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Unformatted text preview: Characterizing a Tunably Difficult Problem in Genetic Programming Omer A. Chaudhri, Jason M. Daida, Jonathan C. Khoo, Wendell S. Richardson, Rachel B. Harrison, and William J. Sloat The University of Michigan, Artificial Intelligence Laboratory and Space Physics Research Laboratory 2455 Hayward Avenue, Ann Arbor, Michigan 48109-2143, email@example.com, (734) 647-4581, (734) 764-5137 FAX Abstract This paper examines the behavioral phenomena that occur with the tuning of the binomial-3 problem. Our analysis identifies a distinct set of phenomena that may be generalizable to other problems. These phenomena also bring into question whether GA theory has any bearing on GP theory. 1 INTRODUCTION A common assumption in genetic programming theory is that phenomena that occur under genetic algorithms (GA) have roughly analogous counterparts in genetic programming (GP). After all, genetic programming is a derivative from genetic algorithms. Many of their procedural steps are similarin- deed, GP is more alike GA than is different. Where the two differ lies in what is seemingly a secondary issue: that GP (of- ten) uses a tree representation to structure information rather than, say, a linear representation. Given the various imple- mentations of GP and GA, this difference is even less clear, since some GP systems use a linear representation and some GA systems use a tree-like representation. Consequently, given this degree of similarity between GA and GP, the assumption of analogous phenomena is understandable. Is the assumption correct? We would claim perhaps, under some circumstances. If we took the position, however, that phenomena that occur under GP have no counterpart in GA, we would need to re-examine just what phenomena does oc- cur under GP. If the phenomena were found to be substan- tially different, it would beg the issue of whether theory in GA has any bearing on GP theory. This paper re-examines phenomena that occur under GP as a problem is tuned for difficulty. (For this paper, we define phenomena as behavioral occurances, patterns, that are observed in the output from a GP system.) Although the output we obtain is strictly static (i.e., non-time varying and represents but a single snapshot of performance for a particular trial), by tuning and observing the output, we can infer something about GPs internal dynamics. (The process we use is akin to finding an unknown transfer function to a black box.) For this paper then, we examine in detail the behavioral phe- nomena that occurs with the tuning of a single problem. Our investigation represents a longitudinal study with the purpose of understanding GP dynamics . This is in contrast to exam- ining the behavioral phenomenon that occurs under multiple problems. Multiple problems represent a latitudinal approach to understanding gross characteristics of GP. For example, lati- tudinal studies, like [Luke and Spector 1998], have been used to discuss efficacy of methods (e.g., crossover v. mutation).to discuss efficacy of methods (e....
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- Fall '07