The effect of crossover on the behavior of the GA in dynamic environments: a case study using the shaky ladder hyperplane-defined functions

One argument as to why the hyperplane-defined functions (hdf's) are a good testbed for the genetic algorithm (GA) is that the hdf's are built in the same way that the GA works. In this paper we test that hypothesis in a new setting by exploring the GA on a subset of the hdf's which are dynamic---the shaky ladder hyperplane-defined functions (sl-hdf's). In doing so we gain insight into how the GA makes use of crossover during its traversal of the sl-hdf search space. We begin this paper by explaining the sl-hdf's. We then conduct a series of experiments with various crossover rates and various rates of environmental change. Our results show that the GA performs better with than without crossover in dynamic environments. Though these results have been shown on some static functions in the past, they are re-confirmed and expanded here for a new type of function (the hdf) and a new type of environment (dynamic environments). Moreover we show that crossover is even more beneficial in dynamic environments than it is in static environments. We discuss how these results can be used to develop a richer knowledge about the use of building blocks by the GA.