This paper introduces a new approach to genetic programming (GP), based on a numerical technique, which integrates a GP-based adaptive search of tree structures, and a local parameter tuning mechanism employing statistical search (a system identification technique). In traditional GP, recombination can cause frequent disruption of building blocks or mutation can cause abrupt changes in the semantics. To overcome these difficulties, we supplement traditional GP with a local hill-climbing search, using a parameter tuning procedure. More precisely, we integrate the structural search of traditional GP with a multiple regression analysis method and establish our adaptive program, called STROGANOFF (STructured Representation On Genetic Algorithms for NOn-linear Function Fitting). The fitness evaluation is based on a minimum description length (MDL) criterion, which effectively controls the tree growth in GP. We demonstrate its effectiveness by solving several system identification (numerical) problems and compare the performance of STROGANOFF with traditional GP and another standard technique (radial basis functions). We then extend STROGANOFF to symbolic (nonnumerical) reasoning by introducing multiple types of nodes, using a modified MDL-based selection criterion and a pruning of the resultant trees. The effectiveness of this numerical approach to GP is demonstrated by successful application to symbolic regression problems.

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