The genetic algorithm was combined with the simplex self-mapping fixed point algorithm to solve the n-dimensional closure cavity function optimization problems.Solution space of the optimization problem would be transformed as ndimensional standard simplex by homeomorphism mapping,then the vertex label information of the individual loading simplex of n-dimensional standard simplex could be calculated with K₂(m) triangulation and integer label,and the coding and genetic operators were designed by vertex label information and function.When the loading simplexes of individuals were transformed into the completely labeled simplexes,the algorithm would be terminated and the approximate solution of the optimization problem would be obtained.The results of a computing example showed that the improved algorithm converged in the 6th generation, which had high global optimization form and computing efficiency.