Abstract
We will propose new global optimization procedure which utilizes the concept of tunneling algorithm in this paper. There exist two phases in the tunneling algorithm for global minimization problems, 1) minimization phase and 2) tunneling phase. In the minimization phase, the local minimum is searched. In the tunneling phase, the point in the lower valley is searched.
In this paper, we will propose an annealing type of random tunneling search in the tunneling phase. First, we set the temperature at some degree and generate the increment (δx) from the local minimum (x*), according to the Cauchy distribution. A new point x(=x*+δx) is evaluated whether it is in the lower valley or not. If the point in the lower valley is not found after the predetermined number of trials, the temperature is set a little lower according to its cooling schedule and we repeat the same procedure again.
The wide range of search becomes possible owing to the property of Cauchy distribution and temperature cooling. We also abopt multistart scheme in order not to miss the global minimum.
Several test problems are solved. The proposed method hardly misses the global minimum and is very promising for future application research.
