Fractal Algorithm for Finding Global Optimal Solution

For solving global optimization problems, a new algorithm, which is called fractal algorithm, is presented. Feasible region is partitioned by fractal combining with golden section. Bad region is deleted gradually and finally optimal solution is remained. The full advantage of the local fine structure of fractal and the quick convergence of golden section method were taken. Hence it is high efficient and high speedy. The algorithm has following character: strong adaptability, adapting to a class of complex function. It needs only that the object function has one order derivative. The minimum can be found at any precision at which a computer can work. On the other hand, this method needs so little memory that it almost can be implemented on any personal computer and its efficiency is not almost influenced. The proof of convergence of the algorithm is given. The illustrations show the algorithm is effective.