Study of An Improved Genetic Algorithm Based on Fixed Point theory and hJ1 triangulation in Euclidean Space

Abstract

<p>Aiming at the convergence precision defects of standard genetic algorithm, the fixed point theory is introduced into the genetic algorithms. The population of individual is regarded as the triangulation of the point. Hence the vertex label information of the individual simplex would guide the algorithm to the optimization researching and convergence judgment which could be calculated with the hJ1 triangulation and integer label. When the loading simplexes of individuals are transferred into the completely labeled simplexes, the algorithm will be terminated and the global optimal solution will be got. Finally, some functions are used to demonstrate the effectiveness and strong stability of the algorithm through solving the minimum points distinguished by using the Hessian Matrix and then compared with the standard genetic algorithms and J1 triangulation.</p&gt

A Special Mutation Operator in the Genetic Algorithm for Fixed Point Problems

“…The relationship between the genetic algorithm and the fixed points is a two-way relationship. In this sense, in some studies, fixed point properties have been used to improve the performance of genetic algorithms [13][14][15][16][17][18], and in some studies, updated models of genetic algorithms have been used to solve fixed point problems [19][20][21][22].…”

“…Therefore, the remaining parameters can be obtained based on this choice of the classical PSO algorithm. Zhang et al [16] introduced a GA that the population of individual is regarded as the triangulation of the point. They used the vertex label information of the individual simplex of individual to design selection operator, crossover, and mutation operators.…”