An Improved Genetic Algorithm Based on hK1 Subdivision and Fixed Point

In this paper an improved genetic algorithm is proposed to solve optimal problems applying fixed-point algorithms of continuous self-mapping in Euclidean space. The algorithm operates on an hK₁ subdivision of searching space and generates the integer labels at the vertices, and then crossover operators and mutation operators relying on the integer labels are designed. In this case, whether every individual of the population is a completely labeled simplex can be used as an objective convergence criterion and determined whether the algorithm will be terminated. The algorithm combines genetic algorithms with fixed point algorithms, and can maintain the proper diversity, stability and convergence of the population. Finally, a numerical example is provided to examine.