Tutorial On Evolutionary Techniques And Fuzzy Logic In .
Tutorial onEvolutionary Techniques and FuzzyLogic in Power SystemsPrepared for the IEEE-PES Summer Meeting in SeattleJuly, 2000Course Coordinator:Mohamed A. El-Sharkawi, University of WashingtonContributors:Chapter 1: Theory of Evolutionary ComputationRussel Eberhart, Purdue School of Engineering and Technology,Indiana University Purdue University IndianapolisChapter 2: An Introduction to Fuzzy InferenceRobert J. Marks, University of WashingtonChapter 3: Application of Evolutionary Technique to Power SystemSecurity AssessmentCraig Jensen, Microsoft CorporationM. A. El-Sharkawi, University of WashingtonRobert J. Marks, University of WashingtonChapter 4: Application of EC to Optimization, Model Identification,Training and ControlAlexandre P. Alves da Silva, Federal Engineering School at Itajuba,BrazilChapter 5: Fuzzy Systems Applications to Power SystemsKevin Tomsovic, Washington State University
Evolutionary Techniques and Fuzzy Logic in Power SystemsTable of ContentsChapter 1: Theory of Evolutionary Computation . 41.1 Introduction. 41.2 EC Paradigm Attributes . 41.3 Implementation . 41.4 Genetic Algorithms . 51.4.1 Introduction. 51.4.2 An Overview of Genetic Algorithms . 51.4.3 A Simple GA Example Problem . 61.4.4 A Review of GA Operations . 81.5 Particle Swarm Optimization . 111.5.1 Introduction. 111.5.2 Simulating Social Behavior . 121.5.3 The Particle Swarm Optimization Concept. 131.5.4 Training a Multilayer Perceptron . 131.6 Conclusions. 151.7 Acknowledgments. 161.8 Selected Bibliography. 16Chapter 2: An Introduction to Fuzzy Inference . 192.1 Fuzzy Sets . 192.2 Differences Between Fuzzy Membership Functions and Probability Density Functions . 192.3 Fuzzy Logic . 212.3.1 Fuzzy If-Then Rules . 222.3.2 Numerical Interpretation of the Fuzzy Antecedent . 222.3.3 Matrix Descriptions of Fuzzy Rules . 242.4 Application to Control . 242.5 Variations. 252.5.1 Alternate Fuzzy Logic. 252.5.2 Defuzzification. 252.5.3 Weighting Consequents . 262.6 Further Reading . 26Chapter 3: Application of Evolutionary Technique to Power System Security Assessment . 273.1 Abstract. 273.2 Introduction. 273.3 NN's for DSA. 283.4 Evolutionary-Based Query Learning Algorithm. 283.5 Case Study – IEEE 17 Generator System . 293.6 Conclusions. 303.7 References. 30Chapter 4: Application of EC to Optimization, Model Identification, Training and Control . 324.1 Optimization . 324.1.1 Modern Heuristic Search Techniques . 324.1.2 Power System Applications . 334.1.3 Example . 344.2 MODEL IDENTIFICATION . 344.2.1 Dynamic Load Modeling . 354.2.2 Short-Term Load Forecasting . 354.3 TRAINING . 364.3.1 Pruning Versus Growing. 364.3.2 Types of Approximation Functions . 374.3.3 The Polynomial Network . 37
4.4 CONTROL. 384.5 ACKNOWLEDGMENTS . 384.6 REFERENCES . 38Chapter 5: Fuzzy Systems Applications to Power Systems . 415.1 Introduction. 415.2 Power System Applications . 425.2.1 Rule-based Fuzzy Systems. 425.2.2 Fuzzy Controllers. 435.2.3 Fuzzy Decision-Making and Optimization . 435.3 Basics of Fuzzy Mathematics . 435.4 Example: Control Application . 455.4.1 A Controller Design Methodology. 465.4.2 Illustrative example. 485.5 Example: Diagnostic Application . 485.6 Future Trends. 515.6.1 Membership values . 525.6.2 Fuzzy Operators . 525.6.3 Performance analysis . 525.6.4 Relation to ANN and other Soft Computational Methods . 525.7 References. 52Course Instructors . 54
Chapter 1: Theory of Evolutionary Computation1.1 IntroductionEvolutionary computation (EC) paradigms generally differfrom traditional search and optimization paradigms in threemain ways:1. EC paradigms utilize a population of points (potentialsolutions) in their search,2. EC paradigms use direct “fitness” information instead offunction derivatives or other related knowledge, and3. EC paradigms use probabilistic, rather thandeterministic, transition rules.In addition, EC implementations sometimes encode theparameters in binary or other symbols, rather than workingwith the parameters themselves. We now examine thesedifferences in more detail.1.2 EC Paradigm AttributesMost traditional optimization paradigms move from onepoint in the decision hyperspace to another, using somedeterministic rule. One of the drawbacks of this approach isthe likelihood of getting stuck at a local optimum. ECparadigms, on the other hand, start with a population ofpoints (hyperspace vectors). They typically generate a newpopulation with the same number of members each epoch, orgeneration. Thus, many maxima or minima can be exploredsimultaneously, lowering the probability of getting stuck.Operators such as crossover and mutation effectivelyenhance this parallel search capability, allowing the search todirectly “tunnel through” from one promising hyperspaceregion to another.EC paradigms do not require information that is auxiliaryto the problem, such as function derivatives. Many hillclimbing search paradigms, for example, require thecalculation of derivatives in order to explore the localmaximum. In EC optimization paradigms the fitness of eachmember of the population is calculated from the value of thefunction being optimized, and it is common to use thefunction output as the measure of fitness. Fitness is a directmetric of the performance of the individual populationmember on the function being optimized.The fact that EC paradigms use probabilistic transitionrules certainly does not mean that a strictly random search isbeing carried out. Rather, stochastic operators are applied tooperations that direct the search toward regions of thehyperspace that are likely to have higher values of fitness.Thus, for example, reproduction (selection) is often carriedout with a probability that is proportional to the individual’sfitness value.Some EC paradigms, and especially canonical geneticalgorithms, use special encodings for the parameters of theproblem being solved. In genetic algorithms, the parametersare often encoded as binary strings, but any finite alphabetcan be used. These strings are almost always of fixedlength, with a fixed total number of 1s and 0s, in the case ofa binary string, being assigned to each parameter. By “fixedlength” it is meant that the string length does not vary duringthe running of the EC paradigm. The string length (numberof bits for a binary string) assigned to each parameterdepends on its maximum range for the problem beingsolved, and on the precision required.1.3 ImplementationRegardless of the paradigm implemented, evolutionarycomputation tools often follow a similar procedure:1. Initialize the population,2. Calculate the fitness for each individual in thepopulation,3. Reproduce selected individuals to form a newpopulation,4. Perform evolutionary operations, such as crossover andmutation, on the population, and5. Loop to step 2 until some condition is met.Initialization is most commonly done by seeding thepopulation with random values. When the parameters arerepresented by binary strings, this simply means generatingrandom strings of 1s and 0s (with a uniform probability foreach value) of the fixed length described earlier. It issometimes feasible to seed the population with “promising”values, known to be in the hyperspace region relatively closeto the optimum. The total number of individuals chosen tomake up the population is both problem and paradigmdependent, but is often in the range of a few dozen to a fewhundred.The fitness value is often proportional to the output valueof the function being optimized, though it may also bederived from some combination of a number of functionoutputs. The fitness function takes as its inputs the outputsof one or more functions, and outputs some probability ofreproduction. It is sometimes necessary to transform thefunction outputs to produce an appropriate fitness metric;sometimes it is not.4
Selection of individuals for reproduction to constitute anew population (often called a new generation) is usuallybased upon fitness values. The higher the fitness, the morelikely it is that the individual will be selected for the newgeneration.Some paradigms that are consideredevolutionary, however, such as particle swarm optimization,can retain all population members from epoch to epoch.In many, if not most, cases, a global optimum exists at onepoint in the decision hyperspace. Furthermore, there may bestochastic or chaotic noise present. Sometimes the globaloptimum changes dynamically because of externalinfluences; frequently there are very good local optima aswell. For these and other reasons, the bottom line is that it isoften unreasonable to expect any optimization method tofind a global optimum (even if it exists) within a finite time.The best that can be hoped for is to find near-optimumsolutions, and to hope that the time it takes to find themincreases less than exponentially with the number ofvariables. One leading EC researcher (H.-P. Schwefel 1994)suggests that the focus should be on “meliorization”(improvement) rather than optimization. We agree.Put another way, evolutionary computation is often thesecond-best way to solve a problem. Classical methods suchas linear programming should often be tried first, as shouldcustomized approaches that take full advantage ofknowledge about the problem.Why should we be satisfied with second best? Well, forone thing, classical and customized approaches willfrequently not be feasible, and EC paradigms will be usablein a vast number of situations. For another, a real strength ofEC paradigms is that they are generally quite robust. In thisfield, robustness means that an algorithm can be used tosolve many problems, and even many kinds of problems,with a minimum amount of special adjustments to accountfor special qualities of a particular problem. Typically anevolutionary algorithm requires specification of the length ofthe problem solution vectors, some details of their encoding,and an evaluation function – the rest of the program does notneed to be changed. Finally, robust methodologies aregenerally fast and easy to implement.The next section reviews genetic algorithms. It is one offive areas of evolutionary computation: genetic algorithms,evolutionary programming, evolution strategies, geneticprogramming, and particle swarm optimization. Geneticalgorithms have traditionally received a majority of theattention, and they currently account for many of thesuccessful applications in the literature. Particle swarmoptimization is then discussed in the last section.1.4 Genetic Algorithms1.4.1 IntroductionIt seems that every technology has its jargon; geneticalgorithms are no exception. Therefore, we begin byreviewing some of the basic terminology that is needed tounderstand the genetic algorithm (GA) literature. A sampleproblem is then presented to illustrate how GAs work; astep-by-step analysis illustrates a GA application, withoptions discussed for some of the individual operations.1.4.2 An Overview of Genetic AlgorithmsGenetic algorithms (GAs) are search algorithms that reflectin a primitive way some of the processes of naturalevolution. (As such, they are analogous to artificial neuralnetworks’ status as primitive approximations to biologicalneural processing.) Engineers and computer scientists donot care as much about the biological foundations of GAs astheir utility as analysis tools (another parallel with neuralnetworks).GAs often provide very effective searchmechanisms that can be used in optimization orclassification applications.EC paradigms work with a population of points, ratherthan a single point; each “point” is actually a vector inhyperspace representing one potential, or candidate, solutionto the optimization problem. A population is thus just anensemble, or set, of hyperspace vectors. Each vector iscalled an individual in the population; sometimes anindividual in GA is referred to as a chromosome, because ofthe analogy to genetic evolution of organisms.Because real numbers are often encoded in GAs usingbinary numbers, the dimensionality of the problem vectormight be different from the dimensionality of the bitstringchromosome. The number of elements in each vector(individual) equals the number of real parameters in theoptimization problem.A vector element generallycorresponds to one parameter, or dimension, of
Tutorial on Evolutionary Techniques and Fuzzy Logic in Power Systems Prepared for the IEEE-PES Summer Meeting in Seattle July, 2000 Course Coordinator: Mohamed A. El-Sharkawi, University of Washington Contributors: Chapter 1: Theory of Evolutionary Computation Russel Eberhart, Purdue School of Engineering and Technology,
evolutionary biology. From this point of view, some authors have tried to extend the Darwinian theory universally beyond the domain of evolutionary biology (Cf. Dawkins, 1983), using the three principles of evolutionary theory (inheritance or retention, variation, and adaptation) as a heuristic for evolutionary economic theorizing (Campbell, 1965).
NATURE OF HUMAN INTELLIGENCE Leda Cosmides* and John Tooby* EVOLUTIONARY PSYCHOLOGY The goal of research in evolutionary psychology is to discover and understand the de- sign of the human mind. Evolutionary psychology is an approach to psychology, in which knowledge and principles from evolutionary biology and human evolutionary
data into studies of eco-evolutionary dynamics can provide a better mechanistic understanding of the causes of phenotypic change, help elucidate the mechanisms driving eco-evolutionary dynamics and lead to more accurate evolutionary predictions of eco-evolutionary dynamics in nature (Fig. 2). What genomic data can reveal about
1.1.3 Evolutionary Design by Computers So it is clear that evolutionary design in nature is capable of generating astonishingly in-novative designs. This book demonstrates how evolutionary design by computers is also cap-able of such innovation. To achieve this, the highest achievers in evolutionary design have
Yao: Intro to Evolutionary Computation ’ & % What Is Evolutionary Computation 1. It is the study of computational systems which use ideas and get inspirations from natural evolution. 2. One of the principles borrowed is survival of the fittest. 3. Evolutionary computation (EC) techniques can be used in optimisation, learning and design. 4.
Tutorial Process The AVID tutorial process has been divided into three partsÑ before the tutorial, during the tutorial and after the tutorial. These three parts provide a framework for the 10 steps that need to take place to create effective, rigorous and collaborative tutorials. Read and note the key components of each step of the tutorial .
Tutorial Process The AVID tutorial process has been divided into three partsÑ before the tutorial, during the tutorial and after the tutorial. These three parts provide a framework for the 10 steps that need to take place to create effective, rigorous and collaborative tutorials. Read and note the key components of each step of the tutorial .
être imposées à l'alimentation dans le cas d'un additif, pesticide, ou d'autres contenus qui sont interdites au Japon, alors que leurs niveaux dépassent les limites approuvées, ou lorsque la présence de mycotoxines, etc. est au-dessus des niveaux admissibles. Par conséquent, les aliments santé et des compléments alimentaires doit être vérifiée sur le site de production avant l .
