Type Inheritance in Strongly Typed Genetic Programming

Genetic Programming GP is an automatic method for generating computer programs which are stored as data structures and manipulated to evolve better programs An extension restricting the search space is Strongly Typed Genetic Programming STGP which has as a basic premise the removal of closure by typing both the arguments and return values of functions and by also typing the terminal set A restriction of STGP is that there are only two levels of typing We extend STGP by allowing a type hierarchy which allows more than two levels of typing Introduction A program written in a language that does not support natural ways to express the required algorithms will necessarily use unnatural methods Unnatural methods are less likely to be correct for all possible situations Sebesta p Strongly Typed Genetic Programming STGP Montana is used to restrict the search space con sidered in the Genetic Programming GP paradigm Koza This is shown in both the paper in which Montana introduced STGP Montana and in our research into multiagent behavioral strategies Haynes et al STGP is able to reduce the search space by only allowing syntactically correct programs to be generated and produced by the crossover and mutation operators Montana types both the function return value and the arguments and requires that the typing restrictions be honored by all operations on the S expressions In order to allow for a minimal function set generic types are introduced Generic types must be instantiated during node construction In e ect generic types allow for a two level type hierarchy as shown in Figure From object oriented programming Sebesta we know that it can be desirable to have more than two levels in a hierarchy A simple example involving cars and numbers illustrates this desire If we consider the class hierarchy shown in Figure and assume the standard arithmetic operators of addition subtraction division and multiplication then we do not want to have specialized versions of these operators for Reals and Integers The standard typing solution is to have a generic function for each of the operators which can handle any type However to type addition as Generic we would have to ensure that addition is overloaded such that it makes sense in all contexts which can be instantiated from Generic Failure to do so leads to the undesirable result that the program in Figure is valid What does it mean to add two Fords Are we simply counting the cars by type that pass us on the highway Or are we trying to add the qualities of one car to another to get a hybrid What we would like to do is to de ne the operator addition in class Numbers appropriately overload it in class Reals and class Integers and force the program in Figure to be invalid This further restricts the allowed inputs while still reducing the total number of functions We are extending the concept of a generic type for the tree to generic types for subtrees Hondas Reals Fords Integers Generic Figure An example STGP type hierarchy Reals Numbers Generic