Unsatisfying functions and multiobjective fuzzy satisfaction design using genetic algorithms

This paper describes a new fuzzy satisfaction method using genetic algorithms (GA) for multiobjective problems. First, an unsatisfying function, which has a one-to-one correspondence with the membership function, is introduced for expressing "fuzziness". Next, the multiobjective design problem is transformed into a satisfaction problem of constraints by introducing an aspiration level for each objective. Here, in order to handle the fuzziness involved in aspiration levels and constraints, the unsatisfying function is used, and the problem is formulated as a multiobjective minimization problem of unsatisfaction ratings. Then, a GA is employed to solve the problem, and a new strategy is proposed to obtain a group of Pareto-optimal solutions in which the decision maker (DM) is interested. The DM can then seek a satisfaction solution by modifying parameters interactively according to preferences.     

Fuzzy rule interpolation based on principle membership functions and uncertainty grade functions of interval type-2 fuzzy sets

Fuzzy rule interpolation is an important research topic in sparse fuzzy rule-based systems. In this paper, we present a new method for dealing with fuzzy rule interpolation in sparse fuzzy rule-based systems based on the principle membership functions and uncertainty grade functions of interval type-2 fuzzy sets. The proposed method deals with fuzzy rule interpolation based on the principle membership functions and the uncertainty grade functions of interval type-2 fuzzy sets. It can deal with fuzzy rule interpolation with polygonal interval type-2 fuzzy sets and can handle fuzzy rule interpolation with multiple antecedent variables. We also use some examples to compare the fuzzy interpolative reasoning results of the proposed method with the ones of an existing method. The experimental result shows that the proposed method gets more reasonable results than the existing method for fuzzy rule interpolation based on interval type-2 fuzzy sets.     

Controller design for time-delay systems using genetic algorithms

This paper presents a new approach to design controllers for time-delay systems by using genetic algorithms (GAs) together with the solvability of linear matrix inequalities (LMIs). Both of the state-feedback controller and the static output feedback controller can be designed with this approach. It is confirmed by numerical examples that this approach achieves less conservative results than previously existing methods on the given examples.     

Fuzzy classifier design using genetic algorithms

A new method for design of a fuzzy-rule-based classifier using genetic algorithms (GAs) is discussed. The optimal parameters of the fuzzy classifier including fuzzy membership functions and the size and structure of fuzzy rules are extracted from the training data using GAs. This is done by introducing new representation schemes for fuzzy membership functions and fuzzy rules. An effectiveness measure for fuzzy rules is developed that allows for systematic addition or deletion of rules during the GA optimization process. A clustering method is utilized for generating new rules to be added when additions are required. The performance of the classifier is tested on two real-world databases (Iris and Wine) and a simulated Gaussian database. The results indicate that highly accurate classifiers could be designed with relatively few fuzzy rules. The performance is also compared to other fuzzy classifiers tested on the same databases.     

Fitting optimal piecewise linear functions using genetic algorithms

Constructing a model for data in R² is a common problem in many scientific fields, including pattern recognition, computer vision, and applied mathematics. Often little is known about the process which generated the data or its statistical properties. For example, in fitting a piecewise linear model, the number of pieces, as well as the knot locations, may be unknown. Hence, the method used to build the statistical model should have few assumptions, yet, still provide a model that is optimal in some sense. Such methods can be designed through the use of genetic algorithms. We examine the use of genetic algorithms to fit piecewise linear functions to data in R². The number of pieces, the location of the knots, and the underlying distribution of the data are assumed to be unknown. We discuss existing methods which attempt to solve this problem and introduce a new method which employs genetic algorithms to optimize the number and location of the pieces. Experimental results are presented which demonstrate the performance of our method and compare it to the performance of several existing methods, We conclude that our method represents a valuable tool for fitting both robust and nonrobust piecewise linear functions     

Extracting linguistic rules from data sets using fuzzy logic and genetic algorithms

Linguistic rules in natural language are useful and consistent with human way of thinking. They are very important in multi-criteria decision making due to their interpretability. In this paper, our discussions concentrate on extracting linguistic rules from data sets. In the end, we firstly analyze how to extract complex linguistic data summaries based on fuzzy logic. Then, we formalize linguistic rules based on complex linguistic data summaries, in which, the degree of confidence of linguistic rules from a data set can be explained by linguistic quantifiers and its linguistic truth from the fuzzy logical point of view. In order to obtain a linguistic rule with a higher degree of linguistic truth, a genetic algorithm is used to optimize the number and parameters of membership functions of linguistic values. Computational results show that the proposed method is an alternative method for extracting linguistic rules with linguistic truth from data sets.     

Optimal residual design for fault diagnosis using multi-objective optimization and genetic algorithms

This paper develops a new approach to the design of optimal residuals in order to diagnose incipient faults based on multi-objective optimization and genetic algorithms. In this approach the residual is generated via an observer. To reduce false and missed alarm rates in fault diagnosis, a number of performance indices are introduced into the observer design. Some performance indices are expressed in the frequency domain to take account of the frequency distributions of faults, noise and modelling uncertainties. All objectives then are reformulated into a set of inequality constraints on performance indices. A genetic algorithm is thus used to search for an optimal solution to satisfy these inequality constraints on performance indices. The approach developed is applied to a flight control system example, and simulation results show that incipient sensor faults can be detected reliably in the presence of modelling uncertainty.     

Expert-driven genetic algorithms for simulating evaluation functions

In this paper we demonstrate how genetic algorithms can be used to reverse engineer an evaluation function’s parameters for computer chess. Our results show that using an appropriate expert (or mentor), we can evolve a program that is on par with top tournament-playing chess programs, outperforming a two-time World Computer Chess Champion. This performance gain is achieved by evolving a program that mimics the behavior of a superior expert. The resulting evaluation function of the evolved program consists of a much smaller number of parameters than the expert’s. The extended experimental results provided in this paper include a report on our successful participation in the 2008 World Computer Chess Championship. In principle, our expert-driven approach could be used in a wide range of problems for which appropriate experts are available.     

New membership functions for effective design and implementation offuzzy systems

The paper proposes new membership functions (mfs) for fuzzy modeling. Existing mfs do not simultaneously satisfy ease in optimization and low-end hardware implementation. The proposed mfs satisfy the two contradicting requirements. The algorithm for hardware implementation is detailed. The performance and applicability of the proposed mfs are illustrated using two well-known benchmarks. Optimized fuzzy models are coded and implemented using the Intel 8XC196KC microcontroller. Results show that the proposed mfs simplify offline design and facilitate online implementation     

Study of one class of membership functions of fuzzy sets

A class of everywhere smooth membership functions of fuzzy sets based on the idea of spline functions is proposed. Formulas connecting the parameters of the membership functions and the coefficients defining the values of the membership functions are given. The solution of the problem of the membership function interpolation is presented.     

Modelling air pollution time-series by using wavelet functions and genetic algorithms

This paper proposes a novel approach based on the use of wavelet functions to model air pollution time series. One peculiarity of the approach is that of combining the use of wavelets and genetic algorithms to search for the best wavelet parameters. A case study, referring to the modelling of daily averages of SO₂ time series recorded in the industrial area of Syracuse (Italy) is reported in order to compare the performance of a wavelet-based prediction model and a Multi-layer perceptron neural model. The results obtained show that there are no significant differences between the neural and the wavelet approach in terms of model performance and computational effort. There is however an appreciable advantage in using the proposed wavelet-based technique in terms of model readability.The paper has been financially supported by the EU in the framework of the APPETISE project (Contract N. IST-99–11764). The author is also grateful to the Municipal and Provincial authorities in Syracuse (Italy) for providing the pollution and meteorological data considered in the paper. Finally the author is grateful to Dr Libero Bertucco who helped to code part of the software package considered in this work.     

Comparing networks with differing neural-node functions using transputer-based genetic algorithms

Different neural net node computational functions are compared using feedforward backpropagation networks. Three node types are examined: the standard model, ellipsoidal nodes and quadratic nodes. After preliminary experiments on simple small problems, in which quadratic nodes performed very well, networks of differing nodes types are applied to the speech recognition 104 speaker E-task using a fixed architecture. Ellipsoidal nodes were found to work well, but not as well as the standard model. Quadratic nodes did not perform well on the larger task. To facilitate an architecture independent comparison a transputer-based genetic algorithm is then used to compare ellipsoidal and mixed ellipsoidal and standard networks with the standard model. These experiments confirmed the earlier conclusion that ellipsoidal networks could not compare favourably with the standard model on the 104 speaker E-task. In an evolutionary search in which layer node types were free to adjust ellipsoidal nodes had a tendency to become extinct or barely survive. If the presence of ellipsoidal nodes was enforced then the resulting networks again performed poorly when compared with the standard model.     

On modeling genetic algorithms for functions of unitation

We discuss a novel model for analyzing the working of Genetic Algorithms (GAs), when the objective function is a function of unitation. The model is exact (not approximate), and is valid for infinite populations. Functions of unitation depend only on the number of 1's in any string. Hence, we only need to model the variations in the distribution of strings with respect to the number of 1's in the strings. We introduce the notion of a Binomial Distributed Population (BDP) as the building block of our model, and we show that the effect of uniform crossover on BDPs is to generate two other BDPs. We demonstrate that a population with any general distribution may be decomposed into several BDPs. We also show that a general multipoint crossover may be considered as a composition of several uniform crossovers. Based on these results, the effects of mutation and crossover on the distribution of strings have been characterized, and the model has been defined. GASIM-a Genetic Algorithm Simulator for functions of unitation-has been implemented based on the model, and the exactness of the results obtained from GASIM has been verified using actual Genetic Algorithm runs. The time complexity of the GA simulator derived from the model is O(l(3)) (where l is the string length), a significant improvement over previous models with exponential time complexities.     

Holder functions and deception of genetic algorithms

We present a deception analysis for Holder functions. Our approach uses a decomposition on the Haar basis, which reflects in a natural way the Holder structure of the function. This allows the relation of the deception, the Holder exponent, and some parameters of the genetic algorithms (GAs). These results prove that deception is connected to the irregularity of the fitness function and shed a new light on the schema theory. In addition, this analysis may assist in understanding the influence of some of the parameters on the performance of a GA     

Intrinsic evolvable hardware platform for digital circuit design and repair using genetic algorithms

A hardware/software platform for intrinsic evolvable hardware is designed and evaluated for digital circuit design and repair on Xilinx Field Programmable Gate Arrays (FPGAs). Dynamic bitstream compilation for mutation and crossover operators is achieved by directly manipulating the bitstream using a layered framework. Experimental results on a case study have shown that benchmark circuit evolution from an unseeded initial population, as well as a complete recovery of a stuck-at fault is achievable using this platform. An average of 0.47 μs is required to perform the genetic mutation, 4.2 μs to perform the single point conventional crossover, 3.1 μs to perform Partial Match Crossover (PMX) as well as Order Crossover (OX), 2.8 μs to perform Cycle Crossover (CX), and 1.1 ms for one input pattern intrinsic evaluation. These represent a performance advantage of three orders of magnitude over the JBITS software framework and more than seven orders of magnitude over the Xilinx design tool driven flow for realizing intrinsic genetic operators on Xilinx Virtex Family devices.     

基于遗传算法的模糊隶属函数的选择

确定合适的隶属函数对模糊控制效果有重要影响,是应用模糊控制的基础,也是难点之一。作者应用遗传算法对模糊温度传感器信号处理过程中的隶属函数进行选择,阐述了基本原理和具体实施过程,最后用一具体的实例来说明该优化算法在模糊隶属函数选择中的应用。结果表明：该方法简单实用,具有较为理想的效果。     

Computer-aided pipeline operation using genetic algorithms and rule learning. PART I: Genetic algorithms in pipeline optimization

In this two-paper series, techniques connected with artificial intelligence and genetics are applied to achieve computer-based control of gas pipeline systems. In this, the first paper, genetic algorithms are developed and applied to the solution of two classical pipeline optimization problems, the steady serial line problem, and the single transient line problem. Simply stated, genetic algorithms are canonical search procedures based on the mechanics of natural genetics. They combine a Darwinian survival of the fittest with a structured, yet randomized, information exchange between artificial chromosomes (strings). Despite their reliance on stochastic processes, genetic algorithms are no simple random walk; they carefully and efficiently exploit historic information to guide future trials.In the two pipeline problems, a simple three-operator genetic algorithm consisting of reproduction, crossover, and mutation finds near-optimal performance quickly. In, the steady serial problem, near-optimal performance is found after searching less than 1100 of 1.1(10¹²) alternatives. Similarly, efficient performance is demonstrated in the transient problem.Genetic algorithms are ready for application to more complex engineering optimization problems. They also can serve as a searning mechanism in a larger rule learning procedure. This application is discussed in the sequal.     

Extraction and reuse of design patterns from genetic algorithms using case-based reasoning

In this paper, we propose a case-based reasoning scheme in which we extract domain knowledge (in the form of design patterns) from a genetic algorithm used to optimize combinational logic circuits at the gate level. Such information is used in two ways: first, we show how the selection pressure of the genetic algorithm is biased by Boolean simplification rules that are normally adopted by human designers, including some which are not completely straightforward. Secondly, we reuse some of these design patterns extracted from the evolutionary process to reduce convergence times of a genetic algorithm using previously found solutions as cases to solve similar problems.The second author acknowledges support from CONACyT through project No. 32999-A. The third author acknowledges partial support for this work through CONACyT Project No. I-39324-A.     

Economic design of autoregressive moving average control chart using genetic algorithms

When designing control charts, it is usually assumed that the observations from the process at different time points are independent. However, this assumption may not be true for some production processes, e.g., the continuous chemical processes. The presence of autocorrelation in the process data can result in significant effect on the statistical performance of control charts. Jiang, Tsui, and Woodall (2000) developed a control chart, called the autoregressive moving average (ARMA) control chart, which has been shown suitable for monitoring a series of autocorrelated data. In the present paper, we develop the economic design of ARMA control chart to determine the optimal values of the test and chart parameters of the chart such that the expected total cost per hour is minimized. An illustrative example is provided and the genetic algorithm is applied to obtain the optimal solution of the economic design. A sensitivity analysis shows that the expected total cost associated with the control chart operation is positively affected by the occurrence frequency of the assignable cause, the time required to discover the assignable cause or to correct the process, and the quality cost per hour while producing in control or out of control, and is negatively influenced by the shift magnitude in process mean.     

On improving multiobjective genetic algorithms for design optimization

This paper presents some improvements to Multi-Objective Genetic Algorithms (MOGAs). MOGA modifies certain operators within the GA itself to produce a multiobjective optimization technique. The improvements are made to overcome some of the shortcomings in niche formation, stopping criteria and interaction with a design decision-maker. The technique involves filtering, mating restrictions, the idea of objective constraints, and detecting Pareto solutions in the non-convex region of the Pareto set. A step-by-step procedure for an improved MOGA has been developed and demonstrated via two multiobjective engineering design examples: (i) two-bar truss design, and (ii) vibrating platform design. The two-bar truss example has continuous variables while the vibrating platform example has mixed-discrete (combinatorial) variables. Both examples are solved by MOGA with and without the improvements. It is shown that MOGA with the improvements performs better for both examples in terms of the number of function evaluations.