Abstract
This paper describes a new global maximum searching method for one-dimensional multimodal unknown functions. The searching method is composed of three stages and selects sequentially a subdomain based on a criterion function in each stage. In the first stage, the subdomain which length is the largest, is selected. If the lengths of subdomains are equal, the observed values at the two end points are also considered. In the second stage, subdomains in which a local maximum exists are searched and a subdomain is selected considering the values at the two end points and the lengths of subdomains.
Measures of error for local maximum searching are introduced to check if a local maximum has converged to a specified accuracy or cannot be the global maximum. In the third stage, the local maximum, which is determined to be the global maximum at the end of the second stage, is estimated using a second order interpolation polinomial.
It is clearly explained that through the three stages, the method can search maximum points surely and successfully with any required accuracy.
Performance of the proposed method is evaluated and compared with the previous method by Kubota for a few function models with different parameters of peaks. The simulated results show that the global maximum points are obtained with remarkably high efficiency and the method saves largely computation for local searching even for functions with extremely steep peaks.
