GA and CHC. Two evolutionary algorithms to solve the root identification problem in geometric constraint solving

Abstract

Geometric problems defined by constraints have an exponential number of solution instances in the number of geometric elements involved. Generally, the user is only interested in one instance such that, besides fulfilling the geometric constraints, exhibits some additional properties. Selecting a solution instance amounts to selecting a given root every time the geometric constraint solver needs to compute the zeros of a multi valuated function. The problem of selecting a given root is known as the Root Identification Problem. In this paper we present a comparative study of a basic genetic algorithm against the CHC algorithm. Both techniques are based on an automatic search in the space of solutions driven by a set of extra constraints. A number of case studies illustrate the performance of the methods. © Springer-Verlag Berlin Heidelberg 2004.