A new parallel and distributed shortest path algorithm forhierarchically clustered data networks

This paper presents new efficient shortest path algorithms to solve single origin shortest path problems (SOSP problems) and multiple origins shortest path problems (MOSP problems) for hierarchically clustered data networks. To solve an SOSP problem for a network with n nodes, the distributed version of our algorithm reaches the time complexity of O(log(n)), which is less than the time complexity of O(log ² (n)) achieved by the best existing algorithm. To solve an MOSP problem, our algorithm minimizes the needed computation resources, including computation processors and communication links for the computation of each shortest path so that we can achieve massive parallelization. The time complexity of our algorithm for an MOSP problem is O(m log(n)), which is much less than the time complexity of O(M log² (0)) of the best previous algorithm. Here, M is the number of the shortest paths to be computed and m is a positive number related to the network topology and the distribution of the nodes incurring communications, m is usually much smaller than M. Our experiment shows that m is almost a constant when the network size increases. Accordingly, our algorithm is significantly faster than the best previous algorithms to solve MOSP problems for large data networks     

A bi-objective approach for shortest-path network interdiction

In the literature, solution approaches to the shortest-path network interdiction problem have been developed for optimizing a single figure-of-merit of the network configuration when considering limited amount of resources available to interdict network links. This paper presents a newly developed evolutionary algorithm that allows approximating the optimal Pareto set of network interdiction strategies when considering bi-objective shortest path problems. Thus, the paper considers the concurrent optimization of two objectives: (1) maximization of shortest-path length and (2) minimization of interdiction strategy cost. Also, the paper considers the transformation of the first objective into the minimization of the most reliable path reliability. To solve these multi-objective optimization problems, an evolutionary algorithm has been developed. This algorithm is based on Monte Carlo simulation, to generate potential network interdiction strategies, graph theory to analyze strategies’ shortest path or most reliable path and, an evolutionary search driven by the probability that a link will appear in the optimal Pareto set. Examples for different sizes of networks and network behavior are used throughout the paper to illustrate and validate the approach.     

A memory efficient stochastic evolution based algorithm for the multi-objective shortest path problem

Multi-objective shortest path (MOSP) problem aims to find the shortest path between a pair of source and a destination nodes in a network. This paper presents a stochastic evolution (StocE) algorithm for solving the MOSP problem. The proposed algorithm is a single-solution-based evolutionary algorithm (EA) with an archive for storing several non-dominant solutions. The solution quality of the proposed algorithm is comparable to the established population-based EAs. In StocE, the solution replaces its bad characteristics as the generations evolve. In the proposed algorithm, different sub-paths are the characteristics of the solution. Using the proposed perturb operation, it eliminates the bad sub-paths from generation to generation. The experiments were conducted on huge real road networks. The proposed algorithm is comparable to well-known single-solution and population-based EAs. The single-solution-based EAs are memory efficient, whereas, the population-based EAs are known for their good solution quality. The performance measures were the solution quality, speed and memory consumption, assessed by the hypervolume (HV) metric, total number of evaluations and memory requirements in megabytes. The HV metric of the proposed algorithm is superior to that of the existing single-solution and population-based EAs. The memory requirements of the proposed algorithm is at least half than the EAs delivering similar solution quality. The proposed algorithms also executes more rapidly than the existing single-solution-based algorithms. The experimental results show that the proposed algorithm is suitable for solving MOSP problems in embedded systems.     

一种基于桶结构的单源最短路径算法

以单源最短路径为主的最优路径问题是众多社会应用领域内选择最优问题的基础。本文分析了不同实现技术求解单源最短路径问题的算法,结合基于标记设定的Dijkstra算法和基于标记修正的BFM算法的思想,提出了一种基于桶结构的单源最短路径算法。实验结果表明,该算法与前两种算法相比,具有好的运行时间复杂度和可并行性。     

一类标准矩形网络节点间最短路径的求解方法

针对常见的交通道路最短路径问题, 提出标准矩形网络的概念, 分析其节点间最短路径的性质, 并在此基础上给出一种新颖的最短路径求解算法. 该算法利用标准矩形网络的几何性质, 简化了搜索方向和步长的判断, 同时指出常见的交通道路网络一般均可以整体或部分化为标准矩形网络. 与常见的求取最短路径的Dijkstra、Floyd、ACO、A* 等算法进行仿真实验比较, 实验结果表明, 对于大规模标准矩形道路网络, 所提出算法具有更好的寻优精度、稳定性和寻优速度.

     

一种基于双端队列的交通网络最短路径Pallottino优化算法

最短路径算法是计算机科学与地理信息科学领域的研究热点，而标号算法则是最短路径算法中的重要一族。长期以来，对于最短路径的算法实现，绝大多数都是围绕以Dijkstra算法为核心的标号设定算法来展开，而对标号改正算法的研究与应用却非常少见。为了对交通网络最短路径进行更有效、更快速的计算，通过对标号改正算法思想的深入分析，针对其中最具代表性的Pallottino算法，从存储结构和运行结构两方面进行了算法的优化改进，同时分析了该算法的时间复杂度和空间复杂度，并利用实际的大规模城市交通网络进行了效率测试。结果显示，与目前公认最优的标号设定算法中基于逼近桶结构的Dijkstra算法相比，该改进的标号改正Pallottino算法具有更好的适用性和更高的运行效率，因此在交通网络最短路径分析应用中具有很高的应用价值。     

交通网络最短路径标号算法的实现与效率分析

标号算法是交通网络最短路径算法族中应用最广泛的算法,其中以各种D ijkstra算法为核心的标号设定算法是各种商用G IS平台网络分析算法的首选。然而,同样隶属于标号算法的标号改正算法在交通网络路径分析中却罕有应用。为了将标号改正算法应用于交通网络路径分析,首先讨论了标号算法的基本结构;然后分析了标号设定算法和标号改正算法的实现过程、复杂度、运行特点和适用性,进而选择了标号设定和标号改正算法中公认的几种优秀算法———基于逼近桶结构和改进四叉堆的D ijkstra算法(D IKBA与D IKQH)以及Pallottino算法(TWO-Q),并结合交通网络邻接链表结构予以实现;最后采用城市交通网络数据,对几种算法的实际运行效率进行了对比试验,试验结果表明,标号改正算法和标号设定算法优点各异;由于交通网络路径算法的应用越来越强调动态性和网络适用性,而且标号改正算法较之标号设定算法具有更大的适用范围,因此其在交通网络路径分析中具有极大的应用潜力。     

Optimal groundwater monitoring design using an ant colony optimization paradigm

Groundwater long-term monitoring (LTM) is required to assess the performance of groundwater remediation and human being health risk at post-closure sites where groundwater contaminants are still present. The large number of sampling locations can make the LTM costly, especially since LTM may be required over several decades. An optimization algorithm based on the ant colony optimization (ACO) paradigm is developed to minimize the overall data loss due to fewer sampling locations for a given number of monitoring wells. The ACO method is inspired by the ability of an ant colony to identify the shortest route between their nest and a food source. The developed ACO-LTM algorithm is applied to a field site with an existing 30-well LTM network. When compared to the results identified through complete enumeration, the ACO-LTM solutions are globally optimal for the cases with 21 to 27 remaining wells. Results from the developed ACO-LTM algorithm provide a proof-of-concept for the application of the general ACO analogy to the groundwater LTM sampling location optimization problem. A major contribution of this work is the successful development of an efficient and effective stochastic search algorithm for solving the LTM optimization problem based on the ACO paradigm.     

Ants can solve the team orienteering problem

The team orienteering problem (TOP) involves finding a set of paths from the starting point to the ending point such that the total collected reward received from visiting a subset of locations is maximized and the length of each path is restricted by a pre-specified limit. In this paper, an ant colony optimization (ACO) approach is proposed for the team orienteering problem. Four methods, i.e., the sequential, deterministic-concurrent and random-concurrent and simultaneous methods, are proposed to construct candidate solutions in the framework of ACO. We compare these methods according to the results obtained on well-known problems from the literature. Finally, we compare the algorithm with several existing algorithms. The results show that our algorithm is promising.     

Applying multi-objective ant colony optimization algorithm for solving the unequal area facility layout problems

The unequal area facility layout problem (UA-FLP) which deals with the layout of departments in a facility comprises of a class of extremely difficult and widely applicable multi-objective optimization problems with constraints arising in diverse areas and meeting the requirements for real-world applications. Based on the heuristic strategy, the problem is first converted into an unconstrained optimization problem. Then, we use a modified version of the multi-objective ant colony optimization (MOACO) algorithm which is a heuristic global optimization algorithm and has shown promising performances in solving many optimization problems to solve the multi-objective UA-FLP. In the modified MOACO algorithm, the ACO with heuristic layout updating strategy which is proposed to update the layouts and add the diversity of solutions is a discrete ACO algorithm, with a difference from general ACO algorithms for discrete domains which perform an incremental construction of solutions but the ACO in this paper does not. We propose a novel pheromone update method and combine the Pareto optimization based on the local pheromone communication and the global search based on the niche technology to obtain Pareto-optimal solutions of the problem. In addition, the combination of the local search based on the adaptive gradient method and the heuristic department deformation strategy is applied to deal with the non-overlapping constraint between departments so as to obtain feasible solutions. Ten benchmark instances from the literature are tested. The experimental results show that the proposed MOACO algorithm is an effective method for solving the UA-FLP.     

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.     

基于改进蚁群算法的星球探测机器人路径规划技术

对蚁群算法中蚂蚁的个体行为进行改进,解决了星球表面复杂环境下探测机器人的路径规划问题．在个体行为中加入目标导向行为、惯性行为和沿障碍行走行为,并进行加权融合,改进了传统的ACO算法,提高了算法的智能,保证了算法的全局收敛性．在蚁群算法规划的基础上提出一种紧绳算法。对蚁群算法的最后结果进行处理,最终给出了最优规划路径．最后通过仿真对该方法进行验证．     

On improving normal boundary intersection method for generation of Pareto frontier

Gradient-based methods, including Normal Boundary Intersection (NBI), for solving multi-objective optimization problems require solving at least one optimization problem for each solution point. These methods can be computationally expensive with an increase in the number of variables and/or constraints of the optimization problem. This paper provides a modification to the original NBI algorithm so that continuous Pareto frontiers are obtained “in one go,” i.e., by solving only a single optimization problem. Discontinuous Pareto frontiers require solving a significantly fewer number of optimization problems than the original NBI algorithm. In the proposed method, the optimization problem is solved using a quasi-Newton method whose history of iterates is used to obtain points on the Pareto frontier. The proposed and the original NBI methods have been applied to a collection of 16 test problems, including a welded beam design and a heat exchanger design problem. The results show that the proposed approach significantly reduces the number of function calls when compared to the original NBI algorithm.     

时间依赖的网络中最小时间路径算法

时间依赖的网络与传统网络模型相比更具有现实意义，具有广泛的应用领域，交通网络和通信网络可以抽象为时间依赖的网络模型，当模型中弧的工度是时间依赖的变量，最短路径问题的求解变得非常困难，早期的研究者通过具体的网络实例认识到传统最短路径算法在这种情况下是不正确的，因此给出限制性条件使得传统最短路径算法是有效的。该文从最短路径算法的理论基础入手，从理论上证明了传统最短路径算法，如Dijkstra算法和标号设置算法，在时间依赖的网络上不能有效地求解最短路径问题，并且，在没有任何限制性条件下，给出了时间依赖的网络模型，理论基础，求解最小时间路径的优化条件和SPTDN算法，从理论上证明了SPTDN算法的正确性，算法的实验结果是正确的，最后给出了时间依赖的网络应用实例。     

求解多处理机调度问题的蚁群算法

蚁群算法是受自然界中的蚂蚁觅食行为启发而设计的智能优化算法,特别适合处理离散型的组合优化问题。提出一种求解多处理机调度的蚁群算法,利用一个蚂蚁代表一个处理机来选择任务,并通过分析关键路径及每个任务的最早、最迟开始时间来确定每个任务的紧迫程度,让蚂蚁以此来选择任务。实验证明,该算法可比传统算法取得有更好运行效率的调度策略。     

Drone shipping versus truck delivery in a cross-docking system with multiple fleets and products

We propose a new bi-objective multi-product combined cross-docking truck-scheduling model with direct drone shipping and multiple fleets.The proposed model considers two conflicting objective functions (scheduling cost and time) within a multi-objective mixed integer mathematical programming problem. Several constraint sets are also considered for both allocation and scheduling phenomena. An efficient multi-objective epsilon-constraint method is adapted to solve the proposed model. Several numerical examples and metrics are provided to demonstrate the applicability of the proposed model and exhibit the efficacy of the solution procedures and algorithms. The efficient frontiers of the numerical examples are estimated by generating non-dominated solutions. The effects that modifications in the costs associated with the direct shipping of products have on the corresponding Pareto frontiers are analyzed. Finally, sensitivity analysis is used to assess the robustness of the results of the model in the presence of uncertainty.     

Clear and smooth path planning

One of the challenging problems in motion planning is finding an efficient path for a robot in different aspects such as length, clearance and smoothness. We formulate this problem as two multi-objective path planning models with the focus on robot's energy consumption and path's safety. These models address two five- and three-objectives optimization problems. We propose an evolutionary algorithm for solving the problems. For efficient searching and achieving Pareto-optimal regions, in addition to the standard genetic operators, a family of path refiner operators is introduced. The new operators play a local search role and intensify power of the algorithm in both explorative and exploitative terms. Finally, we verify the models and compare efficiency of the algorithm and the refiner operators by other multi-objective algorithms such as strength Pareto evolutionary algorithm 2 and multi-objective particle swarm optimization on several complicated path planning test problems.     

求解约束优化问题的佳点集多目标进化算法

结合数论中的佳点集理论和多目标优化方法,提出一种求解约束优化问题的进化算法。将约束优化问题转化为多目标优化问题,引入佳点集理论,以确保所构造的个体在搜索空间内分布均匀,设计变异算子增加个体多样性,采用分群局部搜索方式,并根据Pareto非支配关系选择群体中的优势个体。实验结果表明,该算法具有较好的稳定性。     

基于混沌神经网络的最短路径路由算法

将最短路径问题映射到混沌神经网络，提出了一种带有混沌噪音的神经网络最短路径路由算法。首先设计了与最短路径有关的网络费用和路径表达方法；其次结合混沌神经网络的数学模型建立神经元的运动方程；最后依据网络费用和约束条件构造神经网络的能量函数。分别在具有9个结点和15个结点的网络拓扑结构上进行了实验，单个和多个分组请求均能快速地找到最短路径。结果表明，该文提出的最短路径路由算法用于高速交换网络是有效可行的。