In genetic programming a general consensus is that the population should be as large as practically possible or sensible. In this paper we examine a batch of problems of combinatory logic, previously successfully tackled with genetic programming, which seemto defy this consensus. Our experimental data gives evidence that smaller populations are competitive or even slightly better. Moreover, hill-climbing appears to exhibit the best performance. While these results are in a way unexpected, theoretical considerations provide a possible explanation in terms of a special constellation rather than a general misconception as to the bene ts of large populations or genetic programming as such. 1

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This chapter addresses the question “what is a building block in genetic programming? ” by examining the smallest subtree possible—a single leaf node. The analysis of these subtrees indicates a considerably more complex portrait of what exactly is meant by a building block in GP than what has traditionally been considered. What is a building block in genetic programming (GP)? Intuitively, we might answer simple pieces of code, subprograms, that GP uses to build more complex programs. Intuitively, too, that idea resonates with some theoretical developments in genetic algorithms. Some

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