An improved genetic algorithm based on subdivision theory and fixed point algorithms

In this paper an improved genetic algorithm is proposed to solve optimal problems based on subdivision theory and fixed point algorithms of continuous self-mapping in Euclidean space. The algorithm operates on a simplicial subdivision of searching space and generates the integer labels at the vertices, and then relying on the integer labels, crossover operators and increasing dimension operators 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 that determined whether the algorithm will be terminated. The algorithm combines genetic algorithms with fixed point algorithms and triangulation theory to maintain the proper diversity, stability and convergence of the population. Finally, several numerical examples are provided to be examined. Numerical results illustrate that the proposed algorithm has higher global optimization capability, computing efficiency and stronger stability than traditional numerical optimization methods and standard genetic algorithms.