Dynamic evolutionary optimisation: an analysis of frequency and magnitude of change

In this paper, we rigorously analyse how the magnitude and frequency of change may affect the performance of the algorithm (1+1) EAdyn on a set of artificially designed pseudo-Boolean functions, given a simple but well-defined dynamic framework. We demonstrate some counter-intuitive scenarios that allow us to gain a better understanding of how the dynamics of a function may affect the runtime of an algorithm. In particular, we present the function Magnitude, where the time it takes for the (1+1) EAdyn to relocate the global optimum is less than n2log n (i.e., efficient) with overwhelming probability if the magnitude of change is large. For small changes of magnitude, on the other hand, the expected time to relocate the global optimum is eΩ(n) (i.e., highly inefficient). Similarly, the expected runtime of the (1+1) EAdyn on the function Balance is O(n2) (efficient) for a high frequencies of change and nΩ(√n) (highly inefficient) for low frequencies of change. These results contribute towards a better understanding of dynamic optimisation problems in general and show how traditional analytical methods may be applied in the dynamic case.