Investigation of the Performance of Different Mapping Orders for GE on the Max Problem

We present an analysis of how the genotype-phenotype map in Grammatical Evolution (GE) can effect performance on the Max Problem. Earlier studies have demonstrated a performance decrease for Position Independent Grammatical Evolution (πGE ) in this problem domain. In πGE the genotype-phenotype map is changed so that the evolutionary algorithm controls not only what the next expansion will be but also the choice of what position in the derivation tree is expanded next. In this study we extend previous work and investigate whether the ability to change the order of expansion is responsible for the performance decrease or if the problem is simply that a certain order of expansion in the genotype-phenotype map is responsible. We conclude that the reduction of performance in the Max problem domain by πGE is rooted in the way the genotype-phenotype map and the genetic operators used with this mapping interact.