RBF neural network based on q-Gaussian function in function approximation

To enhance the generalization performance of radial basis function (RBF) neural networks, an RBF neural network based on a q-Gaussian function is proposed. A q-Gaussian function is chosen as the radial basis function of the RBF neural network, and a particle swarm optimization algorithm is employed to select the parameters of the network. The non-extensive entropic index q is encoded in the particle and adjusted adaptively in the evolutionary process of population. Simulation results of the function approximation indicate that an RBF neural network based on q-Gaussian function achieves the best generalization performance.     

RBF neural network based on q-Gaussian function in function approximation

To enhance the generalization performance of radial basis function (RBF) neural networks, an RBF neural network based on a q-Gaussian function is proposed. A q-Gaussian function is chosen as the radial basis function of the RBF neural network, and a particle swarm optimization algorithm is employed to select the parameters of the network. The non-extensive entropic index q is encoded in the particle and adjusted adaptively in the evolutionary process of population. Simulation results of the function approximation indicate that an RBF neural network based on q-Gaussian function achieves the best generalization performance.     

Parameter estimation of q-Gaussian Radial Basis Functions Neural Networks with a Hybrid Algorithm for binary classification

A classification problem is a decision-making task that many researchers have studied. A number of techniques have been proposed to perform binary classification. Neural networks are one of the artificial intelligence techniques that has had the most successful results when applied to this problem. Our proposal is the use of q-Gaussian Radial Basis Function Neural Networks (q-Gaussian RBFNNs). This basis function includes a supplementary degree of freedom in order to adapt the model to the distribution of data. A Hybrid Algorithm (HA) is used to search for a suitable architecture for the q-Gaussian RBFNN. The use of this type of more flexible kernel could greatly improve the discriminative power of RBFNNs. In order to test performance, the RBFNN with the q-Gaussian basis functions is compared to RBFNNs with Gaussian, Cauchy and Inverse Multiquadratic RBFs, and to other recent neural networks approaches. An experimental study is presented on 11 binary-classification datasets taken from the UCI repository. Moreover, aerial imagery taken in mid-May, mid-June and mid-July was used to evaluate the potential of the methodology proposed for discriminating Ridolfia segetum patches (one of the most dominant and harmful weeds in sunflower crops) in two naturally infested fields in southern Spain.     

Generation of cubic power-law for high frequency intra-day returns: Maximum Tsallis entropy framework

A theoretical framework based on the maximum Tsallis entropy is proposed to explain the tail behavior of the intra-day stock returns, providing a rationale for the cubic law behavior for high frequency data. The specification of first two time-dependent moment constraints yields a q-Gaussian distribution for the intra-day stock returns. The value of the parameter q is estimated by minimizing appropriately modified Jensen–Shannon (JS) divergence in Tsallis entropy framework between q-Gaussian distribution and empirical NASDAQ 100 data. The estimated value of q yields the well-known empirically observed cubic law tail behavior of the intra-day stock returns which has been observed for high frequency data sets. To validate the cubic law stylized fact, five more data sets from high frequency NASDAQ 100, S&P 500 and NYSE index have been examined and it is found that the cubic law operates.     

Improving the non-extensive medical image segmentation based on Tsallis entropy

Thresholding techniques for image segmentation is one of the most popular approaches in Computational Vision systems. Recently, M. Albuquerque has proposed a thresholding method (Albuquerque et al. in Pattern Recognit Lett 25:1059–1065, 2004) based on the Tsallis entropy, which is a generalization of the traditional Shannon entropy through the introduction of an entropic parameter q. However, the solution may be very dependent on the q value and the development of an automatic approach to compute a suitable value for q remains also an open problem. In this paper, we propose a generalization of the Tsallis theory in order to improve the non-extensive segmentation method. Specifically, we work out over a suitable property of Tsallis theory, named the pseudo-additive property, which states the formalism to compute the whole entropy from two probability distributions given an unique q value. Our idea is to use the original M. Albuquerque’s algorithm to compute an initial threshold and then update the q value using the ratio of the areas observed in the image histogram for the background and foreground. The proposed technique is less sensitive to the q value and overcomes the M. Albuquerque and k-means algorithms, as we will demonstrate for both ultrasound breast cancer images and synthetic data.     

基于快速自适应差分进化算法的电力系统经济负荷分配

提出一种求解复杂电力系统经济负荷分配问题的快速自适应差分进化算法(FSADE).从矢量运算角度对变异算子进行分析,提出了一种改进的变异算子,大大提高了算法的收敛速率.根据个体的进化过程,引入自学习机制,对个体的变异和交叉概率常数进行自适应地调整,提高了算法的鲁棒性.3个不同规模的算例仿真结果表明,与其他4种典型智能优化算法相比, FSADE具有更好的计算精度和计算速度,是一种求解电力系统经济负荷分配问题的有效方法.     

Multi-objective evolutionary algorithm using problem-specific genetic operators for community detection in networks

Automatic network clustering is an important method for mining the meaningful communities of complex networks. Uncovered communities help to understand the potential system structure and functionality. Many algorithms that use multiple optimization criteria and optimize a population of solutions are difficult to apply to real systems because they suffer a long optimization process. In this paper, in order to accelerate the optimization process and to uncover multiple significant community structures more effectively, a multi-objective evolutionary algorithm is proposed and evaluated using problem-specific genetic mutation and group crossover, and problem-specific initialization. Since crossover operators mainly contribute to performance of genetic algorithms, more problem-specific group crossover operators are introduced and evaluated for intelligent evolution of population. The experiments on both artificial and real-world networks demonstrate that the proposed evolutionary algorithm with problem-specific genetic operations has effective performance on discovering the community structure of networks.

     

Constrained self-adaptive differential evolution based design of robust optimal fixed structure controller

This paper presents a constrained Self-adaptive Differential Evolution (SaDE) algorithm for the design of robust optimal fixed structure controllers with uncertainties and disturbance. Almost all real world optimization problems have constraints which should be satisfied along with the best optimal solution for the problem. In evolutionary algorithms (EAs) the presence of constraints reduces the feasible region and complicates the search process. Therefore, a suitable method to handle the constraints must also be executed. In the SaDE algorithm, four mutation strategies and the control parameter CR are self-adapted. Self-adaptive Penalty (SP) method is introduced into the SaDE algorithm for constraint handling. The performance of SaDE algorithm is demonstrated on the design of robust optimal fixed structure controller of three systems, namely the linearized magnetic levitation system, F-8 aircraft linearized model and a SISO plant. For the comparison purpose, reported results of constrained PSO algorithm and five DE algorithms with different strategies and parameter values are taken into account. Statistical performance in 20 independent runs is considered to compare the performance of algorithms. From the obtained results, it is observed that SaDE algorithm is able to self-adapt the mutation strategy and the crossover rate and hence performs better than the other variants of DE and the constrained PSO algorithm. Better performance of SaDE is achieved by sustained maintenance of diversity throughout the evolutionary process thus producing better individuals consistently. This also aids the algorithm to escape from local optima thereby avoiding premature convergence.     

A neural differential evolution identification approach to nonlinear systems and modelling of shape memory alloy actuator

This paper proposes a hybrid modified differential evolution plus back‐propagation (MDE‐BP) algorithm to optimize the weights of the neural network model. In implementing the proposed training algorithm, the mutation phase of the differential evolution (DE) is modified by combining two mutation strategies rand/1 and best/1 to create trial vectors instead of only using one mutation operator or rand/1 or best/1 as the standard DE. The modification aims to balance the global exploration and local exploitation capacities of the algorithm in order to find potential global optimum solutions. Then the local searching ability of the back‐propagation (BP) algorithm is applied in that region so as to swiftly converge to the optimum solution. The performance and efficiency of the proposed method is tested by identifying some benchmark nonlinear systems and modeling the shape memory alloy actuator. The proposed training algorithm is compared with the other algorithms, such as the traditional DE and BP algorithm. As a result, the proposed method can improve the accuracy of the identification process.     

基于强化学习的适应性微粒群算法

惯性权重足微粒群算法(PSO)的重要参数,它可以甲衡算法的全局和局部搜索能力的关系,改善算法的性能.对此,提出一种基于强化学习的适应性微粒群算法(RPSO).首先将不同惯性权重调整策略视为粒子的行动集合;然后通过计算Q函数值.考察粒子多步进化的效果;进而选择粒_了最优进化策略,动态调整惯性权重,以增强算法寻找全局最优的...     

A grid-enabled asynchronous metamodel-assisted evolutionary algorithm for aerodynamic optimization

A Grid-enabled asynchronous metamodel-assisted evolutionary algorithm is presented and assessed on a number of aerodynamic shape optimization problems. An efficient way of implementing surrogate evaluation models or metamodels (artificial neural networks) in the context of an asynchronous evolutionary algorithm is proposed. The use of metamodels relies on the inexact pre-evaluation technique already successfully applied to synchronous (i.e. generation-based) evolutionary algorithms, which needs to be revisited so as to efficiently cooperate with the asynchronous search method. The so-created asynchronous metamodel-assisted evolutionary algorithm is further enabled for Grid Computing. The Grid deployment of the algorithm relies on three middleware layers: GridWay, Globus Toolkit and Condor. Single- and multi-objective CFD-based designs of isolated airfoils and compressor cascades are handled using the proposed algorithm and the gain in CPU cost is demonstrated.     

The sandpile mutation Genetic Algorithm: an investigation on the working mechanisms of a diversity-oriented and self-organized mutation operator for non-stationary functions

This paper reports the investigation on the sandpile mutation, an unconventional mutation control scheme for binary Genetic Algorithms (GA) inspired by the Self-Organized Criticality (SOC) theory. The operator, which is based on a SOC system known as sandpile, is able to generate mutation rates that, unlike those given by other methods of parameter control, oscillate between low values and very intense mutations events. The distribution of the mutation rates suggests that the algorithm can be an efficient and yet simple and context-independent approach for the optimization of non-stationary fitness functions. This paper studies the mutation scheme of the algorithm and proposes a new strategy that optimizes is performance. The results also demonstrate the advantages of using the fitness distribution of the population for controlling the mutation. An extensive experimental setup compares the sandpile mutation GA (GGA_SM) with two state-of-the-art evolutionary approaches to non-stationary optimization and with the Hypermutation GA, a classical approach to dynamic problems. The results demonstrate that GGA_SM is able to improve the other algorithms in several dynamic environments. Furthermore, the proposed method does not increase the parameter set of traditional GAs. A study of the distribution of the mutation rates shows that the distribution depends on the type of problem and dynamics, meaning that the algorithm is able to self-regulate the mutation. The effects of the operator on the diversity of the population during the run are also investigated. Finally, a study on the effects of the topology of the sandpile mutation on its performance demonstrates that an alternative topology has minor effects on the performance.     

Rr-cr-IJADE: An efficient differential evolution algorithm for multilevel image thresholding

There is a need for a new method of segmentation to improve the efficiency of expert systems that need segmentation. Multilevel thresholding is a widely used technique that uses threshold values for image segmentation. However, from a computational stand point, the search for optimal threshold values presents a challenging task, especially when the number of thresholds is high. To get the optimal threshold values, a meta-heuristic or optimization algorithm is required. Our proposed algorithm is referred to as R_r-cr-IJADE, which is an improved version of R_cr-IJADE. R_r-cr-IJADE uses a newly proposed mutation strategy, “DE/rand-to-rank/1”, to improve the search success rate. The strategy uses the parameter F adaptation, crossover rate repairing, and the direction from a randomly selected individual to a ranking-based leader. The complexity of the proposed algorithm does not increase, compared to its ancestor. The performance of R_r-cr-IJADE, using Otsu's function as the objective function, was evaluated and compared with other state-of-the-art evolutionary algorithms (EAs) and swarm intelligence algorithms (SIs), under both ‘low-level’ and ‘high-level’ experimental sets. Within the ‘low-level’ sets, the number of thresholds varied from 2 to 16, within 20 real images. For the ‘high-level’ sets, the threshold numbers chosen were 24, 32, 40, 48, 56 and 64, within 2 synthetic pseudo images, 7 satellite images, and three real images taken from the set of 20 real images. The proposed R_r-cr-IJADE achieved higher success rates with lower threshold value distortion (TVD) than the other state-of-the-art EA and SI algorithms.     

A bootstrap goodness of fit test for the generalized Pareto distribution

This paper proposes a bootstrap goodness of fit test for the Generalized Pareto distribution (GPd) with shape parameter γ. The proposed test is an intersection–union test which tests separately the cases of γ≥0 and γ<0 and rejects if both cases are rejected. If the test does not reject, then it is known whether the shape parameter γ is either positive or negative. A Monte Carlo simulation experiment was conducted to assess the power of performance of the intersection–union test. The GPd hypothesis was tested on a data set containing Mexico City’s ozone levels. ¹     

Adaptive evolutionary clustering

In many practical applications of clustering, the objects to be clustered evolve over time, and a clustering result is desired at each time step. In such applications, evolutionary clustering typically outperforms traditional static clustering by producing clustering results that reflect long-term trends while being robust to short-term variations. Several evolutionary clustering algorithms have recently been proposed, often by adding a temporal smoothness penalty to the cost function of a static clustering method. In this paper, we introduce a different approach to evolutionary clustering by accurately tracking the time-varying proximities between objects followed by static clustering. We present an evolutionary clustering framework that adaptively estimates the optimal smoothing parameter using shrinkage estimation, a statistical approach that improves a naïve estimate using additional information. The proposed framework can be used to extend a variety of static clustering algorithms, including hierarchical, k-means, and spectral clustering, into evolutionary clustering algorithms. Experiments on synthetic and real data sets indicate that the proposed framework outperforms static clustering and existing evolutionary clustering algorithms in many scenarios.     

A novel method for real parameter optimization based on Gene Expression Programming

Gene Expression Programming (GEP) is a new technique of evolutionary algorithm that implements genome/phoneme representation in computing programs. Due to its power in global search, it is widely applied in symbolic regression. However, little work has been done to apply it to real parameter optimization yet. This paper proposes a real parameter optimization method named Uniform-Constants based GEP (UC-GEP). In UC-GEP, the constant domain directly participates in the evolution. Our research conducted extensive experiments over nine benchmark functions from the IEEE Congress on Evolutionary Computation 2005 and compared the results to three other algorithms namely Meta-Constants based GEP (MC-GEP), Meta-Uniform-Constants based GEP (MUC-GEP), and the Floating Point Genetic Algorithm (FP-GA). For simplicity, all GEP methods adopt a one-tier index gene structure. The results demonstrate the optimal performance of our UC-GEP in solving multimodal problems and show that at least one GEP method outperforms FP-GA on all test functions with higher computational complexity.     

基于一次指数平滑法的自适应差分进化算法

提出一个策略和控制参数自适应的差分进化(ESADE)算法.ESADE算法将指数平滑法和轮盘赌选择法结合到一起,根据先前成功的经验在策略候选池中为每个个体自适应地选择变异策略来匹配进化的不同阶段.在进化过程中,ESADE算法使用柯西分布和正态分布为控制参数产生适当的值,并使用指数平滑法进行自适应.大量的仿真实验结果表明,ESADE算法要优于其他差分进化算法.     

Multiple-attribute group decision-making based on power Bonferroni operators of linguistic q-rung orthopair fuzzy numbers

In this paper, a new conception of linguistic q-rung orthopair fuzzy number (Lq-ROFN) is proposed where the membership and nonmembership of the q-rung orthopair fuzzy numbers ( q-ROFNs) are represented as linguistic variables. Compared with linguistic intuitionistic fuzzy numbers and linguistic Pythagorean fuzzy numbers, the Lq-ROFNs can more fully describe the linguistic assessment information by considering the parameter q to adjust the range of fuzzy information. To deal with the multiple-attribute group decision-making (MAGDM) problems with Lq-ROFNs, we proposed the linguistic score and accuracy functions of the Lq-ROFNs. Further, we introduce and prove the operational rules and the related properties characters of Lq-ROFNs. For aggregating the Lq-ROFN assessment information, some aggregation operators are developed, involving the linguistic q-rung orthopair fuzzy power Bonferroni mean (BM) operator, linguistic q-rung orthopair fuzzy weighted power BM operator, linguistic q-rung orthopair fuzzy power geometric BM (GBM) operator, and linguistic q-rung orthopair fuzzy weighted power GBM operator, and then presents their rational properties and particular cases, which cannot only reduce the influences of some unreasonable data caused by the biased decision-makers, but also can take the interrelationship between any two different attributes into account. Finally, we propose a method to handle the MAGDM under the environment of Lq-ROFNs by using the new proposed operators. Further, several examples are given to show the validity and superiority of the proposed method by comparing with other existing MAGDM methods.     

Some q‐Rung Orthopai Fuzzy Bonferroni Mean Operators and Their Application to Multi‐Attribute Group Decision Making

In the real multi‐attribute group decision making (MAGDM), there will be a mutual relationship between different attributes. As we all know, the Bonferroni mean (BM) operator has the advantage of considering interrelationships between parameters. In addition, in describing uncertain information, the eminent characteristic of q‐rung orthopair fuzzy sets (q‐ROFs) is that the sum of the qth power of the membership degree and the qth power of the degrees of non‐membership is equal to or less than 1, so the space of uncertain information they can describe is broader. In this paper, we combine the BM operator with q‐rung orthopair fuzzy numbers (q‐ROFNs) to propose the q‐rung orthopair fuzzy BM (q‐ROFBM) operator, the q‐rung orthopair fuzzy weighted BM (q‐ROFWBM) operator, the q‐rung orthopair fuzzy geometric BM (q‐ROFGBM) operator, and the q‐rung orthopair fuzzy weighted geometric BM (q‐ROFWGBM) operator, then the MAGDM methods are developed based on these operators. Finally, we use an example to illustrate the MAGDM process of the proposed methods. The proposed methods based on q‐ROFWBM and q‐ROFWGBM operators are very useful to deal with MAGDM problems.     

Supervised adaptive clustering: A hybrid neural network clustering algorithm

A neural network architecture is introduced which implements a supervised clustering algorithm for the classification of feature vectors. The network is selforganising, and is able to adapt to the shape of the underlying pattern distribution as well as detect novel input vectors during training. It is also capable of determining the relative importance of the feature components for classification. The architecture is a hybrid of supervised and unsupervised networks, and combines the strengths of three wellknown architectures: learning vector quantisation, backpro-pagation and adaptive resonance theory. Network performance is compared to that of learning vector quantisation, back-propagation and cascade-correlation. It is found that performance is generally as good as or better than the performance of these other architectures, while training time is considerably shorter. However, the main advantage of the hybrid architecture is its ability to gain insight into the feature pattern space.Nomenclature O _j The output value of thejth unit - I _i Theith component of the input pattern - W _ij The weight of the cluster connection between theith input and thejth unit - B _ij The weight of the shape connection between theith input and thejth unit - N The dimension of the input patterns - v _j The vigilance parameter of thejth unit - v _init The initial vigilance parameter value - v _rate The change in the vigilance parameter value - X _i Theith direction in anN-dimensional coordinate system - T _k The classification tag of thekth unit - C The classification tag of the current input vector - (p) The learning rate at thepth epoch for the cluster weights - p The current epoch - P The total number of epochs - E _k The error associated with thekth unit - The constant learning rate for the shape weights - a _j The age in epochs of thejth unit