An Introduction to Genetic Algorithms - Boente

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these random effects, Bedau and Packard subtracted u0 from u. They showed that, in general, the only genes that take part in activity waves are those with usage greater than u0 Next, Bedau and Packard defined P (t,u), the "net persistence," as the proportion of genes in the population at time t that have usage u or greater. As can be seen in figure 3.13, an activity wave is occurring at time t' and usage value u' if P (t, u) is changing in the neighborhood around (t',u'). Right before time t' there will be a sharp increase in P (t, u), and right above usage value u' there will be a sharp decrease in P(t,u). Bedau and Packard thus quantified activity waves by measuring the rate of change of P(t,u) with respect to u. They measured the creation of activity waves by evaluating this rate of change right at the baseline u0. This is how they defined A(t): That is, the evolutionary activity is the rate at which net persistence is dropping at u = u0. In other words, A (t) will be positive if new activity waves continue to be produced. Bedau and Packard denned "evolution" in terms of A (t): if A(t) is positive, then evolution is occurring at time t, and the magnitude of A(t) gives the "amount" of evolution that is occurring at that time. The bottom plot of figure 3.13 gives the value of A(t) versus time in the given run. Peaks in A(t) correspond to the formation of new activity waves. Claiming that life is a property of populations and not of individual organisms, Bedau and Packard ambitiously proposed A(t) as a test for life in a system—if A(t) is positive, then the system is exhibiting life at time t. The important contribution of Bedau and Packard's 1992 paper is the attempt to define a macroscopic quantity such as evolutionary activity. In subsequent (as yet unpublished) work, they propose a macroscopic law relating mutation rate to evolutionary activity and speculate that this relation will have the same form in every evolving system (Mark Bedau and Norman Packard, personal communication). They have also used evolutionary activity to characterize differences between simulations run with different parameters (e.g., different degrees of selective pressure), and they are attempting to formulate general laws along these lines. A large part of their current work is determining the best way to measure evolutionary activity in other models of evolution—for example, they have done some preliminary work on measuring evolutionary activity in Echo (Mark Bedau, personal communication). It is clear that the notion of gene usage in the Strategic Bugs model, in which the relationship between genes and behavior is completely straightforward, is too simple. In more realistic models it will be considerably harder to define such quantities. However, the formulation of macroscopic measures of evolution and adaptation, as well as descriptions of the microscopic mechanisms by which the macroscopic quantities emerge, is, in my opinion, essential if evolutionary computation is to be made into an explanatory science and if it is to contribute significantly to real evolutionary biology. Thought Exercises 1. 2. Chapter 3: Genetic Algorithms in Scientific Models Assume that in Hinton and Nowlan's model the correct setting is the string of 20 ones. Define a "potential winner" (Belew 1990) as a string that contains only ones and question marks (i.e., that has the potential to guess the correct answer), (a) In a randomly generated population of 1000 strings, how many strings do you expect to be potential winners? (b) What is the probability that a potential winner with m ones will guess the correct string during its lifetime of 1000 guesses? 84
3. 4. 5. 6. Write a few paragraphs explaining as clearly and succinctly as possible (a) the Baldwin effect, (b) how Hinton and Nowlan's results demonstrate it, (c) how Ackley and Littman's results demonstrate it, and (d) how Ackley and Littman's approach compares with that of Hinton and Nowlan. Given the description of Echo in section 3.3, think about how Echo could be used to model the Baldwin effect. Design an experiment that might demonstrate the Baldwin effect. Given the description of Echo in section 3.3, design an experiment that could be done in Echo to simulate sexual selection and to compare its strength with that of natural selection. Is Bedau and Packard's "evolutionary activity" measure a good method for measuring adaptation? Why or why not? Think about how Bedau and Packard's "evolutionary activity" measure could be used in Echo. What kinds of "usage" statistics could be recorded, and which of them would be valuable? Computer Exercises 1. 2. Write a genetic algorithm to replicate Hinton and Nowlan's experiment. Make plots from your results similar to those in figure 3.4, and compare your plots with that figure. Do a run that goes for 2000 generations. At what frequency and at what generation do the question marks reach a steady state? Could you roughly predict this frequency ahead of time? Run a GA on the fitness function f(x) = the number of ones in x, where x is a chromosome of length 20. (See computer exercise 1 in chapter 1 for suggested parameters.) Compare the performance of the GA on this problem with the performance of a modified GA with the following form of sexual selection: a. Add a bit to each string in the initial population indicating whether the string is "male" (0) or "female" (1). (This bit should not be counted in the fitness evaluation.) Initialize the population with half females and half males. b. Separate the two populations of males and females. c. Chapter 3: Genetic Algorithms in Scientific Models Choose a female with probability proportional to fitness. Then choose a male with probability proportional to fitness. Assume that females prefer males with more zeros: the probability that a female will agree to mate with a given male is a function of the number of zeros in the male (you should define the function). If the female agrees to mate, form two offspring via single−point crossover, and place the male child in the next generation's male population and 85
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An Introduction to Genetic Algorith
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Table of Contents Chapter 4: Theore
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Chapter 1: Genetic Algorithms: An O
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1.4 SEARCH SPACES AND FITNESS LANDS
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potential energy is a measure of ho
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A simple method of implementing fit
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from an initial state to a goal. Fo
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Robert Axelrod of the University of
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instances of H at time t, and let
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What is the total payoff after 10 g
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6. * c. d. a. b. Chapter 1: Genetic
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As a simple example, consider a pro
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Chapter 2: Genetic Algorithms in Pr
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it to get one fitness case correct:
Page 38 and 39: Evolving Cellular Automata Chapter
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Page 42 and 43: up most of the computation time. Ch
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Page 48 and 49: where Ã is the standard deviation
Page 54 and 55: the brain. In a feedforward network
Page 58 and 59: Figure 2.21: An illustration of Mil
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Page 66 and 67: COMPUTER EXERCISES 1. 2. 3. 4. 5. 6
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Page 74 and 75: Chapter 3: Genetic Algorithms in Sc
Page 76 and 77: Figure 3.6: A schematic illustratio
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Page 94 and 95: (4.1) The goal is to find n = n* th
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Page 100 and 101: Steepest−ascent hill climbing (SA
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Page 110 and 111: Defining ri,j(k) and is somewhat tr
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Page 120 and 121: COMPUTER EXERCISES 1. 2. 3. 4. 5. 6
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Page 124 and 125: Inversion works by choosing two poi
Page 128 and 129: The one hitch is that, as was seen
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* 10. * 11. * 12. * Chapter 4: Theo
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Chapter 6: Conclusions and Future D
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Chapter 6: Conclusions and Future D
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Appendix A: Selected General Refere
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Evolution Artificielle Foundations
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Kaufmann. Appendix B: Other Resourc
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Morgan Kaufmann. Appendix B: Other
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Appendix B: Other Resources Forrest
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Appendix B: Other Resources Grefens
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Kirkpatrick, S., Gelatt, C.D., Jr.,
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Appendix B: Other Resources Mitchel
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Appendix B: Other Resources Roughga
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Appendix B: Other Resources Vose, M
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An Introduction to Genetic Algorithms - Boente

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