Parameter tuning for PBIL and CHC algorithms to solve the root identification problem in geometric constraint solving

Abstract

Evolutive algorithms are among the most successful approaches for solving a number of problems where systematic search in huge domains must be performed. One problem of practical interest that falls into this category is known as emph{The Root Identification Problem} in Geometric Constraint Solving, where one solution to the geometric problem must be selected among a number of possible solutions bounded by an exponential number. In previous works we have shown that applying genetic algorithms, a category of evolutive algorithms, to solve the Root Identification Problem is both feasible and effective. The behavior of evolutive algorithms is characterized by a set of parameters that have an effect on the algorithms' performance. In this paper we report on an empirical statistical study conducted to establish the influence of the driving parameters in the PBIL and CHC evolutive algorithms when applied to solve the Root Identification Problem. We also identify ranges for the parameter values that optimize the algorithms performance.