Pruning population size in XCS for complex problems

In this report, we show how to prune the population size of the Learning Classifier System XCS for complex problems. We say a problem is complex, when the number of specified bits of the optimal start classifiers (the prob lem dimension) is not constant. First, we derive how to estimate an equiv- alent problem dimension for complex problems based on the optimal start classifiers. With the equivalent problem dimension, we calculate the optimal maximum population size just like for regular problems, which has already been done. We empirically validate our results. Furthermore, we introduce a subsumption method to reduce the number of classifiers. In contrast to existing methods, we subsume the classifiers after the learning process, so subsuming does not hinder the evolution of optimal classifiers, which has been reported previously. After subsumption, the number of classifiers drops to about the order of magnitude of the optimal classifiers while the correctness rate nearly stays constant