Parameter tuning of PBIL and CHC evolutionary algorithms applied to solve the Root Identification Problem

Evolutionary algorithms are among the most successful approaches for solving a number of problems where systematic searches in huge domains must be performed. One problem of practical interest that falls into this category is known as 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 evolutionary algorithms, to solve the Root Identification Problem is both feasible and effective. In this work, we report on an empirical statistical study conducted to establish the influence of the driving parameters in the PBIL and CHC evolutionary algorithms when they are used to solve the Root Identification Problem. We identify a set of values that optimize algorithms performance. The driving parameters considered for the PBIL algorithm are population size, mutation probability, mutation shift and learning rate. For the CHC algorithm we studied population size, divergence rate, differential threshold and the set of best individuals. In both cases we applied unifactorial and multifactorial analysis, post hoc tests and best parameter level selection. Experimental results show that CHC outperforms PBIL when applied to solve the Root Identification Problem.