A Glowworm Swarm Optimization algorithm for the Vehicle Routing Problem with Stochastic Demands

The Glowworm Swarm Optimization (GSO) algorithm is a relatively new swarm intelligence algorithm that simulates the movement of the glowworms in a swarm based on the distance between them and on a luminescent quantity called luciferin. This algorithm has been proven very efficient in the problems that has been applied. However, there is no application of this algorithm, at least to our knowledge, in routing type problems. In this paper, this nature inspired algorithm is used in a hybrid scheme (denoted as Combinatorial Neighborhood Topology Glowworm Swarm Optimization (CNTGSO)) with other metaheuristic algorithms (Variable Neighborhood Search (VNS) algorithm and Path Relinking (PR) algorithm) for successfully solving the Vehicle Routing Problem with Stochastic Demands. The major challenge is to prove that the proposed algorithm could efficiently be applied in a difficult combinatorial optimization problem as most of the applications of the GSO algorithm concern solutions of continuous optimization problems. Thus, two different solution vectors are used, the one in the continuous space (which is updated as in the classic GSO algorithm) and the other in the discrete space and it represents the path representation of the route and is updated using Combinatorial Neighborhood Topology technique. A migration (restart) phase is, also, applied in order to replace not promising solutions and to exchange information between solutions that are in different places in the solution space. Finally, a VNS strategy is used in order to improve each glowworm separately. The algorithm is tested in two problems, the Capacitated Vehicle Routing Problem and the Vehicle Routing Problem with Stochastic Demands in a number of sets of benchmark instances giving competitive and in some instances better results compared to other algorithms from the literature.     

Heuristics for the probabilistic traveling salesman problem with deadlines based on quasi-parallel Monte Carlo sampling

The Probabilistic Traveling Salesman Problem with Deadlines (PTSPD) is a Stochastic Vehicle Routing Problem with a computationally demanding objective function. In this work we propose an approximation for that objective function based on Monte Carlo Sampling and using the novel approach of quasi-parallel evaluation of samples. We perform comprehensive computational studies that reveal the efficiency of this approximation. Additionally, we examine different Local Search Algorithms and present a Random Restart Local Search Algorithm for solving the PTSPD together with an extensive computational study on a large set of benchmark instances.     

Particle Swarm Optimization for the Vehicle Routing Problem with Stochastic Demands

This paper introduces a new hybrid algorithmic approach based on Particle Swarm Optimization (PSO) for successfully solving one of the most popular supply chain management problems, the Vehicle Routing Problem with Stochastic Demands (VRPSD). The VRPSD is a well known NP-hard problem in which a vehicle with finite capacity leaves from the depot with full load and has to serve a set of customers whose demands are known only when the vehicle arrives to them. A number of different variants of the PSO are tested and the one that performs better is used for solving benchmark instances from the literature.     

Honey Bees Mating Optimization algorithm for large scale vehicle routing problems

Honey Bees Mating Optimization algorithm is a relatively new nature inspired algorithm. In this paper, this nature inspired algorithm is used in a hybrid scheme with other metaheuristic algorithms for successfully solving the Vehicle Routing Problem. More precisely, the proposed algorithm for the solution of the Vehicle Routing Problem, the Honey Bees Mating Optimization (HBMOVRP), combines a Honey Bees Mating Optimization (HBMO) algorithm with the Multiple Phase Neighborhood Search–Greedy Randomized Adaptive Search Procedure (MPNS–GRASP) and the Expanding Neighborhood Search (ENS) algorithm. Besides these two procedures, the proposed algorithm has, also, two additional main innovative features compared to other Honey Bees Mating Optimization algorithms concerning the crossover operator and the workers. Two sets of benchmark instances are used in order to test the proposed algorithm. The results obtained for both sets are very satisfactory. More specifically, in the fourteen classic instances proposed by Christofides, the average quality is 0.029% and in the second set with the twenty large scale vehicle routing problems the average quality is 0.40%.     

基于交叉熵法解决随机需求车辆路径问题

提出一种解决随机需求车辆路径问题(VRPSD)新方法。首先,采用预防性补救措施,建立了VRPSD模型,其次,为提高标准交叉熵(SCE)法性能,对用于更新Markov转移矩阵的路径,设计了根据分位值改变大小的自适应调整方法。仿真结果验证了该算法解决VRPSD的有效性。     

An iterated local search heuristic for the split delivery vehicle routing problem

This paper concerns the Split Delivery Vehicle Routing Problem (SDVRP). This problem is a relaxation of the Capacitated Vehicle Routing Problem (CVRP) since the customers׳ demands are allowed to be split. We deal with the cases where the fleet is unlimited (SDVRP-UF) and limited (SDVRP-LF). In order to solve them, we implemented a multi-start Iterated Local Search (ILS) based heuristic that includes a novel perturbation mechanism. Extensive computational experiments were carried out on benchmark instances available in the literature. The results obtained are highly competitive, more precisely, 55 best known solutions were equaled and new improved solutions were found for 243 out of 324 instances, with an average and maximum improvement of 1.15% and 2.81%, respectively.     

Multiple Phase Neighborhood Search-GRASP for the Capacitated Vehicle Routing Problem

Greedy Randomized Adaptive Search Procedure (GRASP) has been proved to be a very efficient algorithm for the solution of the Traveling Salesman Problem. Also, it has been proved that expanding the local search with the use of two or more different local search strategies helps the algorithm to avoid trapping in a local optimum. In this paper, a new modified version of GRASP, called Multiple Phase Neighborhood Search-GRASP (MPNS-GRASP), for the solution of the Vehicle Routing Problem is proposed. In this method, a stopping criterion based on Lagrangean Relaxation and Subgradient Optimization is utilized. In addition, a different way for expanding the neighborhood search is used based on a new strategy, the Circle Restricted Local Search Moves strategy. The algorithm was tested on two sets of benchmark instances and gave very satisfactory results. In both sets of instances the results have solution qualities with average values near to the optimum values and in a number of them the algorithm finds the optimum. The computational time of the algorithm is decreased significantly compared to other heuristic and metaheuristic algorithms due to the fact that the new strategy, the Expanding Neighborhood Search Strategy, is used.     

Hybridized ant colony algorithm for the Multi Compartment Vehicle Routing Problem

Multi Compartment Vehicle Routing Problem is an extension of the classical Capacitated Vehicle Routing Problem where different products are transported together in one vehicle with multiple compartments. Products are stored in different compartments because they cannot be mixed together due to differences in their individual characteristics. The problem is encountered in many industries such as delivery of food and grocery, garbage collection, marine vessels, etc. We propose a hybridized algorithm which combines local search with an existent ant colony algorithm to solve the problem. Computational experiments are performed on new generated benchmark problem instances. An existing ant colony algorithm and the proposed hybridized ant colony algorithm are compared. It was found that the proposed ant colony algorithm gives better results as compared to the existing ant colony algorithm.     

多车场CARP问题的改进遗传算法求解

带有容量限制的弧路径规划问题来源于城市垃圾回收、街道清扫、邮件投递、校车路线安排和洒水车路线安排等实际问题,多车场CARP问题是具有多个车场的CARP问题。提出了一种先划分区域后进行路径规划的方法来求解多车场CARP问题。该方法先将各服务弧按照离车场距离的远近归并到距离最近的车场,从而转化为单车场CARP问题,然后用改进的遗传算法进行求解;在求解过程中,用模拟退火算法对部分服务弧进行局部调整,使服务弧在一定的范围内在不同的车场之间进行调换,从而避免局部收敛,达到全局优化的效果。以洒水车路线安排为实例,实验结果表明,该算法能有效求解一定规模的多车场CARP问题,为实际应用奠定了基础。     

Perturbed Decomposition Algorithm applied to the multi-objective Traveling Salesman Problem

Dealing with multi-objective combinatorial optimization, this article proposes a new multi-objective set-based meta-heuristic named Perturbed Decomposition Algorithm (PDA). Combining ideas from decomposition methods, local search and data perturbation, PDA provides a 2-phase modular framework for finding an approximation of the Pareto front. The first phase decomposes the search into a number of linearly aggregated problems of the original multi-objective problem. The second phase conducts an iterative process: aggregated problems are first perturbed then selected and optimized by an efficient single-objective local search solver. Resulting solutions will serve as a starting point of a multi-objective local search procedure, called Pareto Local Search. After presenting a literature review of meta-heuristics on the multi-objective symmetric Traveling Salesman Problem (TSP), we conduct experiments on several instances of the bi-objective and tri-objective TSP. The experiments show that our proposed algorithm outperforms the best current methods on this problem.     

An adaptive large neighborhood search heuristic for Two-Echelon Vehicle Routing Problems arising in city logistics

In this paper, we propose an adaptive large neighborhood search heuristic for the Two-Echelon Vehicle Routing Problem (2E-VRP) and the Location Routing Problem (LRP). The 2E-VRP arises in two-level transportation systems such as those encountered in the context of city logistics. In such systems, freight arrives at a major terminal and is shipped through intermediate satellite facilities to the final customers. The LRP can be seen as a special case of the 2E-VRP in which vehicle routing is performed only at the second level. We have developed new neighborhood search operators by exploiting the structure of the two problem classes considered and have also adapted existing operators from the literature. The operators are used in a hierarchical scheme reflecting the multi-level nature of the problem. Computational experiments conducted on several sets of instances from the literature show that our algorithm outperforms existing solution methods for the 2E-VRP and achieves excellent results on the LRP.     

A cooperative coevolutionary algorithm for the Multi-Depot Vehicle Routing Problem

The Multi-Depot Vehicle Routing Problem (MDVRP) is an important variant of the classical Vehicle Routing Problem (VRP), where the customers can be served from a number of depots. This paper introduces a cooperative coevolutionary algorithm to minimize the total route cost of the MDVRP. Coevolutionary algorithms are inspired by the simultaneous evolution process involving two or more species. In this approach, the problem is decomposed into smaller subproblems and individuals from different populations are combined to create a complete solution to the original problem. This paper presents a problem decomposition approach for the MDVRP in which each subproblem becomes a single depot VRP and evolves independently in its domain space. Customers are distributed among the depots based on their distance from the depots and their distance from their closest neighbor. A population is associated with each depot where the individuals represent partial solutions to the problem, that is, sets of routes over customers assigned to the corresponding depot. The fitness of a partial solution depends on its ability to cooperate with partial solutions from other populations to form a complete solution to the MDVRP. As the problem is decomposed and each part evolves separately, this approach is strongly suitable to parallel environments. Therefore, a parallel evolution strategy environment with a variable length genotype coupled with local search operators is proposed. A large number of experiments have been conducted to assess the performance of this approach. The results suggest that the proposed coevolutionary algorithm in a parallel environment is able to produce high-quality solutions to the MDVRP in low computational time.     

易腐产品运输调度问题的优化

针对易腐产品在运输过程中容易变质,具有时效性和货物关联性的特点,构建一种带软时间窗的关联运输调度问题的数学模型来考虑易腐产品的配送,并采用免疫克隆选择算法求解这个复杂问题。通过对该问题进行分析建模和数值求解,说明了该模型和算法的合理性和有效性。与遗传算法相比较,免疫克隆选择算法能更有效地解决关联运输调度问题。     

带时间窗车辆路径问题的混合改进型蚂蚁算法

带时间窗车辆路径问题（VRPTW）是VRP的一种重要扩展类型,在蚂蚁算法思想基础上,设计用于求解该问题的混合改进型算法并求解Solomon标准数据库中的大量实例。经过大量数据测试并与其他启发式算法所得结果进行比较,获得了较好的效果。     

Hybrid metaheuristics for the Clustered Vehicle Routing Problem

The Clustered Vehicle Routing Problem (CluVRP) is a variant of the Capacitated Vehicle Routing Problem in which customers are grouped into clusters. Each cluster has to be visited once, and a vehicle entering a cluster cannot leave it until all customers have been visited. This paper presents two alternative hybrid metaheuristic algorithms for the CluVRP. The first algorithm is based on an Iterated Local Search algorithm, in which only feasible solutions are explored and problem-specific local search moves are utilized. The second algorithm is a hybrid genetic search, for which the shortest Hamiltonian path between each pair of vertices within each cluster should be precomputed. Using this information, a sequence of clusters can be used as a solution representation and large neighborhoods can be efficiently explored, by means of bi-directional dynamic programming, sequence concatenation, and appropriate data structures. Extensive computational experiments are performed on benchmark instances from the literature, as well as new large scale instances. Recommendations on the choice of algorithm are provided, based on average cluster size.     

有软时窗多车场开放式车辆路径及其禁忌搜索

有软时窗约束多车场开放式车辆路径问题是在基本的车辆路径问题上增加了时间窗约束和多车场作业的一种变化形式,是一个典型的NP-难问题。建立了问题模型,运用改进的禁忌搜索算法测试了算例。快速获得的高质量解验证了模型的正确性和算法性能的优良性。     

解决移动计算位置管理的离散差分进化算法

位置管理问题是移动计算环境中的一个重要问题。提出了一种解决位置管理问题的离散差分进化算法,给出了种群的离散编码方法和一种新的变异操作机制,提出了基于问题特性的种群初始化启发式方法,以及早熟收敛问题的解决策略。基于随机生成的数据对算法进行了模拟实验,将该算法的结果与遗传算法、禁忌搜索算法及蚁群算法进行了对比。     

Adaptive memory programming for the vehicle routing problem with multiple trips

The Vehicle Routing Problem with Multiple Trips is an extension of the classical Vehicle Routing Problem in which each vehicle may perform several routes in the same planning period. In this paper, an adaptive memory algorithm to solve this problem is proposed. Computational experience is reported over a set of benchmark problem instances.     

蚁群优化算法及其应用

蚂蚁算法是由意大利学者M．Dorigo等人提出的一种新型的模拟进化算法。该算法首先应用于旅行商问题并获得了极大的成功，其后，又被用于求解指派问题、Job—shop调度问题、图着色问题和网络路由问题等。实践证明，蚂蚁算法是一种鲁棒性强、收敛性好、实用性广的优化算法，但同时也存在一些不足，如收敛速度慢和容易出现停滞现象等。     

Immunodomaince based Clonal Selection Clustering Algorithm

Based on clonal selection principle and the immunodominance theory, a new immune clustering algorithm, Immunodomaince based Clonal Selection Clustering Algorithm (ICSCA) is proposed in this paper. Firstly, by introducing a new immunodomaince operator to Clonal Selection Algorithm (CSA), the gene of elites in antibody population can be extracted and generalized to ordinary antibodies so as to gain on-line priori knowledge and share information among individuals. Then, one iteration of Fuzzy C-means clustering algorithm (FCM) and adaptive updating mechanism of antibody population are utilized to improve the diversity of antibody population in order to speed up the convergence speed. The proposed method has been extensively compared with FCM, GA-clustering algorithm (GACA) and Clonal Selection Algorithm based FCM (CSAFCM) over a test suit of several real life data sets and synthetic data sets. Experimental results indicate the superiority of the ICSCA over FCM, GAFCM and CSAFCM on clustering accuracy and robustness.