The χ-ary Extended Compact Classifier System: Linkage Learning in Pittsburgh LCS

This paper proposes a competent Pittsburgh LCS that automatically mines important substructures of the underlying problems and takes problems that were intractable with first-generation Pittsburgh LCS and renders them tractable. Specifically, we propose a χ-ary extended compact classifier system (χeCCS) which uses (1) a competent genetic algorithm (GA) in the form of χ-ary extended compact genetic algorithm, and (2) a niching method in the form restricted tournament replacement, to evolve a set of maximally accurate and maximally general rules. The results clearly show that linkage exists in the multiplexer problem which needs to be accurately discovered and efficiently processed in order to solve the problem in tractable time. The results also show that in accordance with the facetwise models from GA theory, the number of function evaluations required by χeCCs to successfully evolve an optimal rule set scales exponentially with the number of address bits (building block size) and quadratically with the problem size.