A TWO-DIMENSIONAL MAXIMUM SEARCH MEHHOD BY A GLOBAL PRIORITY STRATEGY WITH LOCAL PEAK ESTIMATION:ITS OPTIMAL SWITCHING CRITERION

The paper presents a new global maximum search method for multimodal unknown functions of two variables. The search method is composed of two stages and sequentially samples the candidate point in a subdomain selected using a priority function in each stage. The search domain is auto-similarly divided into triangular subdomains, or cells, during the search process. A measure of accuracy of local maximum search is introduced to check if a local search has converged to a specified accuracy or the maximum of a local peak cannot be the global maximum. A criterion for switching from the first to the second stage, is proposed using a ratio of the observed peak width to the largest cell in the domain. By numerical simulations, the required number of trials is evaluated for some function models with different peak parameters, and the switching criterion is optimally determined. The results show that the proposed method obtains global maximum points with certainty and saves largely computation time even for functions with extremely steep peaks.