智能搜索算法求解最大团问题研究

最大团问题MCP（Maximum Clique Problem）在国外得到了广泛的研究,在国内刚起步,是一类NP完全问题。传统的确定性算法不能有效地进行求解。定义了MCP;介绍了使用启发式算法求解MCP的研究进展;综述了几种典型的智能搜索算法;分析了使用这些典型算法求解MCP的基本思想;研究了这些智能算法在求解MCP时的特点及性能。     

启发式算法求解最大团问题研究

最大团问题(maximum clique problem,MCP)是图论中的一个经典组合优化问题,也是一类NP完全问题,在国际上已有广泛地研究,国内研究刚刚起步.给出了最大团问题的基本定义和其数学描述;阐述了该问题的研究进展;分析和研究了求解该问题的各种典型启发式算法,包括算法的介绍、算法求解最大团问题的基本思路、特点及性能;最后介绍了测试这些启发式算法性能的测试基准图.     

最大团问题的改进遗传算法求解

最大团问题是组合优化中经典的NP完全问题,该问题的枚举算法只适用于求解中小规模的图。提出了基于遗传算法的最大团问题求解算法,引入概率模型指导变异产生新的个体,并结合启发式局部算法搜索最大团。经算例测试,获得了较好的效果。     

基于蚁群算法求解最大团问题

最大团问题是一种典型的NP完全问题, 是图论中一个经典的组合优化问题.研究将蚁群算法应用于求解最大团问题,提出一种求解最大团问题蚁群算法.通过定义最大团问题蚁群算法中的各元素,并改进了蚂蚁搜索解的方法,有效地改善蚁群算法易于过早地收敛于局部最优解的缺陷.仿真实验表明,图中的顶点数较多时,也取得了较好的结果.     

一种基于匹配交叉求解最大团问题的Memetic算法

针对基于适应值的选择交叉机制在优化具有欺骗性的最大团问题中性能退化的问题,提出一种新的基于匹配交叉的Memetic算法.该算法提出交叉匹配度的概念,用来估计两个体交叉所能获得的最佳适应值.通过匹配度的计算对交叉方向的选择进行控制,保证了交叉操作以较大的概率生成新的优良模式.在40个最大团问题标准算例上的测试结果表明,新算法优于目前在最大团问题求解中性能最好的多阶段动态局部搜索算法.     

关于最大团问题的一种新算法

最大团问题是图论中重要的NP完全问题,目前求解最大团问题的方法只适合某些特殊的图,活则消耗时间长,求解效率低。该文提出了一种新的算法,蚁群算法来解决最大团问题。蚁群优化算法是一种基于自然启发的算法,是一种解决组合优化问题的有效方法。实验结果显示,算法的有效性。     

关于最大团问题的一种新算法

最大团问题是图论中重要的NP完全问题,目前求解最大团问题的方法只适合某些特殊的图,活则消耗时间长,求解效率低。该文提出了一种新的算法．蚁群算法来解决最大团问题。蚁群优化算法是一种基于自然启发的算法,是一种解决组合优化问题的有效方法。实验结果显示,算法的有效性。     

最大团问题降阶算法

最大团问题是找出给定图中的一个最大结点子集合,使得子集合中的任意两点之间都有边相连,最大团问题是一个著名的NP-难题,在很多领域中都有着广泛的应用.本文在研究最大团问题数学性质的基础上给出该问题的一个初步降阶方法;在初步降阶的基础上给出一个求解最大团问题的上、下界方法;最后将降阶方法和上下界方法结合起来形成一个全新的降阶算法,该算法不仅可以单独使用,还可以与其它算法结合起来使用达到更好的效果.在文中还介绍了本算法和其它各类算法的优缺点,最后通过多个示例来进一步说明算法的原理及应用情况.     

大规模图例的最大团问题算法分析

最大团问题是一个经典的组合优化问题,在蛋白质功能推测、竞胜标确定、视频对象分割等领域有广泛的应用。随着图例规模的增大,最大团问题求解难度增加,常规图例最大团求解算法已逐渐被大规模图例最大团求解算法取代。介绍求解大规模图例最大团问题的技术支撑点,重点总结基于大规模图例的最大团问题算法,并在大数据计算背景下对融合单层图划分方法和多层图划分方法的MapReduce框架和Spark框架进行优缺点分析。此外,比较k-core方法与k-community方法的应用场景,从算法分类的角度总结不同类型算法的优缺点,对求解大规模图例最大团问题的确定型算法进行梳理,并对代表性的求解算法在公开数据集中的表现进行对比分析。基于分析结果,指出不同算法在求解大规模图例最大团问题时需要重点关注的方面,并展望了智能优化算法、分层式深度强化学习方法、图结构相变分析技术的未来研究方向。     

低度图的最大团求解算法

在图的最大团问题中,当图的顶点数不大于阈值m时,很容易求解其最大团问题,求解算法的时间复杂度为O(d)。给出一种求解低度图的最大团的确定性算法。该算法通过对图按顶点逐步分解实现分别计算,较好地解决低度图的最大团问题。算法时间复杂度为O(d•n3)。其中,n表示图的顶点数,图中顶点的最大度小于m或者图可以通过逐个删除度小于m的顶点而使所有顶点的度都小于m。     

基于多约束QoS问题的启发式算法

由于多媒体通信的需要,QoS路由技术已成为通信网络中研究的热点。通常情况下,在网络中寻找同时满足多个独立加性约束条件的路由是一个NP完全问题。本文探讨了多约束条件下的路径选择(MCP)问题,通过将MCP问题转化为离散化的动态网络,得到了一个性能更好的启发式QoS路由算法,复杂度从O(Tmn)降低为O(Tm),其中m、n分别是节点数和边数,T是算法定义的正整数,并在理论上证明了算法的正确性。最后给出实验举例,并通过与现有算法性能比较,表明改进的启发式算法能快速、有效地解决MCP问题,且适用于大规模的网络系统。     

Branch-and-Bound-Based Local Search Heuristics for Train Timetabling on Single-Track Railway Network

The modified formulation and two branch-and-bound-based local search heuristic algorithms for train timetabling in single-track railway network in the planning application are proposed. The original local search heuristic is modified such that when a neighbor of a currently tested resolved conflict for improvement is evaluated, the depth-first search branch-and-bound algorithm is employed with two branching rules: least-lower-bound and least-delay-time. The detailed implementation of the proposed heuristic algorithms are described, including the neighborhood definitions of overtaking and crossing conflicts, the procedure to detect overtaking and crossing conflicts, and a recursive procedure for the depth-first search branch-and-bound algorithm. The proposed heuristic algorithms, the original heuristic, the equivalent manual solution method and the exact solution method are compared using a toy problem and four problems (26-train, 50-train, 76-train and 108-train) in the Thailand Southern line railway network, which consisted of 266 single-track segments, 15 double-track segments, 282 stations/sidings, and total distance of 1577 km. The proposed heuristic algorithm with the least-lower-bound branching rule outperforms the other heuristics in terms of the solution quality with up to 2.827 % improvement over the equivalent manual solution method and less than 8 % optimality gap. The proposed heuristic algorithms require longer time to terminate than the original heuristic. The proposed heuristic algorithm with the least-lower-bound branching rule converges faster than that with the least-delay-time branching rule in all test problems. Based on the empirical results, the proposed heuristic algorithms are solvable in polynomial time. Furthermore, the proposed heuristic algorithm with the least-lower-bound branching rule is enhanced by embedding a uniform sampling strategy, and it is found that the total CPU time can be saved by about 50 % with marginally worse solution quality.     

A heuristic for multiple choice programming

A linear programming-based heuristic procedure for solving Multiple Choice Programming (MCP) problems is presented. Two pivot schemes which may be viewed as the specialized versions of those in “Pivot and Complement”, an efficient heuristic by Balas and Martin for pure 0–1 programming, are incorporated into the procedure along with the additional features of cut generation, variable fixing and exchage operation. Three types of MCP problems were tested to evaluate the performance of our procedure. The computational results with seventy five test problems indicate that our heuristic is superior to the default option of APEX-III, which dictates to end the search for better solutions if one within ten per cent of optimum has been found, in both its computational efficiency and the quality of the solution obtained.     

Artificial immune algorithm for IIR filter design

Over the recent years, several studies have been carried out by the researchers to describe a general, flexible and powerful design method based on modern heuristic optimisation algorithms for infinite impulse response (IIR) digital filters since these algorithms have the ability of finding global optimal solution in a nonlinear search space. One of the modern heuristic algorithms is the artificial immune algorithm which implements a learning technique inspired by human immune system. However, the immune system has not attracted the same kind of interest from researchers as other heuristic algorithms. In this work, an artificial immune algorithm is described and applied to the design of IIR filters, and its performance is compared to that of genetic and touring ant colony optimisation algorithms.     

一种求解最大团问题的并行交叉熵算法

为了提高交叉熵算法求解最大团问题(maximum clique problem,MCP)的性能,提出一种领导者-跟随者协作求解的并行策略来实现交叉熵算法,从而达到减少计算时间和保障解的质量这两方面的平衡.算法中领导者活跃在并行处理器之间采集数据,并根据当前获得信息对跟随者作出决策;受控的跟随者则主要根据领导者的决策信息自适应地调整搜索空间,完成各自的集团产生任务.采用了OpenMPI在MIMD平台上实现了该算法,并应用到MCP基准测试问题上.加速比和效率分析结果表明,算法具有很好的加速比和效率.而与其它几种当前最好的启发式算法相比,结果表明算法相对于基于种群的启发式算法有一定的性能改善.     

An impatient evolutionary algorithm with probabilistic tabu search for unified solution of some NP-hard problems in graph and set theory via clique finding.

Many graph- and set-theoretic problems, because of their tremendous application potential and theoretical appeal, have been well investigated by the researchers in complexity theory and were found to be NP-hard. Since the combinatorial complexity of these problems does not permit exhaustive searches for optimal solutions, only near-optimal solutions can be explored using either various problem-specific heuristic strategies or metaheuristic global-optimization methods, such as simulated annealing, genetic algorithms, etc. In this paper, we propose a unified evolutionary algorithm (EA) to the problems of maximum clique finding, maximum independent set, minimum vertex cover, subgraph and double subgraph isomorphism, set packing, set partitioning, and set cover. In the proposed approach, we first map these problems onto the maximum clique-finding problem (MCP), which is later solved using an evolutionary strategy. The proposed impatient EA with probabilistic tabu search (IEA-PTS) for the MCP integrates the best features of earlier successful approaches with a number of new heuristics that we developed to yield a performance that advances the state of the art in EAs for the exploration of the maximum cliques in a graph. Results of experimentation with the 37 DIMACS benchmark graphs and comparative analyses with six state-of-the-art algorithms, including two from the smaller EA community and four from the larger metaheuristics community, indicate that the IEA-PTS outperforms the EAs with respect to a Pareto-lexicographic ranking criterion and offers competitive performance on some graph instances when individually compared to the other heuristic algorithms. It has also successfully set a new benchmark on one graph instance. On another benchmark suite called Benchmarks with Hidden Optimal Solutions, IEA-PTS ranks second, after a very recent algorithm called COVER, among its peers that have experimented with this suite.