算法应用于带时间窗车辆路径问题,构造了该问题的表达方法,建立了相应的算法模型,对算法参数进行了分析并提出了相应的参数改进方案。仿真实验表明,改进后的算法可以快速、有效地求解带时间窗车辆路径问题,具有较好的可行性和适用性。     

Vehicle routing problem with time windows considering overtime and outsourcing vehicles

The vehicle routing problem with time windows (VRPTW) is an important problem in third-party logistics and supply chain management. We extend the VRPTW to the VRPTW with overtime and outsourcing vehicles (VRPTWOV), which allows overtime for drivers and the possibility of using outsourced vehicles. This problem can be applied to third-party logistics companies for managing central distributor-local distributors, local distributor-retailers (or customers), and manufacturers. We developed a mixed integer programming model, a genetic algorithm (GA), and a hybrid algorithm based on simulated annealing. The computational results demonstrate the efficiency of the developed algorithms. We also develop a decision support system for the VRPTWOV that is equipped with a vehicle route rescheduling function for realistic situations based on the GA.     

A general heuristic for vehicle routing problems

We present a unified heuristic which is able to solve five different variants of the vehicle routing problem: the vehicle routing problem with time windows (VRPTW), the capacitated vehicle routing problem (CVRP), the multi-depot vehicle routing problem (MDVRP), the site-dependent vehicle routing problem (SDVRP) and the open vehicle routing problem (OVRP).     

带时间窗车辆路径问题的分布式多Agent蚁群算法

带时间窗车辆路径问题(VRPTW)多年来一直受到人们关注。针对以往研究中求解效率有限、求解复杂度有限、难以求解较大规模问题的不足,本文以提高精度和速度为目标,在传统蚁群算法的基础上,改进了状态转移规则,结合了邻域搜索算法;同时将本算法设计为分布式结构。利用多分布式agent系统实现了分布式求解VRPTW问题。针对国际标准算例设计了四个实验,结果表明：本算法在精确度、速度、可靠性以及求解大规模问题方面具有明显优势。     

基于改进蚁群算法的有时间窗车辆路径优化研究

针对有时间窗的车辆路径优化问题．通过对蚁群算法的分析,设定信息素轨迹强度上下限,改进转移概率、信息素的更新方式,以提高算法的收敛速度和全局搜索能力。经过多次实验和计算．证明用改进的蚁群算法能有效地解决有时间窗的车辆路径优化问题。