Domino convergence, drift, and the temporal-salience structure of problems

The convergence speed of building blocks depends on their marginal fitness contribution or on the salience structure of the problem. We use a sequential parameterisation approach to build models of the differential convergence behavior, and derive time complexities for the boundary case which is obtained with an exponentially scaled problem (BinInt). We show that this domino convergence time complexity is linear in the number of building blocks (O(l)) for selection algorithms with constant selection intensity (such as tournament selection and (mu,lambda) or truncation selection), and exponential (O(2(l))) for proportionate selection. These complexities should be compared with the convergence speed for uniformly salient problems which are respectively (O(root l)) and (O(l nl l)). In addition we relate this facetwise model to a genetic drift model, and identify where and when the stochastic fluctuations due to drift overwhelms the domino convergence, resulting in drift stall. The combined models interrelate the strong convergence of salient building blocks and the stochastic drift of less salient ones.