An Introduction to Genetic Algorithms - Boente

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Chapter 3: Genetic Algorithms in Scientific Models Figure 3.3: Mean fitness versus generations for one run of the GA on each of three population sizes. The solid line gives the results for population size 1000, the size used in Hinton and Nowlan's experiments; the open circles the results for population size 250; the solid circles for population size 4000. These plots are from a replication by Belew and are reprinted from Belew 1990 by permission of the publisher. © 1990 Complex Systems. population sizes is given in figure 3.3. (This plot is from a replication of Hinton and Nowlan's experiments performed by Belew (1990).) The solid curve gives the results for population size 1000, the size used in Hinton and Nowlan's experiments. Hinton and Nowlan found that without learning (i.e., with evolution alone) the mean fitness of the population never increased over time, but figure 3.3 shows that with learning the mean fitness did increase, even though what was learned by individuals was not inherited by their offspring. In this way it can be said that learning can guide evolution, even without the direct transmission of acquired traits. Hinton and Nowlan interpreted this increase as being due to the Baldwin effect: those individuals that were able to learn the correct connections quickly tended to be selected to reproduce, and crossovers among these individuals tended to increase the number of correctly fixed alleles, increasing the learning efficiency of the offspring. With this simple form of learning, evolution was able to discover individuals with all their connections fixed correctly. Figure 3.4 shows the relative frequencies of the correct, incorrect, and undecided alleles in the population plotted over 50 generations. As can be seen, over time the frequency of fixed correct connections increased and the frequency of fixed incorrect connections decreased. But why did the frequency of undecided alleles stay so high? Hinton and Nowlan answered Figure 3.4: Relative frequencies of correct (dotted line), incorrect (dashed line), and undecided (solid line) alleles in the population plotted over 50 generations. (Reprinted from Hinton and Nowlan 1987 by permission of the publisher. © 1987 Complex Systems.) 70
Chapter 3: Genetic Algorithms in Scientific Models that there was not much selective pressure to fix all the undecided alleles, since individuals with a small number of question marks could learn the correct answer in a small number of learning trials. If the selection pressure had been increased, the Baldwin effect would have been stronger. Figure 3.5 shows these same results over an extended run. (These results come from Belew's (1990) replication and extension of Hinton and Nowlan's original experiments.) This plot shows that the frequency of question marks goes down to about 30%. Given more time it might go down further, but under this selection regime the convergence was extremely slow. To summarize: Learning can be a way for genetically coded partial solutions to get partial credit. A common claim for learning is that it allows an organism to respond to unpredictable aspects of the environment—aspects that change too quickly for evolution to track genetically. Although this is clearly one benefit of learning, the Baldwin effect is different: it says that learning helps organisms adapt to genetically predictable but difficult aspects of the environment, and that learning indirectly helps these adaptations become genetically encoded. The "learning" mechanism used in Hinton and Nowlan's experiments—random guessing—is of course completely unrealistic as a model of learning. Hinton and Nowlan (1987, p. 500) pointed out that "a more sophisticated learning procedure only strengthens the argument for the Figure 3.5: Relative frequencies of correct (solid circles), incorrect (open circles), and undecided (solid line) alleles in the population plotted over 500 generations, from Belew's replication of Hinton and Nowlan's experiments. (Reprinted from Belew 1990 by permission of the publisher. © 1990 Complex Systems.) importance of the Baldwin effect." This is true insofar as a more sophisticated learning procedure would, for example, further smooth the original "needle in a haystack" fitness landscape in Hinton and Nowlan's learning task, presumably by allowing more individuals to learn the correct settings. However, if the learning procedure were too sophisticated—that is, if learning the necessary trait were too easy—there would be little selection pressure for evolution to move from theability to learn the trait to a genetic encoding of that trait. Such tradeoffs occur in evolution and can be seen even in Hinton and Nowlan's simple model. Computer simulations such as theirs can help us to understand and to measure such tradeoffs. More detailed analyses of Hinton and Nowlan's model were performed by Belew (1990), Harvey (1993), and French and Messinger (1994). A more important departure from biological reality in this model, and one reason why the Baldwin effect showed up so strongly, is the lack of a "phenotype." The fitness of an individual is a direct function of the alleles in its chromosome, rather than of the traits and behaviors of its phenotype. Thus, there is a direct correlation here between learned adaptations and genetic variation—in fact, they are one and the same thing. What if, as in real biology, there were a big distance between the genotypic and phenotypic levels, and learning occurred on the phenotypic level? Would the Baldwin effect show up in that case too, transferring the learned adaptations into genetically encoded traits? The next subsection describes a model that is a bit closer to this more realistic scenario. 71
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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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Page 24 and 25: Chapter 1: Genetic Algorithms: An O
Page 26 and 27: instances of H at time t, and let
Page 28 and 29: What is the total payoff after 10 g
Page 30 and 31: 6. * c. d. a. b. Chapter 1: Genetic
Page 32 and 33: As a simple example, consider a pro
Page 34 and 35: Chapter 2: Genetic Algorithms in Pr
Page 36 and 37: it to get one fitness case correct:
Page 38 and 39: Evolving Cellular Automata Chapter
Page 42 and 43: up most of the computation time. Ch
Page 46 and 47: the prospect of using GAs to automa
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
Page 62 and 63: experiments with grammatical encodi
Page 64 and 65: function of the average error of th
Page 66 and 67: COMPUTER EXERCISES 1. 2. 3. 4. 5. 6
Page 70 and 71: simulated generations, and such sim
Page 72 and 73: environments, they can fairly quick
Page 76 and 77: Figure 3.6: A schematic illustratio
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Page 82 and 83: an initial population in which the
Page 88 and 89: these random effects, Bedau and Pac
Page 90 and 91: 3. * 4. * the female child in the n
Page 92 and 93: calculating the observed average fi
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 108 and 109: 2. 3. Calculate the fitness f(x) of
Page 110 and 111: Defining ri,j(k) and is somewhat tr
Page 112 and 113: Results of the Formalization How ca
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Page 118 and 119: Figure 4.5: Predicted and observed
Page 120 and 121: COMPUTER EXERCISES 1. 2. 3. 4. 5. 6
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Inversion works by choosing two poi
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Chapter 4: Theoretical Foundations
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The one hitch is that, as was seen
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used in the work of Tanese (1989),
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Two individuals are chosen at rando
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Chapter 4: Theoretical Foundations
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strategies community, in which para
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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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