Empirical analysis of schemata in Genetic Programming using maximal schemata and MSG

Plenteous research studies schemata in Genetic Programming (GP), though little of it is been empirical, due to the vast numbers of typical schemata in even small populations. In this research, we define maximal schemata, and extend our TRIPS algorithm to the more general Max-Schema-Growth (MSG) algorithm, applicable to a wider range of schema forms (TRIPS only handles standard fragment schemata). We present MSG specialized to work with unordered-fragments schemata (tree-fragments with unordered functions), and compare the number of maximal schemata found of these two forms. For most maximal fragments, another maximal fragment was also found that differed only by the orders of function node arguments. We conclude that maximal unordered-fragments may represent a greater range of common patterns between programs than standard maximal fragments, though the greater reach comes at a price with a severe increase in the time taken by the algorithm.