Fitness landscape analysis in the optimization of coefficients of curve parametrizations

Abstract

Parametric representations of geometric objects, such as curves or surfaces, may have unnecessarily huge integer coefficients. Our goal is to search for an alternative parametric representation of the same object with significantly smaller integer coefficients. We have developed and implemented an evolutionary algorithm that is able to find solutions to this problem in an efficient as well as robust way. In this paper we analyze the fitness landscapes associated with this evolutionary algorithm. We here discuss the use of three different strategies that are used to evaluate and order partial solutions. These orderings lead to different landscapes of combinations of partial solutions in which the optimal solutions are searched. We see that the choice of this ordering strategy has a huge inuence on the characteristics of the resulting landscapes, which are in this paper analyzed using a set of metrics, and also on the quality of the solutions that can be found by the subsequent evolutionary search.