Deciding Well

We have identified what we think the GA is processing—building blocks; we have ensured that there is a sufficient initial supply of BBs and that the best ones grow in market share on average; and just now, we have taken the time to understand how long such market share growth takes, but how do we know whether the best building blocks are actually the ones that come to dominate the population? Answering this question is the focus of this chapter. Specifically, building on the identification of the building block decision problem as a problem in statistical decision making (Holland, 1973), we examine a number of little models of BB decision making. Starting with the generation-wise decision model that gave an initial bound on the relation between solution quality and population size, we conclude by presenting a simple, accurate model based on the solution to the gambler’s ruin problem. In the best tradition of little models, this back-of-an-envelope calculation is giving surprisingly accurate estimates of decision quality across a range of population sizes, problem sizes and complexity, and GA operators and selection schemes.