Hybridization of Chaos and Flower Pollination Algorithm over K-Means for data clustering

Classical clustering algorithms like K-means often converge to local optima and have slow convergence rates for larger datasets. To overcome such situations in clustering, swarm based algorithms have been proposed. Swarm based approaches attempt to achieve the optimal solution for such problems in reasonable time. Many swarm based algorithms such as Flower Pollination Algorithm (FPA), Cuckoo Search Algorithm (CSA), Black Hole Algorithm (BHA), Bat Algorithm (BA) Particle Swarm Optimization (PSO), Firefly Algorithm (FFA), Artificial Bee Colony (ABC) etc have been successfully applied to many non-linear optimization problems. In this paper, an algorithm is proposed which hybridizes Chaos Optimization and Flower Pollination over K-means to improve the efficiency of minimizing the cluster integrity. The proposed algorithm referred as Chaotic FPA (CFPA) is compared with FPA, CSA, BHA, BA, FFA, and PSO over K-Means for data clustering problem. Experiments are conducted on sixteen benchmark datasets. Algorithms are compared on four different performance parameters — cluster integrity, execution time, number of iterations to converge (NIC) and stability. Results obtained are analyzed statistically using Non-parametric Friedman test. If Friedman test rejects the Null hypothesis then pair wise comparison is done using Nemenyi test. Experimental Result demonstrates the following: (a) CFPA and BHA have better performance on the basis of cluster integrity as compared to other algorithms; (b) Prove the superiority of CFPA and CSA over others on the basis of execution time; (c) CFPA and FPA converges earlier than other algorithms to evaluate optimal cluster integrity; (d) CFPA and BHA produce more stable results than other algorithms.     

若干新型群智能优化算法的对比研究

随着计算机技术的发展,算法技术也在不断交替更新。近年来,群体智能算法受到了广泛的关注和研究,并在诸如机器学习、过程控制、工程预测等领域取得了进展。群智能优化算法属于生物启发式方法,广泛应用在解决最优化问题上,传统的群智能算法为解决一些实际问题提供了新思路,但是也在一些实验中暴露出不足。近年来,许多学者相继提出了很多新型群智能优化算法,选取了最近几年国内外提出的比较典型的群智能算法,蝙蝠算法（Bat Algorithm,BA）、灰狼优化算法（Grey Wolf Optimization,GWO）、蜻蜓算法（Dragonfly Algorithm,DA）、鲸鱼优化算法（Whale Optimization Algorithm,WOA）、蝗虫优化算法（Grasshopper Optimization Algorithm,GOA）和麻雀搜索算法（Sparrow Search Algorithm,SSA）,并进一步通过22个标准的CEC测试函数从收敛速度、精度和稳定性等方面对比了这些算法的实验性能,并对比分析了其相关的改进方法。最后总结了群智能优化算法的特点,探讨了其今后的发展潜力。     

Harris Hawk Optimization Algorithm Based on Cauchy Distribution Inverse Cumulative Function and Tangent Flight Operator

Harris Hawk Optimization (HHO) algorithm is a new population-based and nature-inspired optimization paradigm, which has strong global search ability, but its diversified local search strategies easily make it fall into local optimum. In order to enhance its search mechanism and speed of convergence, an new improved HHO algorithm based on the inverse cumulative function operator of Cauchy distribution and tangent flight operator was proposed. The proposed two operators are used as scale factors to control the step size. The walk path of Cauchy inverse cumulative integral function shows that its trajectory step length is relative to the average, which can further enhance the search stability of the algorithm. The Tangent flight has the function of balanced exploitation and exploration, and enhances the convergence ability of the algorithm. In order to verify the performance of the proposed algorithm, the 30 benchmark functions of the 2017 Institute of Electrical and Electronic Engineers (IEEE) Conference on Evolutionary Computation (CEC2017) and two practical engineering design problems are adopted to carry out the simulation experiments. On the other hand, the covariance matrix adaptation evolutionary strategies (CMA-ES), arithmetic optimization algorithm (AOA), butterfly optimization algorithm (BOA), bat algorithm (BA), whale optimization algorithm (WOA), sine cosine algorithm (SCA), and the proposed HHO algorithms were used for comparison experiments. Simulation results show that the proposed the Cauchy-distribution and Tangent-Flight Harris Hawk Optimization (CTHHO) Algorithm has strong optimization capability.

     

Comparison-based algorithms are robust and randomized algorithms are anytime

Randomized search heuristics (e.g., evolutionary algorithms, simulated annealing etc.) are very appealing to practitioners, they are easy to implement and usually provide good performance. The theoretical analysis of these algorithms usually focuses on convergence rates. This paper presents a mathematical study of randomized search heuristics which use comparison based selection mechanism. The two main results are that comparison-based algorithms are the best algorithms for some robustness criteria and that introducing randomness in the choice of offspring improves the anytime behavior of the algorithm. An original Estimation of Distribution Algorithm combining both results is proposed and successfully experimented.     

Improved imperialist competitive algorithm with mutation operator for continuous optimization problems

Imperialist competitive algorithm is a nascent meta-heuristic algorithm which has good performance. However, it also often suffers premature convergence and falls into local optimal area when employed to solve complex problems. To enhance its performance further, an improved approach which uses mutation operators to change the behavior of the imperialists is proposed in this article. This improved approach is simple in structure and is very easy to be carried out. Three different mutation operators, the Gaussian mutation, the Cauchy mutation and the Lévy mutation, are investigated particularly by experiments. The experimental results suggest that all the three improved algorithms have faster convergence rate, better global search ability and better stability than the original algorithm. Furthermore, the three improved algorithms are also compared with other two excellent algorithms on some benchmark functions and compared with other four existing algorithms on one real-world optimization problem. The comparisons suggest that the proposed algorithms have their own specialties and good applicability. They can obtain better results on some functions than those contrastive approaches.

     

New directional bat algorithm for continuous optimization problems

Bat algorithm (BA) is a recent optimization algorithm based on swarm intelligence and inspiration from the echolocation behavior of bats. One of the issues in the standard bat algorithm is the premature convergence that can occur due to the low exploration ability of the algorithm under some conditions. To overcome this deficiency, directional echolocation is introduced to the standard bat algorithm to enhance its exploration and exploitation capabilities. In addition to such directional echolocation, three other improvements have been embedded into the standard bat algorithm to enhance its performance. The new proposed approach, namely the directional Bat Algorithm (dBA), has been then tested using several standard and non-standard benchmarks from the CEC’2005 benchmark suite. The performance of dBA has been compared with ten other algorithms and BA variants using non-parametric statistical tests. The statistical test results show the superiority of the directional bat algorithm.     

Modified non-dominated sorting genetic algorithm III with fine final level selection

Dominance resistance is a challenge for Pareto-based multi-objective evolutionary algorithms to solve the high-dimensional optimization problems. The Non-dominated Sorting Genetic Algorithm III (NSGA-III) still has such disadvantage even though it is recognized as an algorithm with good performance for many-objective problems. Thus, a variation of NSGA-III algorithm based on fine final level selection is proposed to improve convergence. The fine final level selection is designed in this way. The θ-dominance relation is used to sort the solutions in the critical layer firstly. Then I_SDE index and favor convergence are employed to evaluate convergence of individuals for different situations. And some better solutions are selected finally. The effectiveness of our proposed algorithm is validated by comparing with nine state-of-the-art algorithms on the Deb-Thiele-Laumanns-Zitzler and Walking-Fish-Group test suits. And the optimization objectives are varying from 3 to 15. The performance is evaluated by the inverted generational distance (IGD), hypervolume (HV), generational distance (GD). The simulation results show that the proposed algorithm has an average improvement of 55.4%, 60.0%, 63.1% of 65 test instances for IGD, HV, GD indexes over the original NSGA-III algorithm. Besides, the proposed algorithm obtains the best performance by comparing 9 state-of-art algorithms in HV, GD indexes and ranks third for IGD indicator. Therefore, the proposed algorithm can achieve the advantages over the benchmarks.

     

Finite-time consensus for multi-agent networks with unknown inherent nonlinear dynamics

The objective of this paper is to analyze the finite-time convergence of a nonlinear but continuous consensus algorithm for multi-agent networks with unknown inherent nonlinear dynamics. Due to the existence of the unknown inherent nonlinear dynamics, the stability analysis and the finite-time convergence analysis are more challenging than those under the well-studied consensus algorithms for known linear systems. For this purpose, we propose a novel comparison based tool. By using this tool, it is shown that the proposed nonlinear consensus algorithm can guarantee finite-time convergence if the directed switching interaction graph has a directed spanning tree at each time interval. Specifically, the finite-time convergence is shown by comparing the closed-loop system under the proposed consensus algorithm with some well-designed closed-loop system whose stability properties are easier to obtain. Moreover, the stability and the finite-time convergence of the closed-loop system using the proposed consensus algorithm under a (general) directed switching interaction graph can even be guaranteed by the stability and the finite-time convergence of some well-designed nonlinear closed-loop system under some special directed switching interaction graph. This provides a stimulating example for the potential applications of the proposed comparison based tool in the stability analysis of linear/nonlinear closed-loop systems by making use of known results in linear/nonlinear systems.     

Community detection from biological and social networks: A comparative analysis of metaheuristic algorithms

In order to analyze complex networks to find significant communities, several methods have been proposed in the literature. Modularity optimization is an interesting and valuable approach for detection of network communities in complex networks. Due to characteristics of the problem dealt with in this study, the exact solution methods consume much more time. Therefore, we propose six metaheuristic optimization algorithms, which each contain a modularity optimization approach. These algorithms are the original Bat Algorithm (BA), Gravitational Search Algorithm (GSA), modified Big Bang–Big Crunch algorithm (BB-BC), improved Bat Algorithm based on the Differential Evolutionary algorithm (BADE), effective Hyperheuristic Differential Search Algorithm (HDSA) and Scatter Search algorithm based on the Genetic Algorithm (SSGA). Four of these algorithms (HDSA, BADE, SSGA, BB-BC) contain new methods, whereas the remaining two algorithms (BA and GSA) use original methods. To clearly demonstrate the performance of the proposed algorithms when solving the problems, experimental studies were conducted using nine real-world complex networks − five of which are social networks and the rest of which are biological networks. The algorithms were compared in terms of statistical significance. According to the obtained test results, the HDSA proposed in this study is more efficient and competitive than the other algorithms that were tested.     

基于自适应多普勒及动态邻域的改进BA算法

蝙蝠算法（Bat Algorithm,BA）是一类新型元启发式算法,针对其在算法后期寻优精度降低、易陷入局部极值的不足,提出一种具有自适应多普勒策略及动态邻域策略的改进算法。根据蝙蝠个体在捕食过程中与猎物间存在的相对运动现象,引入自适应多普勒策略改进频率参数,增强算法全局探索的寻优能力。将动态邻域策略与BA算法有机结合,增加蝙蝠个体寻优结构的多样性,改善算法易陷入局部最优的不足。从理论上分析了改进后算法的收敛性和运算复杂性。在数值实验部分对改进后的算法进行了性能及应用测试：对10个经典标准测试函数在不同维度下进行对比实验,将其应用于求解螺旋压缩弹簧优化设计问题,并与其他算法进行了对比分析。实验结果证明了具有自适应多普勒策略及动态邻域策略的改进算法具有更优的收敛速度、收敛精度以及稳定鲁棒性。     

天牛须遗传杂交算法的研究与应用

为加强自适应遗传算法在高压选择下的全局搜索能力,提出了一种结合天牛须搜索的杂交算法。利用天牛须搜索算子对遗传算法产生的新个体进行局部改良,以增强导向作用和局部搜索能力。采用数据驱动策略改善算法杂交引起的复杂度问题,对不同维度变量进行基于目标函数的灵敏度分析,优化其进化路径从而达到提高算法运行效率的目的。通过定量实验研究算法在桁架尺寸优化问题上的应用效果,并定性分析数据背后的原因展示算法的优点和特点。研究结果表明：在桁架结构尺寸优化研究中,用钢量最低的经济效益方案为2 490.56?kg,与现有元启发式算法研究结果吻合,证实了算法的准确性及有效性;40 000个经济效益方案用钢量平均值为2 491.43 kg,标准差为8.05,收敛率达到98%,与其他元启发式算法相比证实了该算法较高的稳定性。     

Non-negative Matrix Factorization with Symmetric Manifold Regularization

Non-negative matrix factorization (NMF) is becoming an important tool for information retrieval and pattern recognition. However, in the applications of image decomposition, it is not enough to discover the intrinsic geometrical structure of the observation samples by only considering the similarity of different images. In this paper, symmetric manifold regularized objective functions are proposed to develop NMF based learning algorithms (called SMNMF), which explore both the global and local features of the manifold structures for image clustering and at the same time improve the convergence of the graph regularized NMF algorithms. For different initializations, simulations are utilized to confirm the theoretical results obtained in the convergence analysis of the new algorithms. Experimental results on COIL20, ORL, and JAFFE data sets demonstrate the clustering effectiveness of the proposed algorithms by comparing with the state-of-the-art algorithms.

     

On finite-time and fixed-time consensus algorithms for dynamic networks switching among disconnected digraphs

ABSTRACT

This paper aims to analyse the stability of a class of consensus algorithms with finite-time or fixed-time convergence for dynamic networks composed of agents with first-order dynamics. In particular, in the analysed class a single evaluation of a nonlinear function of the consensus error is performed per each node. The classical assumption of switching among connected graphs is dropped here, allowing to represent failures and intermittency in the communications between agents. Thus, conditions to guarantee finite and fixed-time convergence, even while switching among disconnected graphs, are provided. Moreover, the algorithms of the considered class are computationally simpler than previously proposed finite-time consensus algorithms for dynamic networks, which is an essential feature in scenarios with computationally limited nodes and energy efficiency requirements such as in sensor networks. Simulations illustrate the performance of the proposed consensus algorithms. In the presented scenarios, results show that the settling time of the considered algorithms grows slower than other consensus algorithms for dynamic networks as the number of nodes increases.     

加速收敛的粒子群优化算法

在基本粒子群优化算法的理论分析的基础上,提出一种加速收敛的粒子群优化算法,并从理论上证明了该算法的快速收敛性,同时对该算法中的参数进行了优化.为了防止其在快速收敛的同时陷入局部最优,采用依赖部分最差粒子信息的变异操作.最后通过与其他几种经典粒子群优化算法的性能比较,表明了该算法的高效和稳健,且明显优于现有的几种经典的粒子群算法.     

Harmonized salp chain-built optimization

As an optimization paradigm, Salp Swarm Algorithm (SSA) outperforms various population-based optimizers in the perspective of the accuracy of obtained solutions and convergence rate. However, SSA gets stuck into sub-optimal solutions and degrades accuracy while solving the complex optimization problems. To relieve these shortcomings, a modified version of the SSA is proposed in the present work, which tries to establish a more stable equilibrium between the exploration and exploitation cores. This method utilizes two different strategies called opposition-based learning and levy-flight (LVF) search. The algorithm is named m-SSA, and its validation is performed on a well-known set of 23 classical benchmark problems. To observe the strength of the proposed method on the scalability of the test problems, the dimension of these problems is varied from 50 to 1000. Furthermore, the proposed m-SSA is also used to solve some real engineering optimization problems. The analysis of results through various statistical measures, convergence rate, and statistical analysis ensures the effectiveness of the proposed strategies integrated with the m-SSA. The comparison of the m-SSA with the conventional SSA, variants of SSA and some other state-of-the-art algorithms illustrate its enhanced search efficiency.

     

基于置信优势关系粗糙集的近似集动态更新方法

置信优势关系粗糙集是处理不完备有序信息的重要模型, 上、下近似集的计算是核心内容之一. 在实际应用中, 属性集通常会发生变化. 根据属性集的增加或减少, 首先讨论置信优势类及劣势类变化情况, 随之给出上、下近似集增量式的变化规律, 提出相应的近似集动态更新方法. 通过Matlab 在UCI 数据集上的实验结果表明, 与非增量式方法相比, 所提出的置信优势关系粗糙集下的上、下近似集的增量式更新方法可行、高效.

     

Distributed Resource Allocation via Accelerated Saddle Point Dynamics

In this paper, accelerated saddle point dynamics is proposed for distributed resource allocation over a multi-agent network, which enables a hyper-exponential convergence rate. Specifically, an inertial fast-slow dynamical system with vanishing damping is introduced, based on which the distributed saddle point algorithm is designed. The dual variables are updated in two time scales, i.e., the fast manifold and the slow manifold. In the fast manifold, the consensus of the Lagrangian multipliers and the tracking of the constraints are pursued by the consensus protocol. In the slow manifold, the updating of the Lagrangian multipliers is accelerated by inertial terms. Hyper-exponential stability is defined to characterize a faster convergence of our proposed algorithm in comparison with conventional primal-dual algorithms for distributed resource allocation. The simulation of the application in the energy dispatch problem verifies the result, which demonstrates the fast convergence of the proposed saddle point dynamics.      

A novel hybrid approach for feature selection in software product lines

Software Product Line (SPL) customizes software by combining various existing features of the software with multiple variants. The main challenge is selecting valid features considering the constraints of the feature model. To solve this challenge, a hybrid approach is proposed to optimize the feature selection problem in software product lines. The Hybrid approach ‘Hyper-PSOBBO’ is a combination of Particle Swarm Optimization (PSO), Biogeography-Based Optimization (BBO) and hyper-heuristic algorithms. The proposed algorithm has been compared with Bird Swarm Algorithm (BSA), PSO, BBO, Firefly, Genetic Algorithm (GA) and Hyper-heuristic. All these algorithms are performed in a set of 10 feature models that vary from a small set of 100 to a high-quality data set of 5000. The detailed empirical analysis in terms of performance has been carried out on these feature models. The results of the study indicate that the performance of the proposed method is higher to other state-of-the-art algorithms.

     

The local discontinuous Galerkin method for 2D nonlinear time-fractional advection–diffusion equations

This paper presents a numerical solution of time-fractional nonlinear advection–diffusion equations (TFADEs) based on the local discontinuous Galerkin method. The trapezoidal quadrature scheme (TQS) for the fractional order part of TFADEs is investigated. In TQS, the fractional derivative is replaced by the Volterra integral equation which is computed by the trapezoidal quadrature formula. Then the local discontinuous Galerkin method has been applied for space-discretization in this scheme. Additionally, the stability and convergence analysis of the proposed method has been discussed. Finally some test problems have been investigated to confirm the validity and convergence of the proposed method.

     

基于趋化校正的哈里斯鹰优化算法

针对哈里斯鹰优化（HHO）算法收敛速度慢、易陷入局部最优的缺点,提出了一种改进HHO算法,即基于趋化校正（CC）的哈里斯鹰优化（CC-HHO）算法。首先,通过计算最优解下降率和变化权重来识别收敛曲线的状态;其次,将细菌觅食优化（BFO）算法的CC机制引入局部搜索阶段来提高寻优的精确性;再次,将生物在运动时的能量消耗规律融入逃逸能量因子和跳跃距离的更新过程中,从而更好地平衡算法的探索与开发;然后,对最优解和次优解的不同组合进行精英选择来拓展算法全局搜索的广泛性;最后,当搜索陷入局部最优时,通过对逃逸能量施加扰动来实现强制跳出。通过10个基准函数对改进算法的性能进行测试,结果显示CC-HHO算法对单峰函数的搜索精度比引力搜索算法（GSA）、粒子群优化（PSO）算法、鲸优化算法（WOA）以及另外4种改进的HHO算法提升超过10个数量级;对多峰函数也有超过1个数量级的优势;在保证搜索稳定性平均提升超过10%的前提下,所提算法的收敛速度明显优于上述几种优化算法,收敛趋势更加明显。实验结果表明,CC-HHO算法有效地提高了原算法的搜索效率和鲁棒性。