Studying XCS/BOA learning in Boolean functions: structure encoding and random Boolean functions

Recently, studies with the XCS classifier system on Boolean functions have shown that in certain types of functions simple crossover operators can lead to disruption and, consequently, a more effective recombination mechanism is required. Simple crossover operators were replaced by recombination based on estimation of distribution algorithms (EDAs). The combination showed that XCS with such a statistics-based crossover operator can solve challenging hierarchical functions more efficiently. This study elaborates the gained competence further investigating the coding scheme for the EDA component (BOA in our case) of XCS as well as performance in randomly generated Boolean function problems. Results in hierarchical Boolean functions show that the originally used 2-bit coding scheme induces a certain learning bias that stresses additional diversity in the evolving XCS population. A 1-bit coding scheme as well as a restricted 2-bit coding scheme confirm the suspected bias. The alternative encodings decrease the unnecessary bias towards specificity and increase performance robustness. The paper concludes with a discussion on the challenges ahead for XCS in Boolean function problems as well as on the implications of the obtained results for real-valued and multiple-valued classification problems, multi-step problems, and function approximation problems.

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