Evolutionary Computation : A Unified Approach

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3.5. GENETIC ALGORITHMS 41 Define selection probabilities p(i) for each parent i so that p(i) is proportional to u(i). Generate m offspring by probabilistically selecting parents to produce offspring. Select only the offspring to survive. End Repeat Notice that the pseudo-code actually specifies a particular form of selection, called fitnessproportional selection. It is easy to show that using this selection mechanism, individuals in the current population with average fitness will produce on average one offspring, while above-average individuals produce more than one and below-average individuals less than one (Holland, 1975). Figure 3.7 illustrates the effect that this has on the average fitness of an evolving population. Notice first that fitness-proportional selection appears to be stronger initially than that of ES, but then weakens considerably. The second, and more striking, outcome to note is that, since all parents die off after one generation, it is possible for the average fitness of the next generation (the offspring) to drop. Is this desirable For simple landscapes, probably not. But for more complex, multipeaked landscapes this can decrease the likelihood of converging to a local optimum. 3.5.1 Multi-parent Reproduction Another important difference between GAs and the other models is the way in which offspring are produced. From the beginning, Holland stressed the importance of sexual reproduction as a source of variation in the offspring produced (Holland, 1967). The basic idea is that offspring inherit gene values from more than one parent. This mixing (recombining) of parental gene values, along with an occasional mutation, provides the potential for a much more aggressive exploration of the space. Holland’s initial ideas for this took the form of a “1 point crossover” operator in which a randomly chosen initial segment of genes was inherited from one parent and the remaining segment inherited from a second parent. These ideas were later generalized to “2 point crossover” and “n point crossover” operators (De Jong, 1975). Since all of these crossover operators are equivalent for individuals with exactly two genes, we run a GA with crossover (GA-X) on landscape L2 and plot the effects on average population fitness in figure 3.8. In this case, crossover provides an additional source of variation involving larger initial steps, improving the initial rate of convergence. Since crossover does not introduce new gene values, its influence diminishes as the population becomes more homogeneous, and the behavior of GA-X becomes nearly identical to a GA with no crossover.
42 CHAPTER 3. CANONICAL EVOLUTIONARY ALGORITHMS 55 50 45 Fitness: Local Average 40 35 30 25 20 ES(1,10) GA(10,10) 15 10 0 100 200 300 400 500 Number of Births Figure 3.7: Average population fitness of a GA on landscape L2. 55 50 45 Fitness: Local Average 40 35 30 25 20 15 ES(1,10) GA(10,10) GA-X(10,10) 10 0 100 200 300 400 500 Number of Births Figure 3.8: Average population fitness of a GA with crossover on landscape L2.
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5.2. EA-BASED OPTIMIZATION 97 5.2.2
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5.2. EA-BASED OPTIMIZATION 101 700
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5.2. EA-BASED OPTIMIZATION 103 5.2.
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5.3. EA-BASED SEARCH 105 • In the
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5.4. EA-BASED MACHINE LEARNING 107
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5.5. EA-BASED AUTOMATED PROGRAMMING
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5.5. EA-BASED AUTOMATED PROGRAMMING
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5.7. SUMMARY 113 the effect of impr
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116 CHAPTER 6. EVOLUTIONARY COMPUTA
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Chapter 7 Advanced EC Topics The pr
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7.2. DYNAMIC LANDSCAPES 213 nested
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7.2. DYNAMIC LANDSCAPES 215 10 8 Fi
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7.2. DYNAMIC LANDSCAPES 217 10 8 Fi
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7.3. EXPLOITING PARALLELISM 219 7.2
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7.4. EVOLVING EXECUTABLE OBJECTS 22
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7.5. MULTI-OBJECTIVE EAS 223 be of
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7.7. BIOLOGICALLY INSPIRED EXTENSIO
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Chapter 8 The Road Ahead As a well-
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Appendix A Source Code Overview Rat
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A.1. EC1: A VERY SIMPLE EC SYSTEM 2
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A.3. EC3: A MORE FLEXIBLE EC SYSTEM
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A.3. EC3: A MORE FLEXIBLE EC SYSTEM
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Bibliography Altenberg, L. (1994).
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BIBLIOGRAPHY 243 Collins, R. and D.
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BIBLIOGRAPHY 245 Frank, S. A. (1995
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BIBLIOGRAPHY 247 Jansen, T., K. De
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BIBLIOGRAPHY 249 Potter, M. A., J.
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BIBLIOGRAPHY 251 Spears, W. (2000).
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Index 1-point crossover operator, 2
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INDEX 255 graph structures, 74-76,
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Evolutionary Computation : A Unified Approach

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