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8
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Introduction to Evolutionary Computing
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Evolution is an optimization process, where the aim is to improve the ability of individuals to survive. Evolutionary computing (EC) is the emulation of the process of natural selection in a search procedure. In nature, organisms have certain characteristics that influence their ability to survive and reproduce. These characteristics are represented by long strings of information contained in the chromosomes of the organism. After sexual reproduction the chromosomes of the offspring consist of a combination of the chromosomal information from each parent. Hopefully, the end result will be offspring chromosomes that contain the best characteristics of each parent. The process of natural selection ensures that the more "fit" individuals have the opportunity to mate most of the time, leading to the expectation that the offspring have a similar, or better fitness. Occasionally, chromosomes are subjected to mutations which cause changes to the characteristics of the corresponding individuals. These changes can have a negative influence on the individual's ability to survive or reproduce. On the other hand, mutation may actually improve the fitness of an individual, thereby improving its chances of survival and of taking part in producing offspring. Without mutation, the population tends to converge to a homogeneous state where individuals vary only slightly from each other. Evolution via natural selection of a randomly chosen population of individuals can be thought of as a search through the space of possible chromosome values. In that sense, an evolutionary algorithm (EA) is a stochastic search for an optimal solution to a given problem. The evolutionary search process is influenced by the following main components of EA: an encoding of solutions to the problem as a chromosome;
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CHAPTER 8. INTRODUCTION TO EVOLUTIONARY
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a function to evaluate the fitness, or survival strength of individuals; initialization of the initial population; selection operators; and reproduction operators. Each of these aspects is introduced and discussed briefly in the sections that follow. More detailed discussions follow in the chapters on the different EC paradigms. A comparison between classical optimization and EC is given in Section 8.7. A general EA is given in Section 8.6. EAs have been applied to a wide range of problem areas, including planning, for example, routing optimization and scheduling; design, for example, the design of filters, neural network architectures and structural optimization; control, for example, controllers for gas turbine engines, and visual guidance systems for robots; classification and clustering; function approximation and time series modeling; regression; composing music; and data mining. EAs have shown advantages over existing algorithmic solutions in the above application areas. It is interesting to note that EAs are being increasingly applied to areas in which computers have not been used before.
Representation of Solutions - The Chromosome
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An evolutionary algorithm utilizes a population of individuals, where each individual represents a candidate solution to the problem. The characteristics of an individual are represented by a chromosome, or genome. The characteristics represented by a chromosome can be divided into classes of evolutionary information: genotypes and phenotypes. A genotype describes the genetic composition of an individual as inherited from its parents. Genotypes provide a mechanism to store experiential
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8.2. FITNESS FUNCTION
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evidence as gathered by parents. A phenotype is the expressed behavioral traits of an individual in a specific environment. A complex relationship can exist between the genotype and phenotype. Two such relationships are [Mayr 1963]: pleiotropy, where random modification of genes cause unexpected variations in the phenotypic traits; and polygeny, where several genes interact to produce a specific phenotypic trait. To change this behavioral characteristic, all the associated genes need to change. Each chromosome represents a point in search space. A chromosome consists of a number of genes, where the gene is the functional unit of inheritance. Each gene represents one characteristic of the individual, with the value of each gene referred to as an allele. In terms of optimization, a gene represents one parameter of the optimization problem. A very important step in the design of an EA is to find an appropriate chromosome representation. The efficiency and complexity of a search algorithm greatly depend on the representation scheme, where classical optimization techniques usually use vectors of real numbers, different EAs use different representation schemes. For example, genetic algorithms (GA) mostly use a binary string representation, where the binary values may represent Boolean values, integers or even discretized real numbers, genetic programming (GP) makes use of a tree representation to represent programs and evolutionary programming (EP) uses real-valued variables. The different representation schemes are described in more detail in the chapters that follow.
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