Ensuring Building Block Supply

Abstract

In chapter 5, we defined what we meant by building blocks and acknowledged their importance. In the last chapter, we looked at search problems through the lens of building blocks and tried to envision various dimensions of problem difficulty from that standpoint. Here it is important to take BBs quite seriously, almost physically, and make sure that the GA is well supplied with a good stock of the building blocks necessary to solve the problem at hand. In this chapter, we consider this supply question in isolation and estimate the size of population necessary to ensure that the raw BBs are present and available for subsequent selection and genetic operation. As it turns out, the supply population requirement is often superseded by the so-called decision-making population size to be taken up in a subsequent chapter. Moreover, more sophisticated equations combine the requirements of supply and decision in a single model. Nonetheless, we examine the supply question in isolation, because the calculations are straightforward, revealing, and easily verified. We start by briefly reviewing prior work in this area and then turn to deriving a facetwise model with some straightforward probabilistic calculation.