An Introduction to Genetic Algorithms - Boente

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Chapter 3: Genetic Algorithms in Scientific Models reservoir is empty. Thus, bugs must find food continually in order to survive. Each bug's behavior is controlled by an internal lookup table that maps sensory data from the bug's local neighborhood to a vector giving the direction and distance of the bug's next foray. The sensory data come from five sites centered on the bug's current site, and the state at each site is encoded with two bits representing one of four levels of food that can be sensed (00 = least food; 01 = more food; 10 = even more food; 11 = most food). Thus, a bug's current state (input from five sites) is encoded by ten bits. The vector describing the bug's next movement is encoded by eight bits—four bits representing one of 16 possible directions (north, north−northeast, northeast, etc.) in which to move and four bits representing one of 16 possible distances to travel (0–15 steps) in that direction. Since there are 10 bits that represent sensory data, there are 2 10 possible states the bug can be in, and a complete lookup table has 2 10 = 1024 entries, each of which consists of an eight−bit movement vector. Each eight−bit entry is considered to be a single "gene," and these genes make up the bug's "chromosome." One such chromosome is illustrated in figure 3.12. Crossovers can occur only at gene (lookup table entry) boundaries. The simulation begins with a population of 50 bugs, each with a partially randomly assigned lookup table. (Most of the entries in each lookup table initially consist of the instruction "do nothing.") A time step consists of each bug's assessing its local environment and moving according to the corresponding instruction in its lookup table. When a bug encounters a site containing food, it eats the food. When it has sufficient energy in its internal reservoir (above some predefined threshold), it reproduces. A bug can reproduce asexually (in which case it passes on its chromosome to its offspring with some low probability of mutation at each gene) or sexually (in which case it mates with a spatially adjacent bug, producing offspring whose genetic material is a combination of that of the parents, possibly with some small number of mutations). To measure evolutionary activity, Bedau and Packard kept statistics on gene use for every gene that appeared in the population. Each gene in a bug was assigned a counter, initialized to 0, which was incremented every Figure 3.12: Illustration of the chromosome representation in the Strategic Bugs model. Crossovers occur only at gene (lookup−table entry) boundaries. 82
Chapter 3: Genetic Algorithms in Scientific Models time the gene was used—that is, every time the specified input situation arose for the bug and the specified action was taken by the bug. When a parent passed on a gene to a child through asexual reproduction or through crossover, the value of the counter was passed on as well and remained with the gene. The only time a counter was initialized to zero was when a new gene was created through mutation. In this way, a gene's counter value reflected the usage of that gene over many generations. When a bug died, its genes (and their counters) died with it. For each time step during a run, Bedau and Packard (1992) plotted a histogram of the number of genes in the population displaying a given usage value u (i.e., a given counter value). One such plot is shown here at the top of figure 3.13. The x axis in this plot is time steps, and the y axis gives usage values u. A vertical slice along the y axis gives the distribution of usage values over the counters in the population at a given time step, with the frequency of each usage value indicated by the grayscale. For example, the leftmost vertical column (representing the initial population) has a black region near zero, indicating that usage values near zero are most common (genes cannot have high usage after so little time). All other usage values are white, indicating that no genes had yet reached that level of usage. As time goes on, gray areas creep up the page, indicating that certain genes persisted in being used. These genes presumably were the ones that helped the bugs to survive and reproduce—the ones Figure 3.13: Plots of usage statistics for one run of the Strategic Bugs model. Top plot: Each vertical column is a histogram over u (usage values), with frequencies of different u values represented on a gray scale. On this scale, white represents frequency 0 and black represents the maximum frequency. These histograms are plotted over time. Bottom plot: Evolutionary activity A(t) is plotted versus t for this run. Peaks in A(t) correspond to the formation of new activity waves. (Reprinted from Christopher G. Langton et al. (eds.). Artificial Life: Volume II, ©1992 by Addison−Wesley Publishing Company, Inc. Reprinted by permission of the publisher.) that encoded traits being selected. Bedau and Packard referred to these gray streaks as "waves of activity." New waves of activity indicated the discovery of some new set of genes that proved to be useful. According to Bedau and Packard, the continual appearance of new waves of activity in an evolving population indicates that the population is continually finding and exploiting new genetic innovations. Bedau and Packard defined a single number, the evolutionary activity A(t),that roughly measures the degree to which the population is acquiring new and useful genetic material at time t. In mathematical terms, Bedau and Packard defined u0 as the "baseline usage"—roughly the usage that genes would obtain if selection were random rather than based on fitness. As an initial attempt to compensate for 83
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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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Page 38 and 39: Evolving Cellular Automata Chapter
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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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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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