An ant colony optimization algorithm for the bi-objective shortest path problem

Multi-objective shortest path problem (MOSP) is an extension of a traditional single objective shortest path problem that seeks for the efficient paths satisfying several conflicting objectives between two nodes of a network. MOSP is one of the most important problems in network optimization with wide applications in telecommunication industries, transportation and project management. This research presents an algorithm based on multi-objective ant colony optimization (ACO) to solve the bi-objective shortest path problem. To analyze the efficiency of the algorithm and check for the quality of solutions, experimental analyses are conducted. Two sets of small and large sized problems that generated randomly are solved. Results on the set problems are compared with those of label correcting solutions that is the most known efficient algorithm for solving MOSP. To compare the Pareto optimal frontiers produced by the suggested ACO algorithm and the label correcting algorithm, some performance measures are employed that consider and compare the distance, uniformity distribution and extension of the Pareto frontiers. The results on the set of instance problems show that the suggested algorithm produces good quality non-dominated solutions and time saving in computation of large-scale bi-objective shortest path problems.     

Transient chaotic neural network-based disjoint multipath routing for mobile ad-hoc networks

Due to mobility of wireless hosts, routing in mobile ad-hoc networks (MANETs) is a challenging task. Multipath routing is employed to provide reliable communication, load balancing, and improving quality of service of MANETs. Multiple paths are selected to be node-disjoint or link-disjoint to improve transmission reliability. However, selecting an optimal disjoint multipath set is an NP-complete problem. Neural networks are powerful tools for a wide variety of combinatorial optimization problems. In this study, a transient chaotic neural network (TCNN) is presented as multipath routing algorithm in MANETs. Each node in the network can be equipped with a neural network, and all the network nodes can be trained and used to obtain optimal or sub-optimal high reliable disjoint paths. This algorithm can find both node-disjoint and link-disjoint paths with no extra overhead. The simulation results show that the proposed method can find the high reliable disjoint path set in MANETs. In this paper, the performance of the proposed algorithm is compared to the shortest path algorithm, disjoint path set selection protocol algorithm, and Hopfield neural network (HNN)-based model. Experimental results show that the disjoint path set reliability of the proposed algorithm is up to 4.5 times more than the shortest path reliability. Also, the proposed algorithm has better performance in both reliability and the number of paths and shows up to 56% improvement in path set reliability and up to 20% improvement in the number of paths in the path set. The proposed TCNN-based algorithm also selects more reliable paths as compared to HNN-based algorithm in less number of iterations.     

An anticipation mechanism for the shortest path problem based on Physarum polycephalum

In this paper, we put forward an anticipation mechanism for the existing Physarum-inspired shortest path finding method. The Physarum-based shortest path finding model can be implemented by an iterative algorithm and has wide applications in many fundamental network optimization problems. In this paper, we mainly focus on the Physarum-inspired shortest path tree model. Normally, we stop the program when the difference between two consecutive iterations is less than a predefined threshold. However, we do not know how to set the specific value for the threshold variable. In order to find out the optimal solution, we need to set the threshold as a very small number. This in turn will consume a lot of time. From this point of view, this algorithm lacks an efficient and reliable mechanism to judge when the optimal solution will be found. In this paper, we introduce an anticipation mechanism to address this issue. Numerical examples are used to demonstrate its reliability and efficiency.     

最短路径路由算法的扩展

本文主要从QoS度量的可乘性、最小性两个方面对最短路径路由算法进行扩展,从而找出了最可靠、最宽的路径.并通过MATLAB6.1进行了实例仿真.     

混合分解和强度帕累托多目标进化算法

在多目标进化优化中,使用分解策略的基于分解的多目标进化算法(MOEA/D)时间复杂度低,使用〖BP(〗强度帕累托策略的〖BP)〗强度帕累托进化算法-2(SPEA2)能得到分布均匀的解集。结合这两种策略,提出一种新的多目标进化算法用于求解具有复杂、不连续的帕累托前沿的多目标优化问题(MOP)。首先,利用分解策略快速逼近帕累托前沿;然后,利用强度帕累托策略使解集均匀分布在帕累托前沿,利用解集重置分解策略中的权重向量集,使其适配于特定的帕累托前沿;最后,利用分解策略进一步逼近帕累托前沿。使用的反向世代距离(IGD)作为度量标准,将新算法与MOEA/D、SPEA2和paλ-MOEA/D在12个基准问题上进行性能对比。实验结果表明该算法性能在7个基准问题上最优,在5个基准问题上接近于最优,且无论MOP的帕累托前沿是简单或复杂、连续或不连续的,该算法均能生成分布均匀的解集。     

基于优先队列的时变网络最短路径算法

提出了基于优先队列的时变网络最短路径算法,能克服传统最短路径算法难以对时变网络求解最短路径的缺陷。提出的时间窗选择策略能够在算法求解过程中为节点选择合适的时间窗以降低路径长度,从而求得精确解。进一步地,算法使用了优先队列组织节点集合以提高计算效率。在随机生成的网络数据以及美国道路数据上的实验表明,基于优先队列的时变网络最短路径算法与经典方法相比,不仅能够求得精确解,运算速度也有所提高。     

A constrained binary knapsack approximation for shortest path network interdiction

A modified shortest path network interdiction model is approximated in this work by a constrained binary knapsack which uses aggregated arc maximum flow as the objective function coefficient. In the modified shortest path network interdiction problem, an attacker selects a path of highest non-detection probability on a network with multiple origins and multiple available targets. A defender allocates a limited number of resources within the geographic region of the network to reduce the maximum network non-detection probability between all origin-target pairs by reducing arc non-detection probabilities and where path non-detection probability is modeled as a product of all arc non-detection probabilities on that path. Traditional decomposition methods to solve the shortest path network interdiction problem are sensitive to problem size and network/regional complexity. The goal of this paper is to develop a method for approximating the regional allocation of defense resources that maintains accuracy while reducing both computational effort and the sensitivity of computation time to network/regional properties. Statistical and spatial analysis methods are utilized to verify approximation performance of the knapsack method in two real-world networks.     

基于A*算法的三维地图最优路径规划

研究了基于A*算法的适合人步行行走的山地环境下三维地图最优路径规划算法及实现.本文考虑了三维山地无路网信息覆盖的条件较差环境,对A*算法进行改进,并利用三维地形DEM数据计算出一条相对平缓且长度较短的三维路径.改进算法对三维条件下路径最短的评价标准由原有的空间距离累加最短改进为先将空间等效成水平距离,再计算距离是否最短.同时,本文充分考虑了搜索点周围环境的整体坡度信息作为启发信息,来降低算法寻找的路径走在陡坡上的概率.实验表明,本算法最终计算出的三维最优路径在平缓度及路径最短上有所改善,基本符合人步行行走的习惯.     

基于模糊时间窗的多目标冷链配送优化

随着生鲜冷链行业竞争逐渐白热化,成本高、时效性强、新鲜度难以保持等问题已成为制约冷链物流配送的瓶颈。为提高生鲜配送效率,考虑客户满意度,以货损成本、惩罚成本等综合配送成本最低为目标函数,构建了一个多目标配送路径优化模型。设计带精英策略的非支配排序遗传算法（Elitist Non-dominated Sorting Genetic Algorithm,NSGA-II）求解该问题,利用Solomon标准数据集进行仿真模拟实验。实验结果对比分析表明,考虑满意度时冷链物流配送所需车辆更少,总路径长度更短,设计的算法可以在较短的时间内获取到帕累托最优解集,能够有效地解决模糊时间窗下的配送路径优化问题。     

SOLVING THE SAILING PROBLEM WITH A NEW PRIORITIZED VALUE ITERATION

In this paper we tackle the sailing strategies problem, a stochastic shortest-path Markov decision process. The problem of solving large Markov decision processes accurately and quickly is challenging. Because the computational effort incurred is considerable, current research focuses on finding superior acceleration techniques. For instance, the convergence properties of current solution methods depend, to a great extent, on the order of backup operations. On one hand, algorithms such as topological sorting are able to find good orderings, but their overhead is usually high. On the other hand, shortest path methods, such as Dijkstra's algorithm, which is based on priority queues, have been applied successfully to the solution of deterministic shortest-path Markov decision processes. Here, we propose improved value iteration algorithms based on Dijkstra's algorithm for solving shortest path Markov decision processes. The experimental results on a stochastic shortest-path problem show the feasibility of our approach.     

Optimal process design of sheet metal forming for minimum springback via an integrated neural network evolutionary algorithm

The process of sheet metal forming is characterized by various process parameters. Accurate prediction of springback is essential for the design of tools used in sheet metal forming operations. In this paper, an evolutionary algorithm is presented that is capable of handling single/multiobjective, unconstrained and constrained formulations of optimal process design problems. To illustrate the use of the algorithm, a relatively simple springback minimization problem (hemispherical cup-drawing) is solved in this paper, and complete formulations of the algorithm are provided to deal with the constraints and multiple objectives. The algorithm is capable of generating multiple optimal solutions in a single run. The evolutionary algorithm is combined with the finite element method for springback computation, in order to arrive at the set of optimal process parameters. To reduce the computational time required by the evolutionary algorithm due to actual springback computations via the finite element method, a neural network model is developed and integrated within the evolutionary algorithm as an approximator. The results clearly show the viability of the use of the evolutionary algorithm and the use of approximators to derive optimal process parameters for metal forming operations.     

游戏引擎最短路径搜索优化遗传算法设计

为满足游戏地图中最短路径搜索求解, 提出了一种优化的自适应遗传算法。该算法采用与游戏地图中节点数和弧段数相关联的节点复杂度算子, 结合种群的整体情况和进化潜力来设定自适应遗传算法的交叉率和变异率。实验表明, 该算法避免了搜索结果陷入局部最优解, 确保最短路径的搜索成功率及提高搜索速度, 在游戏引擎设计中具有一定的实用价值。     

Parallel Algorithms for Dynamic Shortest Path Problems

The development of intelligent transportation systems (ITS) and the resulting need for the solution of a variety of dynamic traffic network models and management problems require faster‐than‐real‐time computation of shortest path problems in dynamic networks. Recently, a sequential algorithm was developed to compute shortest paths in discrete time dynamic networks from all nodes and all departure times to one destination node. The algorithm is known as algorithm DOT and has an optimal worst‐case running‐time complexity. This implies that no algorithm with a better worst‐case computational complexity can be discovered. Consequently, in order to derive algorithms to solve all‐to‐one shortest path problems in dynamic networks, one would need to explore avenues other than the design of sequential solution algorithms only. The use of commercially‐available high‐performance computing platforms to develop parallel implementations of sequential algorithms is an example of such avenue. This paper reports on the design, implementation, and computational testing of parallel dynamic shortest path algorithms. We develop two shared‐memory and two message‐passing dynamic shortest path algorithm implementations, which are derived from algorithm DOT using the following parallelization strategies: decomposition by destination and decomposition by transportation network topology. The algorithms are coded using two types of parallel computing environments: a message‐passing environment based on the parallel virtual machine (PVM) library and a multi‐threading environment based on the SUN Microsystems Multi‐Threads (MT) library. We also develop a time‐based parallel version of algorithm DOT for the case of minimum time paths in FIFO networks, and a theoretical parallelization of algorithm DOT on an ‘ideal’ theoretical parallel machine. Performances of the implementations are analyzed and evaluated using large transportation networks, and two types of parallel computing platforms: a distributed network of Unix workstations and a SUN shared‐memory machine containing eight processors. Satisfactory speed‐ups in the running time of sequential algorithms are achieved, in particular for shared‐memory machines. Numerical results indicate that shared‐memory computers constitute the most appropriate type of parallel computing platforms for the computation of dynamic shortest paths for real‐time ITS applications.     

A New Evolutionary Algorithm for Solving Many-Objective Optimization Problems

In this paper, we focus on the study of evolutionary algorithms for solving multiobjective optimization problems with a large number of objectives. First, a comparative study of a newly developed dynamical multiobjective evolutionary algorithm (DMOEA) and some modern algorithms, such as the indicator-based evolutionary algorithm, multiple single objective Pareto sampling, and nondominated sorting genetic algorithm II, is presented by employing the convergence metric and relative hypervolume metric. For three scalable test problems (namely, DTLZ1, DTLZ2, and DTLZ6), which represent some of the most difficult problems studied in the literature, the DMOEA shows good performance in both converging to the true Pareto-optimal front and maintaining a widely distributed set of solutions. Second, a new definition of optimality (namely, L-optimality) is proposed in this paper, which not only takes into account the number of improved objective values but also considers the values of improved objective functions if all objectives have the same importance. We prove that L-optimal solutions are subsets of Pareto-optimal solutions. Finally, the new algorithm based on L-optimality (namely, MDMOEA) is developed, and simulation and comparative results indicate that well-distributed L-optimal solutions can be obtained by utilizing the MDMOEA but cannot be achieved by applying L-optimality to make a posteriori selection within the huge Pareto nondominated solutions. We can conclude that our new algorithm is suitable to tackle many-objective problems.      

过必经点集且具有额外硬约束的最短路径算法

求解过必经点集的最短路径问题已有多种算法,但其应用到在具有额外硬约束限定条件的场景时存在不足。针对此类问题,提出一种基于深度优先搜索发展的随机搜索算法,由使用者依据现场情况给出数学描述,建模抽象为无向带权图表示;依据路径规划要求定义相关变量,包括路径规划的起点、终点、必经点集以及额外硬约束条件,图信息和节点信息以邻接矩阵的形式保存;搜索过程中对路径的可行性加入额外硬约束条件进行实时判定,最终获得最短路径解。实验仿真和实测结果表明,该算法能有效规避额外硬约束条件下的中间路径,生成合理的最短路径,改善相关问题的可求解性。     

A pareto-based evolutionary algorithm using decomposition and truncation for dynamic multi-objective optimization

Maintaining a balance between convergence and diversity of the population in the objective space has been widely recognized as the main challenge when solving problems with two or more conflicting objectives. This is added by another difficulty of tracking the Pareto optimal solutions set (POS) and/or the Pareto optimal front (POF) in dynamic scenarios. Confronting these two issues, this paper proposes a Pareto-based evolutionary algorithm using decomposition and truncation to address such dynamic multi-objective optimization problems (DMOPs). The proposed algorithm includes three contributions: a novel mating selection strategy, an efficient environmental selection technique and an effective dynamic response mechanism. The mating selection considers the decomposition-based method to select two promising mating parents with good diversity and convergence. The environmental selection presents a modified truncation method to preserve good diversity. The dynamic response mechanism is evoked to produce some solutions with good diversity and convergence whenever an environmental change is detected. In the experimental studies, a range of dynamic multi-objective benchmark problems with different characteristics were carried out to evaluate the performance of the proposed method. The experimental results demonstrate that the method is very competitive in terms of convergence and diversity, as well as in response speed to the changes, when compared with six other state-of-the-art methods.     

A Novel Multiobjective Fireworks Algorithm and Its Applications to Imbalanced Distance Minimization Problems

Recently, multimodal multiobjective optimization problems (MMOPs) have received increasing attention. Their goal is to find a Pareto front and as many equivalent Pareto optimal solutions as possible. Although some evolutionary algorithms for them have been proposed, they mainly focus on the convergence rate in the decision space while ignoring solutions diversity. In this paper, we propose a new multiobjective fireworks algorithm for them, which is able to balance exploitation and exploration in the decision space. We first extend a latest single-objective fireworks algorithm to handle MMOPs. Then we make improvements by incorporating an adaptive strategy and special archive guidance into it, where special archives are established for each firework, and two strategies (i.e., explosion and random strategies) are adaptively selected to update the positions of sparks generated by fireworks with the guidance of special archives. Finally, we compare the proposed algorithm with eight state-of-the-art multimodal multiobjective algorithms on all 22 MMOPs from CEC2019 and several imbalanced distance minimization problems. Experimental results show that the proposed algorithm is superior to compared algorithms in solving them. Also, its runtime is less than its peers’.      

量子密钥分发网络端端密钥协商最优路径选择算法

针对量子密钥分发(QKD)网络端端密钥协商路径选择问题,设计了一种基于改进Dijkstra算法的端端密钥协商最优路径选择算法。首先,基于有效路径策略,剔除网络中的失效链路;然后,基于最短路径策略,通过改进Dijkstra算法,得到密钥消耗最少的多条最短路径;最后,基于最优路径策略,从多条最短路径中选择一条网络服务效率最高的最优路径。分析结果表明,该算法很好地解决了最优路径不唯一、最优路径非最短、最优路径非最优等问题,可以降低QKD网络端端密钥协商时密钥消耗量,提高网络服务效率。     

Optimal route selection based on Monte Carlo method and adaptive amoeba algorithm under uncertain environment

The fuzzy optimal path under uncertainty is one of the basic network optimization problems. Considering the uncertain environment, many fuzzy numbers are used to represent the edge weights, such as interval number and triangular fuzzy number. Then, these fuzzy numbers are converted to real numbers directly. This converting makes the optimal path the shortest path selection problem. However, much information of uncertainty get lost when converting fuzzy numbers to real numbers. In order to ensure all the origan data complete, in this paper, a fuzzy optimal path solving model based on the Monte Carlo method and adaptive amoeba algorithm is proposed. In Monte Carlo process, a random number which belongs to the fuzzy number is generated. Then, Physarum polycephalum algorithm is used to solve the shortest path every time and record the result. After many times calculation, many shortest paths have been found and recorded. At last, by analysing the characters of all the results, the optimal path can be selected. Several numerical examples are given to illustrate the effectiveness of the proposed method, the results show that the proposed method can deal with the fuzzy optimal path problems effectively.     

考虑网络流量的最优路径求解模型和算法

本文旨在解决交通网络中群体车辆的路径选择问题．即为每个车辆寻求最优行驶路径．使之在起迄点间的旅行时间最短．考虑到网络流量对路段旅行时间的影响，先进行流量分配，再同时为各个车辆寻求最短路径．为此，首先给出了考虑流量影响的网络模型，然后建立了基于路段的用于流量分配的变分不等式模型．该模型的解给出了车辆按照最优路径行驶时分配到各路段上的车辆数目．由于该模型是完全基于路段的，从而克服了基于路径方法必须进行路径穷举的缺陷．最后给出了最优路径选择算法，并证明了算法的正确性．本文给出的模型和算法适用于交通畅通、交通拥挤等各种情况．实验结果表明本文提出的模型和算法是非常有效的．