Schema Decomposition for Non-Binary Gene

Abstract

In the theoretical analysis of genetic algorithms, WST (Walsh-Schema Transform) is a well-known method. WST is useful when we analyze genetic algorithms from the viewpoint of schema. However, WST can be used only when the gene is binary : the gene consists of only two types of symbols. We propose WST-like method called OSD (Orthogonal Schema Decomposition) which can be used also for the non-binary gene. In this paper, the definition and the meaning of OSD, the fast algorithm for performing OSD, the relation between OSD and WST and some usages of OSD are shown.