Genetic algorithms for root multiselection in constructive geometric constraint solving

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 multivaluated 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. In a case study we illustrate the performance of the method. (C) 2002 Elsevier Science Ltd. All rights reserved.