An Improved Genetic Algorithm Based on Subdivision Theory

Abstract

In this paper an improved genetic algorithm is proposed to solve optimal problems applying triangulation theory 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 crossover operators and increasing dimension operators relying on the integer labels are designed. In this case, whether each individual 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 subdivision theory, maintaining the proper diversity, stability and convergence of the population. Finally, several numerical examples are provided to be examined. Numerical results indicate that the proposed algorithm has higher global optimization capability, computing efficiency and stronger stability than traditional numerical optimization methods and standard genetic algorithms.