Binary Scanning Search (Biscan) for Conditional Minimization of Weakly Unimodal Functions

Abstract

A method of binary scan search (biscan) is proposed for conditional minimization of weakly unimodal functions. The application area of this method is the optimization of piecewise, stepwise, relay and other weakly unimodal functions, the extremum of which can be localized, both in narrow and extended regions, including the regions of constancy of the minimized function. The algorithm implementing the method is represented by two procedures, the block diagrams of which are given in the article. To evaluate the performance of the biscan, a comparative computational experiment was carried out using examples of minimizing a number of weakly unimodal functions. It is established that, in comparison with competing methods, the biscan gives better performance. The fastest method is provided by minimizing non-constant monotonic functions. To determine the extremum, only five calculations of such a function are required. In comparison with the golden section search, the biscain has a 1,5 times greater speed in solving problems of this type. In minimizing strictly weakly unimodal functions, to which the known methods of minimizing unimodal functions are not applicable, in particular, the golden section search, the biscan operates orders of magnitude faster than the competing sequential search method.