求解无线传感器网络路由问题的蚁群最优化算法及其收敛性

首先将无线传感器网络的路由问题转化成求解最小Steiner树问题,然后给出了求解无线传感器网络路由的蚁群优化算法,并对算法的收敛性进行了证明．最后对找到最优解后信息素值的变化进行了分析．即在限制信息素取值的条件下,当迭代次数充分大时,该算法能以任意接近于1的概率找到最优解,并且当最优解找到后,最优树边上的信息素单调增加,而最优解以外边上的信息素在有限步达到最小值．     

时变挥发率条件下求解Steiner树蚁群优化算法的收敛性

蚁群优化算法是最近提出的求解复杂组合优化问题的启发式算法.在蚁群优化算法中,信息素的更新规则直接影响着算法性能,固定挥发率条件下,虽然也能得到求解Steinei树蚁群优化算法的收敛性结果,但算法的探优能力差,易于陷入局部最优.本文在设计求解最小Steiner树蚁群优化算法时,采用了动态更新信息索挥发率的方法,并给出了时变挥发率条件下算法的收敛性证明.具体的,在时变挥发率条件下,当迭代次数充分大时,该算法能以概率1找到最优解.另外,在动态更新信息素下界的条件下,也能得到类似的收敛性结果.     

多目标度约束最小生成树的蚁群优化算法求解

多目标最小生成树问题与度约束最小生成树问题分别是网络优化中两个NP难题,在实际中一直有着重要的应用.本文针对同时考虑多目标和度约束情况下的最小生成树求解问题,采用蚁群优化算法思想,设计了一种求解方案,并在计算机上用Delphi予以实现.经大量数值算例求解测试,验证了算法的有效性和可行性.     

基于模拟植物生长算法构造Steiner最优树问题研究

Steiner最优树问题是指对于给定区域内的点集,通过引入Steiner点集将区域中的点连接并保证连通的网络达到最小.该问题已成为经典的优化组合问题之一.提出一种基于模拟植物生长算法生成Steiner最优树的连通算法来实现网络连通.通过对实例的实验及结果分析,结果表明本算法不仅可获得最优解,精度和性能也有提高,明显优于其它方法.     

三维欧氏Steiner最小树的Delaunay四面体网格混合智能算法

Steiner最小树问题是组合优化中经典的NP难题,在许多实际问题中有着广泛的应用,而三维欧氏Steiner最小树问题是对二维欧氏Steiner最小树问题的推广。由于三维欧氏Steiner树问题的求解非常困难,至今为止的相关成果较为少见。本文针对该问题,利用Delaunay四面体网格剖分技术,提出了一种混合型智能求解方法,不仅可以尽量避免拓扑结构陷入局部最优,且对较大规模的问题求解亦有良好的效果。算法在Matlab环境下编程实现,经实例测试,获得了满意的效果。     

图着色和标号问题的蚁群优化算法

对图着色问题的最大最小蚁群算法进行了改进,测试结果表明算法有效可行.在此基础上,分别设计了求解图条件着色和标号问题的相应蚁群优化算法,并对中国地图的条件着色、三正则图的条件着色、广义Petersen图的条件着色和标号问题进行了求解优化,改进和完善了目前理论研究的结论.     

蚁群遗传混合算法

将蚁群遗传混合算法分别求解离散空间的和连续空间优化问题.求解旅行商问题的混合算法是以遗传算法为整个算法的框架,利用了蚁群算法中的信息素特性的进行交叉操作;根据旅行商问题的特点,给出了4种变异策略;针对遗传算法存在的过早收敛问题,加入2-0pt方法对问题求解进行了局部优化.与模拟退火算法、标准遗传算法和标准蚁群算法进行比较,4种混合算法效果都比较好,策略D的混合算法效果最好.求解连续空间优化问题是以蚁群算法为整个算法的框架,加入遗传算法的交叉操作和变异操作,用测试函数验证了混合蚁群算法的正确性.     

基于群智能算法的预防性维修周期优化

分析将蚁群优化算法应用于预防性维修周期工程寻优问题时遇到的算法参数选择困难等问题,提出将粒子群优化算法和空间划分方法引入该过程以改进原蚁群算法的寻优规则和历程.建立混合粒子群和蚁群算法的群智能优化策略:PS_ACO(Particle Swarm and Ant Colony Optimization),并将其应用于混联系统预防性维修周期优化过程中,以解决由于蚁群算法中参数选择不当和随机产生维修周期解值带来的求解精度差、寻优效率低等问题.算法的寻优结果对比分析表明:该PS_ACO算法应用于预防性维修周期优化问题,在寻优效率及寻优精度上有部分改进,且可相对削弱算法参数选择对优化结果的影响.     

灾情巡视问题的蚁群两目标优化算法研究

分析目前灾情巡视问题求解方法存在的缺陷,归纳出灾情巡视问题两目标优化模型.针对灾情巡视问题模型特点,引入蚁群算法和多目标优化理论,提出两个灾情巡视问题的蚁群两目标优化算法:算法1将灾情巡视问题的道路网络转化为完全图,增加m-1个(m为巡视组数)虚拟巡视起点,将灾情巡视两目标优化问题转化为单旅行商两目标优化问题,然后使用蚁群算法和多目标优化理论进行迭代求解.算法2使用一只蚂蚁寻找一个子回路,m个子回路构成一个灾情巡视可行方案,采用罚函数法和多目标优化理论构建增广两目标优化评价函数,使用g组,共g×m只蚂蚁共同协作来发现灾情巡视问题的最优解.算法特点:①算法1将灾情巡视两目标优化问题转化为单旅行商两目标优化问题,可以充分利用已有蚁群算法求解单旅行商问题的研究成果;②两个算法引入蚁群算法,提高了算法效率;③两个算法克服目前灾情巡视问题的求解方法不严密性缺陷;④两目标优化算法可以为用户提供多个满足约束条件的Pareto组合解,扩大了用户选择范围,增强了算法的适用性.算法测试表明:灾情巡视问题的蚁群两目标优化算法是完全可行和有效的.     

基于离散群居蜘蛛算法的WSNs分簇路由优化

对无线传感器网络(WSNs)路由优化问题进行研究,提出一种基于离散群居蜘蛛算法的WSNs分簇路由优化方案.首先定量分析节点覆盖冗余度期望值与网络覆盖率的关系,筛选出能够保证网络覆盖率要求的最少网络工作节点,其次研究分簇大小与网络节点密度的关系,动态地确定最佳的分簇个数.基于此,以簇间距离和簇首能量为评价指标构建簇间通信模型,重新定义蜘蛛个体编码方式和更新策略,采用离散群居蜘蛛算法对模型进行求解,最终实现WSNs分簇路由优化.仿真结果表明,方案能够满足网络覆盖要求,而且与其它路由优化算法相比,延长了网络生命周期,降低了网络能耗.     

Neural and delay based heuristics for the Steiner problem in networks

High speed networks such as the B-ISDN must be adequately equipped to handle multipoint communication in a fast and economical manner. Multicast applications include desktop video conferencing, distance learning, distributed database applications, etc. In networks employing the asynchronous transfer mode (ATM) technology, routing a multicast is achieved by constructing a tree that spans the source and all the destinations. For the purpose of routing, the network is modeled as a weighted, undirected graph. The graph-theoretic solution is to find a minimum Steiner tree for the graph given a set of destinations. This formulation suffices for building multicast trees with a single optimization constraint as would be the xcase for best effort transport. For real-time traffic, however, it is necessary to ensure that the delay between the sender and each of the receivers is bounded. In this case the network is modeled as an undirected graph, where the edges have both a cost and a delay associated with them. The graph-theoretic solution is then to find a constrained minimum Steiner tree such that the delay between the source and each of the destinations does not violate the specified bound. Both of these problems are NP-complete. In this paper we review prior work on the multipoint routing problem and discuss the formulation of the unconstrained and constrained Steiner problems. We use the random neural network (RNN) to significantly improve the quality of trees found by the two existing best heuristics for finding Steiner trees - the minimum spanning tree heuristic and the average distance heuristic. We also develop a new heuristic for finding delay constrained Steiner trees. Experimental results are presented which show that the new heuristics improve significantly over existing ones.     

带区间数据的最小风险斯坦纳树问题

考虑了在带区间数据的不确定网络中, 最小风险和模型以及最小最大风险模型下的斯坦纳树问题. 它们推广了相应模型下的最短路问题和最小支撑树问题, 在网络设计中具有更加广泛的应用.我们分别给出了这两个模型下斯坦纳树问题的近似算法, 并对算法性能做了理论分析和证明. 结果显示我们的算法具有优良的常数逼近的性质, 能在多项式时间内算出令人满意的解.     

Minimal curvature-constrained networks

This paper introduces an exact algorithm for the construction of a shortest curvature-constrained network interconnecting a given set of directed points in the plane and a gradient descent method for doing so in 3D space. Such a network will be referred to as a minimum Dubins tree, since its edges are Dubins paths (or slight variants thereof). The problem of constructing a minimum Dubins tree appears in the context of underground mining optimisation, where the objective is to construct a least-cost network of tunnels navigable by trucks with a minimum turning radius. The Dubins tree problem is similar to the Steiner tree problem, except the terminals are directed and there is a curvature constraint. We propose the minimum curvature-constrained Steiner point algorithm for determining the optimal location of the Steiner point in a 3-terminal network. We show that when two terminals are fixed and the third varied in the planar version of the problem, the Steiner point traces out a limaçon.     

Rectilinear group Steiner trees and applications in VLSI design

 Given a set of disjoint groups of points in the plane, the rectilinear group Steiner tree problem is the problem of finding a shortest interconnection (under the rectilinear metric) which includes at least one point from each group. This is an important generalization of the well-known rectilinear Steiner tree problem which has direct applications in VLSI design: in the detailed routing phase the logical units typically allow the nets to connect to several electrically equivalent ports. We present a first (tailored) exact algorithm for solving the rectilinear group Steiner tree problem (and related variants of the problem). The algorithm essentially constructs a subgraph of the corresponding Hanan grid on which existing algorithms for solving the Steiner tree problem in graphs are applied. The reductions of the Hanan grid are performed by applying point deletions and by generating full Steiner trees on the remaining points. Experimental results for real-world VLSI instances with up to 100 groups are presented. Received: November 7, 2000 / Accepted: December 19, 2001 Published online: September 5, 2002     

A branch-and-cut algorithm for the Steiner tree problem with delays

In this paper, we investigate the Steiner tree problem with delays, which is a generalized version of the Steiner tree problem applied to multicast routing. For this challenging combinatorial optimization problem, we present an enhanced directed cut-based MIP formulation and an exact solution method based on a branch-and-cut approach. Our computational study reveals that the proposed approach can optimally solve hard dense instances.     

Particle swarm optimization for the Steiner tree in graph and delay-constrained multicast routing problems

This paper presents the first investigation on applying a particle swarm optimization (PSO) algorithm to both the Steiner tree problem and the delay constrained multicast routing problem. Steiner tree problems, being the underlining models of many applications, have received significant research attention within the meta-heuristics community. The literature on the application of meta-heuristics to multicast routing problems is less extensive but includes several promising approaches. Many interesting research issues still remain to be investigated, for example, the inclusion of different constraints, such as delay bounds, when finding multicast trees with minimum cost. In this paper, we develop a novel PSO algorithm based on the jumping PSO (JPSO) algorithm recently developed by Moreno-Perez et al. (Proc. of the 7th Metaheuristics International Conference, 2007), and also propose two novel local search heuristics within our JPSO framework. A path replacement operator has been used in particle moves to improve the positions of the particle with regard to the structure of the tree. We test the performance of our JPSO algorithm, and the effect of the integrated local search heuristics by an extensive set of experiments on multicast routing benchmark problems and Steiner tree problems from the OR library. The experimental results show the superior performance of the proposed JPSO algorithm over a number of other state-of-the-art approaches.     

On better heuristics for Steiner minimum trees

Finding a shortest network interconnecting a given set of points in a metric space is called the Steiner minimum tree problem. The Steiner ratio is the largest lower bound for the ratio between lengths of a Steiner minimum tree and a minimum spanning tree for the same set of points. In this paper, we show that in a metric space, if the Steiner ratio is less than one and finding a Steiner minimum tree for a set of size bounded by a fixed number can be performed in polynomial time, then there exists a polynomialtime heuristic for the Steiner minimum tree problem with performance ratio bigger than the Steiner ratio. It follows that in the Euclidean plane, there exists a polynomial-time heuristic for Steiner minimum trees with performance ratio bigger than . This solves a long-standing open problem.Part of this work was done while this author visited the Department of Computer Science, Princeton University, supported in part by DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center, under NSF grant STC88-09648, supported in part by NSF grant No. CCR-8920505, and also supported in part by the National Natural Science Foundation of China.     

Gradient-Constrained Minimum Networks. III. Fixed Topology

The gradient-constrained Steiner tree problem asks for a shortest total length network interconnecting a given set of points in 3-space, where the length of each edge of the network is determined by embedding it as a curve with absolute gradient no more than a given positive value m, and the network may contain additional nodes known as Steiner points. We study the problem for a fixed topology, and show that, apart from a few easily classified exceptions, if the positions of the Steiner points are such that the tree is not minimum for the given topology, then there exists a length reducing perturbation that moves exactly 1 or 2 Steiner points. In the conclusion, we discuss the application of this work to a heuristic algorithm for solving the global problem (across all topologies).