Constructive Geometric Constraint Solving: A New Application of Genetic Algorithms

Authors:
Robert Joan-Arinyo;M. V. Luzón;Antonio Soto-Riera
Affiliations:
-;-;-
Venue:
PPSN VII Proceedings of the 7th International Conference on Parallel Problem Solving from Nature
Year:
2002

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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 addicional properties. Selecting a solution instance amounts to selecting a given root everytime 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 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. Some examples illustrate the performance of the method.