Fractal algorithms for finding global optimal solutions

For solving constrained nonlinear 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 remains. The advantages of the local fine structure of fractal and the quick convergence of golden section method are taken. Hence, the fractal algorithm is highly efficient and. highly speedy. The algorithm has the character of strong adaptability to a class of complex function. It requests only that the object function has one order derivative. The minimum can be found at any precision at which a computer can work. Furthermore, this method requests so little memory that it almost can. be implemented on any PC of which the efficiency is almost not influenced. The proof showing convergence of the algorithm, is given. The numerical results show that the algorithm is effective.