A Signal - to - noise Framework for Quantifying Search Di culties

This paper presents a signal-to-noise perspective of the search process in genetic algorithms. First we pose a decision problem in terms of multiple 2-armed, mutually dependent bandits. This presents a theoretical framework for understanding stochastic search techniques in general. The deterministic and nondeterministic e ects on the convolution kernel associated with the bandits are identi ed as signal and noise respectively. We discuss what these quantities mean in a GA and how they can be computed in GA. Next, we present a signal-to-noise perspective of GA hardness. It is noted that there are two fundamental modes of introducing di culty into the decision making process: 1) sending a wrong signal and 2) increasing or decreasing noise depending on the direction of signal. We also note that the di culty due to crosstalk[21] can be quanti ed by the higher order components of the noise kernel. Our experiments on Royal Road functions R1 & R2 [13] clearly demonstrate that increasing signal in the right direction alone does not necessarily make a problem easy for GA, unless the noise is also reduced.