How Good is Fitness Sharing with a Scaling Function

Fitness sharing has been used widely in genetic algorithms for multi-objective function optimization and machine learning. It is often implemented with a scaling function, which adjusts an individual's raw fitness to improve the performance of the genetic algorithm. However, choosing a scaling function is an ad hoc affair that lacks sufficient theoretical foundation, and which often gives results that need further processing with a hill-climbing algorithm. Although this is already known, an explanation as to why this is so has been lacking. This paper explains why fitness sharing with a scaling function performs in this way. We investigate fitness sharing's performance at multiobjective optimization, demonstrate the need for a scaling function of some kind, and discuss what form of scaling function works best. An artificial search space was created for our study. We provide both theoretical and empirical evidence that fitness sharing with a scaling function suffers a dilemma which can ..