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Additional info for Advances in learning classifier systems: third international workshop, IWLCS 2000, Paris, France, September 15-16, 2000 : revised papers
IWLCS 2000, LNAI 1996, pp. 21−28, 2001. Springer-Verlag Berlin Heidelberg 2001 22 L. Bull 2 The Model Goldberg and Segrest  introduced a simple Markov model of a one-bit two-class (binary), generational genetic algorithm. Using a population of size N, they note that there are N+1 possible states i, where i is the population with exactly i individuals of class A, and hence N-i individuals of class B. The model defines an (N+1)x(N+1) transition matrix P(i,j) mapping the current state i to the state j, a population containing exactly j individuals of class A.
Until now, the ACS considered all changing attributes as results from its actions. Butz, Goldberg, and Stolzmann (1999) revealed the limits of such an approach. It was shown that the ACS relies on a perceptual causality in the environment and that any non-determinism challenges the learning mechanism. In particular, an environment was investigated where randomly changing attributes or noise in the actions challenged the ACS. Stolzmann (1997) already proposed the formation of an attention spot in the ACS by introducing an additional ’don’t care’ symbol in the effect part (rule right-hand side).
As the 24 L. e. P(i,i+1) = P(i,i-1) since fA = fB; and when 0:0 = 1000, P(i,i+1) > P(i,i-1). Therefore these results clearly show how an LCS using the prediction-based fitness scheme is sensitive to the reward scheme with regard to the generation of an effective rule-set for the problem domain; the model shows prediction-based fitness promoting incorrect rules. Figure 1b shows the resulting transition matrices for the accuracy-based case. Here it can be seen that there is no significant selective pressure for the overgeneral rule (P(i,i+1) >> P(i,i-1)) and that as the number of instances of the accurate rule increases (>i) its selective pressure decreases from a maximum due to the use of relative accuracy.