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。     

带时间窗车辆路径问题的文化基因算法

针对物流配送中带时间窗的车辆路径问题（Vehicle Routing Problem with Time Windows,VRPTW）,建立了数学模型,并设计了求解VRPTW的文化基因算法。种群搜索采用遗传算法的进化模式,局部搜索采用禁忌搜索机制,并结合可行邻域结构避免对不可行解的搜索,以提高搜索效率。与单纯的遗传算法和禁忌搜索算法进行对比实验,表明该算法是求解VRPTW的一种有效方法。     

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。     

多中心联合配送模式下集货需求随机的VRPSDP问题

针对多中心联合配送模式下集货需求随机的同时配集货车辆路径问题(MDVRPSDDSPJD), 构建了两阶段MDVRPSDDSPJD模型. 预优化阶段基于随机机会约束机制以及车载量约束为客户分配车辆, 生成预优化方案; 重优化阶段采用失败点重优化策略对服务失败点重新规划路径. 根据问题特征, 设计了自适应变邻域文化基因算法(Adaptive memetic algorithm and variable neighborhood search, AMAVNS), 针对文化基因算法易早熟、局部搜索能力弱等缺陷, 将变邻域搜索算法的深度搜索能力运用到文化基因算法的局部搜索策略中, 增强算法的局部搜索能力; 提出自适应邻域搜索次数策略和自适应劣解接受机制平衡种群进化所需的广度和深度. 通过多组算例验证了提出模型及算法的有效性. 研究成果不仅深化和拓展了VRP (Vehicle routing problem)相关理论研究, 也为物流企业制定车辆调度计划提供一种科学合理的方法.     

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。     

Skewed general variable neighborhood search for the cumulative capacitated vehicle routing problem

The cumulative capacitated vehicle routing problem (CCVRP) is a relatively new version of the classical capacitated vehicle routing problem, and it is equivalent to a traveling repairman problem with capacity constraints and a homogeneous vehicle fleet, which aims to minimize the total arrival time at customers. Many real‐world applications can be modeled by this problem, such as the important application resulting from the humanitarian aid following a natural disaster. In this paper, two heuristics are proposed. The first one is a constructive heuristic to generate an initial solution and the second is the skewed variable neighborhood search (SVNS) heuristic. The SVNS algorithm starts with the initial solution. At each iteration, the perturbation phase and the local search phase are used to improve the solution of the CCVRP, and the distance function in acceptance criteria phase is used to improve the exploration of faraway valleys. This algorithm is applied to a set of benchmarks, and the comparison results show that the proposed algorithms provide better solutions than those reported in the previous literature on memetic algorithms and adaptive large neighborhood search heuristics.     

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.     

A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows

In this paper, we present an effective memetic algorithm for the vehicle routing problem with time windows (VRPTW). The paper builds upon an existing edge assembly crossover (EAX) developed for the capacitated VRP. The adjustments of the EAX operator and the introduction of a novel penalty function to eliminate violations of the time window constraint as well as the capacity constraint from offspring solutions generated by the EAX operator have proven essential to the heuristic's performance. Experimental results on Solomon's and Gehring and Homberger benchmarks demonstrate that our algorithm outperforms previous approaches and is able to improve 184 best-known solutions out of 356 instances.     

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.     

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。     

蜂群算法在带时间窗的车辆路径问题中的应用*

根据带时间窗车辆路径问题的实际情况,通过考察车辆数和总行程两个目标函数,给出了该问题的一种新的算法——蜂群算法。通过计算若干benchmark问题,并将结果与其他算法相比较分析,验证了算法的有效性。目前关于蜂群算法的文献较少,故不仅是拓宽蜂群算法应用范围的有效尝试,同时也给带时间窗车辆路径问题提供了一种新的解决方法。     

基于遗传算法求解带时间窗的车辆路由问题

提出一种改进的遗传算法，用于求解带时间窗的车辆路由问题．在算法中采用了直观的自然数缟码机制、三复本锦标赛的选择方法和改进的启发式交叉算子，实验表明该方法用于求解带时间窗的车辆路由问题的有效性．     

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.     

面向带时间窗车辆路径问题的PGSA算法优化

VRPTW问题是带时间窗约束的车辆路径问题,该问题的求解通常被应用到物流的路径规划环节,现实意义突出,属于NP难题,计算量随问题规模增大呈指数增长。PGSA算法是模拟植物生长信息和分支模式的启发式算法,被用于求解组合优化问题。本文以配送总路程最短为目标构建VRPTW问题的约束模型,在原始PGSA算法的基础上,使用双阶段的搜索方案,提高初始解的质量,设计有向生长机制和局部解跳出机制更改原算法生长点的生长策略,提高了PGSA算法的搜索效率。通过在标准数据集上的实验分析,改进后的PGSA算法相比原始PGSA算法,能达到更好的收敛结果,求解效率更高,是一种有效的求解方法。     

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.     

Arc-Guided Evolutionary Algorithm for the Vehicle Routing Problem With Time Windows

This paper presents an arc-guided evolutionary algorithm for solving the vehicle routing problem with time windows, which is a well-known combinatorial optimization problem that addresses the service of a set of customers using a homogeneous fleet of capacitated vehicles within fixed time intervals. The objective is to minimize the fleet size following routes of minimum distance. The proposed method evolves a population of ${mu}$ individuals on the basis of an $({{mu}+{lambda}})$ evolution strategy; at each generation, a new intermediate population of ${lambda}$ individuals is generated, using a discrete arc-based representation combined with a binary vector of strategy parameters. Each offspring is produced via mutation out of arcs extracted from parent individuals. The selection of arcs is dictated by the strategy parameters and is based on their frequency of appearance and the diversity of the population. A multiparent recombination operator enables the self-adaptation of the strategy parameters, while each offspring is further improved via novel memory-based trajectory local search algorithms. For the selection of survivors, a deterministic scheme is followed. Experimental results on well-known large-scale benchmark datasets of the literature demonstrate the competitiveness of the proposed method.      

基于自适应聚合距离的多目标进化算法

随着目标数的增多,种群收敛性与分布性的冲突愈加激烈,传统的多目标进化算法的选择算子难以平衡种群的收敛性与分布性.对此,提出一种基于自适应聚合距离的多目标进化算法.首先,采用参考点支配关系替代原有的Pareto支配关系,以增加选择压力,加强收敛性;其次,提出自适应聚合距离,通过动态变化的惩罚参数来自适应调整收敛性与分布性的比例;最后,设计一种带有淘汰算子的方法以改进小生境选择策略,根据自适应聚合距离的大小进行选择和淘汰操作.为验证算法的可行性,将所提出算法在测试问题上与其他4种优秀的多目标进化算法进行比较,并应用于两个实际应用中,仿真结果表明,所提出算法的综合性能更优,能有效平衡种群的收敛性与分布性.     

文化基因算法在第四方物流路径规划中的应用

第四方物流路径问题是复杂的组合优化问题。基本遗传算法在第四方物流路径问题上存在随着问题规模扩大,算法的成功率和准确率不断下降等缺点。针对基本的遗传算法已经不能满足规模较大的第四方物流问题等缺点,结合实验分析,提出了一种以遗传算法为全局搜索策略的文化基因算法,并针对第四方物流的问题特点设计了相应的局部搜索策略。实验结果表明,与基本遗传算法相比,该混合算法不仅在求解质量上有了较大的改进,并且在大规模第四方物流问题上也能获得质量较好的解,算法的成功率和准确率明显高于基本的遗传算法。因此,基于遗传算法的文化基因算法是解决大规模第四方物流路径问题的一种有效方法。     

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.