Global Optimization Using Evolutionary Algorithm Based on Level Set Evolution and Latin Square

In this paper, a new crossover operator based on Latin square design is presented at first. This crossover operator can generate a set of uniformly scattered offspring around their parents, and it is of the ability of local search and thus can explore the search space efficiently. Then the level set of the objective function is evolved successively by crossover and mutation operators such that it gradually approaches to global optimal solution set. Based on these, a new evolutionary algorithm for nondifferentiable unconstrained global optimization is proposed and its global convergence is proved. At last, the numerical simulations are made for some standard test functions. The performance of the proposed algorithm is compared with that of two widely-cited algorithms. The results indicate the proposed algorithm is effective and has better performance than the compared algorithms for these test functions.