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 new technique to solve the root
identification problem. The technique is based on an automatic search
in the space of solutions performed by a genetic algorithm. The user
specifies the solution of interest by defining a set of additional
constraints on the geometric elements which drive the search of the
genetic algorithm. The method is extended with a sequential niche
technique to compute multiple solutions. A number of case studies
illustrate the performance of the method.Postprint (published version
