An Introduction to Genetic Algorithms - Boente

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Chapter 2: Genetic Algorithms in Problem Solving An initial population of 50 weight vectors was chosen randomly, with each weight being between ‘.0 and + 1.0. Montana and Davis tried a number of different genetic operators in various experiments. The mutation and crossover operators they used for their comparison of the GA with back−propagation are illustrated in Figure 2.18 and Figure 2.19. The mutation operator selects n non−input units and, for each incoming link to those units, adds a random value between ‘.0 and + 1.0 to the weight on the link. The crossover operator takes two parent weight vectors and, for each non−input unit in the offspring vector, selects one of the parents at random and copies the weights on the incoming links from that parent to the offspring. Notice that only one offspring is created. The performance of a GA using these operators was compared with the performance of a back−propagation algorithm. The GA had a population of 50 weight vectors, and a rank−selection method was used. The GA was allowed to run for 200 generations (i.e., 10,000 network evaluations). The back−propagation algorithm was allowed to run for 5000 iterations, where one iteration is a complete epoch (a complete pass through the training data). Montana and Davis reasoned that two network evaluations Figure 2.19: Illustration of Montana and Davis's crossover method. The offspring is created as follows: for each non−input unit, a parent is chosen at random and the weights on the incoming links to that unit are copied from the chosen parent. In the child network shown here, the incoming links to unit 4 come from parent 1 and the incoming links to units 5 and 6 come from parent 2. under the GA are equivalent to one back−propagation iteration, since back−propagation on a given training example consists of two parts—the forward propagation of activation (and the calculation of errors at the output units) and the backward error propagation (and adjusting of the weights). The GA performs only the first part. Since the second part requires more computation, two GA evaluations takes less than half the computation of a single back−propagation iteration. The results of the comparison are displayed in figure 2.20. Here one back−propagation iteration is plotted for every two GA evaluations. The x axis gives the number of iterations, and the y axis gives the best evaluation (lowest sum of squares of errors) found by that time. It can be seen that the GA significantly outperforms back−propagation on this task, obtaining better weight vectors more quickly. 52
This experiment shows that in some situations the GA is a better training method for networks than simple back−propagation. This does not mean that the GA will outperform back−propagation in all cases. It is also possible that enhancements of back−propagation might help it overcome some of the problems that prevented it from performing as well as the GA in this experiment. Schaffer, Whitley, and Eshelman (1992) point out Figure 2.20: Montana and Davis's results comparing the performance of the GA with back−propagation. The figure plots the best evaluation (lower is better) found by a given iteration. Solid line: genetic algorithm. Broken line: back−propagation. (Reprinted from Proceedings of the International Joint Conference on Artficial Intelligence; © 1989 Morgan Kaufmann Publishers, Inc. Reprinted by permission of the publisher.) that the GA has not been found to outperform the best weight−adjustment methods (e.g., "quickprop") on supervised learning tasks, but they predict that the GA will be most useful in finding weights in tasks where back−propagation and its relatives cannot be used, such as in unsupervised learning tasks, in which the error at each output unit is not available to the learning system, or in situations in which only sparse reinforcement is available. This is often the case for "neurocontrol" tasks, in which neural networks are used to control complicated systems such as robots navigating in unfamiliar environments. Evolving Network Architectures Chapter 2: Genetic Algorithms in Problem Solving Montana and Davis's GA evolved the weights in a fixed network. As in most neural network applications, the architecture of the network—the number of units and their interconnections—is decided ahead of time by the programmer by guesswork, often aided by some heuristics (e.g., "more hidden units are required for more difficult problems") and by trial and error. Neural network researchers know all too well that the particular architecture chosen can determine the success or failure of the application, so they would like very much to be able to automatically optimize the procedure of designing an architecture for a particular application. Many believe that GAs are well suited for this task. There have been several efforts along these lines, most of which fall into one of two categories: direct encoding and grammatical encoding. Under direct encoding, a network architecture is directly encoded into a GA chromosome. Under grammatical encoding, the GA does not evolve network architectures: 53
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An Introduction to Genetic Algorith
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Table of Contents Chapter 4: Theore
Page 6 and 7: Chapter 1: Genetic Algorithms: An O
Page 10 and 11: 1.4 SEARCH SPACES AND FITNESS LANDS
Page 12 and 13: potential energy is a measure of ho
Page 14 and 15: A simple method of implementing fit
Page 16 and 17: from an initial state to a goal. Fo
Page 18 and 19: Robert Axelrod of the University of
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 74 and 75: Chapter 3: Genetic Algorithms in Sc
Page 76 and 77: Figure 3.6: A schematic illustratio
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
Page 96 and 97: competition in the d *···* parti
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Page 100 and 101: Steepest−ascent hill climbing (SA
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(4.7) Chapter 4: Theoretical Founda
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2. 3. Calculate the fitness f(x) of
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Defining ri,j(k) and is somewhat tr
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Results of the Formalization How ca
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Chapter 4: Theoretical Foundations
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Figure 4.5: Predicted and observed
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COMPUTER EXERCISES 1. 2. 3. 4. 5. 6
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prone to rather arbitrary orderings
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Inversion works by choosing two poi
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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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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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