Jornal de Ciência da Computação e Biologia de Sistemas

A Novel Improved Genetic Algorithm Based on the Fixed Point Theorem and Triangulation Method

Abstract

Iulian Pop

Genetic algorithms are widely used for solving a multitude of complex problems. Methods for increasing the genetic algorithms accuracy are of great importance. One such method consist of using the fixed point theory combined with an improved genetic algorithm. This paper aims to provide such an algorithm with an increased convergence accuracy. In order to increase the algorithm operates on a simplicial triangulation over the searching space. We use the crossover, mutation and increase dimension genetic operators to obtain a convergent population that contains only fully labelled simplexes. In order to obtain better results, we use a custom increase dimension operator that significantly boosts the overall fitness. The increase dimension operator converts non-labelled individuals into nearly labelled/fully labelled ones. The solution, the global optimum point, is obtained after applying the Hessian matrix onto the final population. Our obtained results clearly show an improvement over existing work due to implementation particularities of the algorithm.