A two-dimensional maximum searching method by a combined global priority strategy with local peak estimation

This paper presents a maximum search procedure using a combined global priority strategy with local peak estimation for two-dimensional multimodal unknown functions. The functions are supposed to be continuous but need not to be smooth. An efficient sequential algorithm is presented for arrangement of search points, using search subdomains with three adjoining sampled points. The search procedure is composed of two stages to select the suitable sampling strategy according to different global information. In the first stage, the subdomain largest in length is selected. In the second stage, the subdomains in which a local maximum exists are searched. Measures of error for local maximum search are introduced to check if a local maximum has converged to a specified accuracy or if it cannot be the global maximum. The effectiveness of the algorithm is validated by computer simulations for some example functions and comparisons with previous results by another deterministic, sequential algorithm which uses interpolation techniques for global search. [In Japanese.]