The Evolution of Size and Shape

Introduction The rapid growth of programs produced by genetic programming (GP) is a well documented phenomenon [Koza, 1992; Blickle and Thiele, 1994; Nordin and Banzhaf, 1995; McPhee and Miller, 1995; Soule et al., 1996; Greeff and Aldrich, 1997; Soule, 1998] . This growth, often referred to as "code bloat", need not be correlated with increases in the fitness of the evolving programs and consists primarily of code which does not change the semantics of the evolving program. The rate of growth appears to vary depending upon the particular genetic programming paradigm being used, but exponential rates of growth have been documented [Nordin and Banzhaf, 1995] . Code bloat occurs in both tree based and linear genomes [Nordin, 1997; Nordin and Banzhaf, 1995; Nordin et al., 1997] and with automatically defined functions [Langdon, 1995] . Recent research suggests that code bloat will occur in most fitness based search techniques which allow variable length solutions [Langdon, 1998b; Lang