The tendency for programs in genetic programming (GP) populations to grow in length has been widely reported [Tac93,Tac94,Ang94,Tac95,Lan95,NB95,SFD96]. In our previous work on this phenomenon (referred to as ``bloat'') [LP97,Lan97a,Lan97b] we have investigated the effect of commonly used fitness functions with a variety of genetic algorithm, population based and non-population based search techniques. These experiments have shown that bloat is not a unique phenomenon to genetic programming and we argue that it is inherent in discrete variable length representations using a simple scalar static fitness function. [Lan97b] also contains evidence to suggest that non-performance effecting code (sometimes referred to as ``introns'') may also be a contributing factor. These explanations stress the role of simple static scalar fitness functions in selecting children which behave in the same way as their parents. In this paper we broaden our investigation to consider fitness functions which avoid selecting such children and dynamic fitness functions (where the test case changes every generation).
We continue to use the well known genetic programming bench mark problem of evolving control programs to guide an artificial ant along an intermediate trail of food pellets. The first experiments use the well known Santa Fe trail [Koz92], while this is replaced in the second set of experiments by randomly generated trails which are changed each generation (i.e. the population ``sees'' each trail only once). In these experiments the effects of changing the fitness function are studied, all the other parameters are the same in each experiment.
In Sect. 2 we briefly describe the artificial ant problem and the genetic programming system used to solve it. In Sect. 3 we describe the fitness functions used in the two sets of experiments and introduce the penalty for copying the behaviour of ancestors. Our results are given in Sects. 4 and 5, which are followed by our conclusions in Sect. 6.