Robust solver based on modified particle swarm optimization for improved solution of diffusion transport through containment facilities

Accurate estimation of mass transport parameters is necessary for overall design and evaluation processes of the waste disposal facilities. The mass transport parameters, such as effective diffusion coefficient, retardation factor and diffusion accessible porosity, are estimated from observed diffusion data by inverse analysis. Recently, particle swarm optimization (PSO) algorithm has been used to develop inverse model for estimating these parameters that alleviated existing limitations in the inverse analysis. However, PSO solver yields different solutions in successive runs because of the stochastic nature of the algorithm and also because of the presence of multiple optimum solutions. Thus the estimated mean solution from independent runs is significantly different from the best solution. In this paper, two variants of the PSO algorithms are proposed to improve the performance of the inverse analysis. The proposed algorithms use perturbation equation for the gbest particle to gain information around gbest region on the search space and catfish particles in alternative iterations to improve exploration capabilities. Performance comparison of developed solvers on synthetic test data for two different diffusion problems reveals that one of the proposed solvers, CPPSO, significantly improves overall performance with improved best, worst and mean fitness values. The developed solver is further used to estimate transport parameters from 12 sets of experimentally observed diffusion data obtained from three diffusion problems and compared with published values from the literature. The proposed solver is quick, simple and robust on different diffusion problems.     

Cooperative Velocity Updating model based Particle Swarm Optimization

Particle swarm optimization (PSO) has shown its good performance in many optimization problems. This paper proposes a Cooperative Velocity Updating algorithm based Particle Swarm Optimization (CVUPSO), which is inspired by the competition and cooperation methods of different populations in natural swarm living, such as bees, ants, birds, fish, etc. In this algorithm, before an elite is introduced from other sub-swarms or a new particle is randomly born, the weak particle will be eliminated out of its sub-swarm. In each iteration process, every sub-swarm abandons a least potential particle. The CVUPSO recorded four special positions: pbest, lbest, gbest and lworst. The pbest represents the current particle’s best position while lbest represents the current sub swarm’s best position, and gbest is the best position among the whole swarm, lworst is the position of the particle with the worst performance. A new update method is adopted in CVUPSO, where the particles are more likely to follow lbest than follow gbest in the early stage of iteration, but opposite in the later stage. In this paper, two variants of CVUPSO are proposed, one variant is CVUPSO with Random inertia weight (for short CVUPSO-R), and another is CVUPSO with Exponential decline inertia weight (for short CVUPSO-E). By making comparative experiments on several widely used benchmark functions, analysis results show that the performance of these two improved variants are more promising than the recently developed PSO algorithms for searching multiple peak values of multiple objects optimization problem.     

Rule base reduction for knowledge-based fuzzy controllers with application to a vacuum cleaner

A rule base reduction and tuning algorithm is proposed as a design tool for the knowledge-based fuzzy control of a vacuum cleaner. Given a set of expert-based control rules in a fuzzy rule base structure, proposed algorithm computes the inconsistencies and redundancies in the overall rule set based on a newly proposed measure of equality of the individual fuzzy sets. An inconsistency and redundancy measure is proposed and computed for each rule in the rule base. Then the rules with high inconsistency and redundancy levels are removed from the fuzzy rule base without affecting the overall performance of the controller. The algorithm is successfully tested experimentally for the control of a commercial household vacuum cleaner. Experimental results demonstrate the effective use of the proposed algorithm.     

Association rule mining using binary particle swarm optimization

In this paper, we developed a binary particle swarm optimization (BPSO) based association rule miner. Our BPSO based association rule miner generates the association rules from the transactional database by formulating a combinatorial global optimization problem, without specifying the minimum support and minimum confidence unlike the a priori algorithm. Our algorithm generates the best M rules from the given database, where M is a given number. The quality of the rule is measured by a fitness function defined as the product of support and confidence. The effectiveness of our algorithm is tested on a real life bank dataset from commercial bank in India and three transactional datasets viz. books database, food items dataset and dataset of the general store taken from literature. Based on the results, we infer that our algorithm can be used as an alternative to the a priori algorithm and the FP-growth algorithm.     

Inducing Constructor Systems from Example-Terms by Detecting Syntactical Regularities

We present a technique for inducing functional programs from few, well chosen input/output-examples (I/O-examples). Potential applications for automatic program or algorithm induction are to enable end users to create their own simple programs, to assist professional programmers, or to automatically invent completely new and efficient algorithms. In our approach, functional programs are represented as constructor term rewriting systems (CSs) containing recursive rules. I/O-examples for a target function to be implemented are a set of pairs of terms (F(i_i),o_i) meaning that F(i_i)—denoting application of function F to input i_i—is rewritten to o_i by a CS implementing the function F. Induction is based on detecting syntactic regularities between example terms. In this paper we present theoretical results and describe an algorithm for inducing CSs over arbitrary signatures/data types which consist of one function defined by an arbitrary number of rules with an arbitrary number of non-nested recursive calls in each rule. Moreover, we present empirical results based on a prototypical implementation.     

Evolutionary design of a fuzzy classifier from data

Genetic algorithms show powerful capabilities for automatically designing fuzzy systems from data, but many proposed methods must be subjected to some minimal structure assumptions, such as rule base size. In this paper, we also address the design of fuzzy systems from data. A new evolutionary approach is proposed for deriving a compact fuzzy classification system directly from data without any a priori knowledge or assumptions on the distribution of the data. At the beginning of the algorithm, the fuzzy classifier is empty with no rules in the rule base and no membership functions assigned to fuzzy variables. Then, rules and membership functions are automatically created and optimized in an evolutionary process. To accomplish this, parameters of the variable input spread inference training (VISIT) algorithm are used to code fuzzy systems on the training data set. Therefore, we can derive each individual fuzzy system via the VISIT algorithm, and then search the best one via genetic operations. To evaluate the fuzzy classifier, a fuzzy expert system acts as the fitness function. This fuzzy expert system can effectively evaluate the accuracy and compactness at the same time. In the application section, we consider four benchmark classification problems: the iris data, wine data, Wisconsin breast cancer data, and Pima Indian diabetes data. Comparisons of our method with others in the literature show the effectiveness of the proposed method.     

A faster convergence and concise interpretability TSK fuzzy classifier deep-wide-based integrated learning

Hierarchical TSK fuzzy system was proposed to approach the exponential growth of IF-THEN rules which named “fuzzy rule explosion”. However, it could not get better performance in few layers for instability of TSK fuzzy system, such that hierarchical TSK fuzzy system suffers from bad interpretability and slow convergence along with too much layers. To get a better solution, this study employs a faster convergence and concise interpretability TSK fuzzy classifier deep-wide-based integrated learning (FCCI-TSK) which has a wide structure to adopt several ensemble units learning in a meantime, and the best performer will be picked up to transfer its learning knowledge to next layer with the help of stacked generalization principle. The ensemble units are integrated by negative correlation learning (NCL). FCCI-TSK adjusts the input of the next layer with a better guidance such that it can quicken the speed of convergence and reduce the number of layers. Besides, leading with guidance, it can achieve higher accuracy and better interpretability with more simple structure. The contributions of this study include: (1) To enhance the performance of fuzzy classifier, we mix NCL and stacked generalization principle together in FCCI-TSK; (2) To overcome the phenomenon of “fuzzy rule explosion”, we adopt deep-wide integrated learning and information discarding to accelerate convergence and obtain concise interpretability in the meantime. Comparing with other 11 algorithms, the results on twelve UCI datasets show that FCCI-TSK has the best performance overall and the convergence of FCCI-TSK is also examined.     

MULTITUNING FUZZY CONTROL SYSTEMS DESIGN

A multituning fuzzy control system structure that involves two simple, but effective tuning mechanisms, is proposed: one is called fuzzy control rule tuning mechanism (FCRTM); the other is called dynamic scalar tuning mechanism (DSTM). In FCRTM, it is used to generate the necessary control rules with a center extension method. In DSTM, it contains three fuzzy IF-THEN rules for determining the appropriate scaling factors for the fuzzy control system. In this paper, a method based on the genetic algorithm (GA) is proposed to simultaneously choose the appropriate parameters in FCRTM and DSTM. That is, the proposed GA-based method can automatically generate the required rule base of fuzzy controller and efficiently determine the appropriate map for building the dynamic scalars of fuzzy controller. A multiobjective fitness function is proposed to determine an appropriate parameter set such that not only the selected fuzzy control structure has fewer fuzzy rules, but also the controlled system has a good control performance. Finally, an inverted pendulum control problem is given to illustrate the effectiveness of the proposed control scheme.     

FINDING SIMPLIFIED FUZZY IF-THEN RULES FOR FUNCTION APPROXIMATION PROBLEMS USING A FUZZY DATA MINING APPROACH

ABSTRACT

A fuzzy if-then rule whose consequent part is a real number is referred to as a simplified fuzzy rule. Since no defuzzification is required for this rule type, it has been widely used in function approximation problems. Furthermore, data mining can be used to discover useful information by exploring and analyzing data. Therefore, this paper proposes a fuzzy data mining approach to discover simplified fuzzy if-then rules from numerical data in order to approximate an unknown mapping from input to output. Since several pre-specified parameters for deriving fuzzy rules are not easily specified, they are automatically determined by the genetic algorithm with binary chromosomes. To evaluate performance of the proposed method, computer simulations are performed on various numerical data sets, showing that the fitting ability and the generalization ability of the proposed method are comparable to the known fuzzy rule-based methods.     

一种基于模糊分类的模糊神经网络辨识方法

针对非线性辨识问题,基于改进的T-S模型,提出一种自适应模糊神经网络模型(AFNN)。首先,基于模糊竞争学习算法确定系统的模糊空间和模糊规则数,并得出每个样本对每条规则的适用程度。其次,利用卡尔曼滤波算法在线辨识AFNN的后件参数。AFNN具有结构简洁,逼近能力强,能够显著提高辨识精度,并且辨识的模糊模型简单有效。最后,将该AFNN用于非线性系统的模糊辨识,仿真结果验证了该方法的有效性。     

Robust algorithms that locate local extrema of a function of one variable from interval measurement results: A remark

The problem of locating local maxima and minima of a function from approximate measurement results is vital for many physical applications: inspectral analysis, chemical species are identified by locating local maxima of the spectra; inradioastronomy, sources of celestial radio emission, and their subcomponents, are identified by locating local maxima of the measured brightness of the radio sky;elementary particles are identified by locating local maxima of the experimental curves. Since measurements are never absolutely precise, as a result of the measurements, we have aclass of possible functions. If we measuref(x _i ) with interval uncertainty, this class consists of all functionsf for whichf(x _i ) ε [y _i ??, y _i +?], wherey _i are the results of measuringf(x _i ), andε is the measurement accuracy. For this class, in [2], a linear-time algorithm was described. In real life, a measuring instrument can sometimes malfunction, leading to the so-calledoutliers, i.e., measurementsy _i that can be way offf(x _i ) (and thus do not restrict the actual valuesf(x _i ) at all). In this paper, we describerobust algorithms, i.e., algorithms that find the number of local extrema in the presence of possible outliers. These algorithms solve an important practical problem, but they are not based on any new mathematical results: they simply use algorithms from [2] and [3].     

A genetic approach to the design of autonomous agents for futures trading

We propose a genetic algorithm-based method for designing an autonomous trader agent. The task of the proposed method is to find an optimal set of fuzzy if–then rules that best represents the behavior of a target trader agent. A highly profitable trader agent is used as the target in the proposed genetic algorithm. A trading history for the target agent is obtained from a series of futures trading. The antecedent part of fuzzy if–then rules considers time-series data of spot prices, while the consequent part indicates the order of trade (Buy, Sell, or No action) with its degree of certainty. The proposed method determines the antecedent part of fuzzy if–then rules. The consequent part of fuzzy if–then rules is automatically determined from the trading history of the target trader agent. The autonomous trader agent designed by the proposed genetic algorithm consists of a fixed number of fuzzy if–then rules. The decision of the autonomous trader agent is made by fuzzy inference from the time-series data of spot prices. This work was presented in part at the 11th International Symposium on Artificial Life and Robotics, Oita, Japan, January 23–25, 2006     

Mining the fuzzy control rules of aeration in a Submerged Biofilm Wastewater Treatment Process

This paper presents a special rule base extraction analysis for optimal design of an integrated neural-fuzzy process controller using an “impact assessment approach.” It sheds light on how to avoid some unreasonable fuzzy control rules by screening inappropriate fuzzy operators and reducing over fitting issues simultaneously when tuning parameter values for these prescribed fuzzy control rules. To mitigate the design efforts, the self-learning ability embedded in the neural networks model was emphasized for improving the rule extraction performance. An aeration unit in an Aerated Submerged Biofilm Wastewater Treatment Process (ASBWTP) was picked up to support the derivation of a solid fuzzy control rule base. Four different fuzzy operators were compared against one other in terms of their actual performance of automated knowledge acquisition in the system based on a partial or full rule base prescribed. Research findings suggest that using bounded difference fuzzy operator (O_b) in connection with back propagation neural networks (BPN) algorithm would be the best choice to build up this feedforward fuzzy controller design.     

Unsupervised classification of polarimetric SAR image with dynamic clustering: An image processing approach

This paper proposes a new unsupervised classification approach for automatic analysis of polarimetric synthetic aperture radar (SAR) image. Classification of the information in multi-dimensional polarimetric SAR data space by dynamic clustering is addressed as an optimization problem and two recently proposed techniques based on particle swarm optimization (PSO) are applied to find optimal (number of) clusters in a given input data space, distance metric and a proper validity index function. The first technique, so-called multi-dimensional (MD) PSO, re-forms the native structure of swarm particles in such a way that they can make inter-dimensional passes with a dedicated dimensional PSO process. Therefore, in a multi-dimensional search space where the optimum dimension is unknown, swarm particles can seek both positional and dimensional optima. Nevertheless, MD PSO is still susceptible to premature convergence due to lack of divergence. To address this problem, fractional global best formation (FGBF) technique is then presented, which basically collects all promising dimensional components and fractionally creates an artificial global-best particle (aGB) that has the potential to be a better “guide” than the PSO’s native gbest particle. In this study, the proposed dynamic clustering process based on MD-PSO and FGBF techniques is applied to automatically classify the color-coded representations of the polarimetric SAR information (i.e. the type of scattering, backscattering power) extracted by means of the Pauli or the Cloude–Pottier decomposition algorithms. The performance of the proposed method is evaluated based on fully polarimetric SAR data of the San Francisco Bay acquired by the NASA/Jet Propulsion Laboratory Airborne SAR (AIRSAR) at L-band. The proposed unsupervised technique determines the number of classes within polarimetric SAR image for optimal classification performance while preserving spatial resolution and textural information in the classified results. Additionally, it is possible to further apply the proposed dynamic clustering technique to higher dimensional (N-D) feature spaces of fully polarimetric SAR data.     

Hoeffding bound based evolutionary algorithm for symbolic regression

In symbolic regression area, it is difficult for evolutionary algorithms to construct a regression model when the number of sample points is very large. Much time will be spent in calculating the fitness of the individuals and in selecting the best individuals within the population. Hoeffding bound is a probability bound for sums of independent random variables. As a statistical result, it can be used to exactly decide how many samples are necessary for choosing i individuals from a population in evolutionary algorithms without calculating the fitness completely. This paper presents a Hoeffding bound based evolutionary algorithm (HEA) for regression or approximation problems when the number of the given learning samples is very large. In HEA, the original fitness function is used in every k generations to update the approximate fitness obtained by Hoeffding bound. The parameter 1?δ is the probability of correctly selecting i best individuals from population P, which can be tuned to avoid an unstable evolution process caused by a large discrepancy between the approximate model and the original fitness function. The major advantage of the proposed HEA algorithm is that it can guarantee that the solution discovered has performance matching what would be discovered with a traditional genetic programming (GP) selection operator with a determinate probability and the running time can be reduced largely. We examine the performance of the proposed algorithm with several regression problems and the results indicate that with the similar accuracy, the HEA algorithm can find the solution more efficiently than tradition EA. It is very useful for regression problems with large number of training samples.     

Evolving Compact and Interpretable Takagi–Sugeno Fuzzy Models With a New Encoding Scheme

Developing Takagi–Sugeno fuzzy models by evolutionary algorithms mainly requires three factors: an encoding scheme, an evaluation method, and appropriate evolutionary operations. At the same time, these three factors should be designed so that they can consider three important aspects of fuzzy modeling: modeling accuracy, compactness, and interpretability. This paper proposes a new evolutionary algorithm that fulfills such requirements and solves fuzzy modeling problems. Two major ideas proposed in this paper lie in a new encoding scheme and a new fitness function, respectively. The proposed encoding scheme consists of three chromosomes, one of which uses unique chained possibilistic representation of rule structure. The proposed encoding scheme can achieve simultaneous optimization of parameters of antecedent membership functions and rule structures with the new fitness function developed in this paper. The proposed fitness function consists of five functions that consider three evaluation criteria in fuzzy modeling problems. The proposed fitness function guides evolutionary search direction so that the proposed algorithm can find more accurate compact fuzzy models with interpretable antecedent membership functions. Several evolutionary operators that are appropriate for the proposed encoding scheme are carefully designed. Simulation results on three modeling problems show that the proposed encoding scheme and the proposed fitness functions are effective in finding accurate, compact, and interpretable Takagi–Sugeno fuzzy models. From the simulation results, it is shown that the proposed algorithm can successfully find fuzzy models that approximate the given unknown function accurately with a compact number of fuzzy rules and membership functions. At the same time, the fuzzy models use interpretable antecedent membership functions, which are helpful in understanding the underlying behavior of the obtained fuzzy models.     

基于模糊分类的模糊神经网络辨识方法及应用

基于改进的T-S模型，提出一种自适应模糊神经网络模型(AFNN)，给出了网络的连接结构和学习算法。基于竞争学习算法的模糊分类器确定系统的模糊空间和模糊规则数，并得出每个样本对每条规则的适用程度。利用卡尔曼滤波算法在线辨识删的后件参数。AFNN结构简洁，逼近能力强，能够显著提高辨识精度，并且在线辨识的模糊模型简单有效。将该AFNN用于非线性系统的模糊辨识和化工过程连续搅拌反应器(CSTR)的建模中，仿真结果验证了该方法的有效性，表明该网络能够实现复杂非线性系统的建模，而且建模精度高、收敛速度快。可当作复杂系统建模的一种有效手段。     

Evolving compact and interpretable Takagi-Sugeno fuzzy models with a new encoding scheme.

Developing Takagi-Sugeno fuzzy models by evolutionary algorithms mainly requires three factors: an encoding scheme, an evaluation method, and appropriate evolutionary operations. At the same time, these three factors should be designed so that they can consider three important aspects of fuzzy modeling: modeling accuracy, compactness, and interpretability. This paper proposes a new evolutionary algorithm that fulfills such requirements and solves fuzzy modeling problems. Two major ideas proposed in this paper lie in a new encoding scheme and a new fitness function, respectively. The proposed encoding scheme consists of three chromosomes, one of which uses unique chained possibilistic representation of rule structure. The proposed encoding scheme can achieve simultaneous optimization of parameters of antecedent membership functions and rule structures with the new fitness function developed in this paper. The proposed fitness function consists of five functions that consider three evaluation criteria in fuzzy modeling problems. The proposed fitness function guides evolutionary search direction so that the proposed algorithm can find more accurate compact fuzzy models with interpretable antecedent membership functions. Several evolutionary operators that are appropriate for the proposed encoding scheme are carefully designed. Simulation results on three modeling problems show that the proposed encoding scheme and the proposed fitness functions are effective in finding accurate, compact, and interpretable Takagi-Sugeno fuzzy models. From the simulation results, it is shown that the proposed algorithm can successfully find fuzzy models that approximate the given unknown function accurately with a compact number of fuzzy rules and membership functions. At the same time, the fuzzy models use interpretable antecedent membership functions, which are helpful in understanding the underlying behavior of the obtained fuzzy models.     

Hierarchical Cluster-Based Multispecies Particle-Swarm Optimization for Fuzzy-System Optimization

This paper proposes a hierarchical cluster-based multispecies particle-swarm optimization (HCMSPSO) algorithm for fuzzy-system optimization. The objective of this paper is to learn Takagi–Sugeno–Kang (TSK) type fuzzy rules with high accuracy. In the HCMSPSO-designed fuzzy system (FS), each rule defines its own fuzzy sets, which implies that the number of fuzzy sets for each input variable is equal to the number of fuzzy rules. A swarm in HCMSPSO is clustered into multiple species at an upper hierarchical level, and each species is further clustered into multiple subspecies at a lower hierarchical level. For an FS consisting of $r$ rules, $r$ species (swarms) are formed in the upper level, where one species optimizes a single fuzzy rule. Initially, there are no species in HCMSPSO. An online cluster-based algorithm is proposed to generate new species (fuzzy rules) automatically. In the lower layer, subspecies within the same species are formed adaptively in each iteration during the particle update. Several simulations are conducted to verify HCMSPSO performance. Comparisons with other neural learning, genetic, and PSO algorithms demonstrate the superiority of HCMSPSO performance.