Vieno kintamojo funkcijų minimizavimo algoritmų analizė

Abstract

This paper investigates three methods of one variable function optimizing methods, executes the comparison of their efficiency and generalizes the results of this research. At first there is a review of historical aspects of optimization theory, definition of optimization concept, introduction to task formulation. Presentation of optimization importance, the role of objective function in the process of optimization. Introduction to the classification of optimization tasks and optimization of various systems. In this paper there is an analysis of three methods of optimization: “Half distribution”, “Golden cut”, “Powell”. There was created a program for calculating and comparing of the selected optimization methods. During the investigation it was determined that when there is a small precision (0,1; 0,01), the change of minimum of the function and the value of that point are great. When you increase the value of precision the change of minimum of the function and the value of that point are very small. When the precision value is about (0,0001 .. 0,000001) there is a difference in only 6-th – 9-th value after the comma. The use of “Powell” method requires least steps of calculating, the use of “Half distribution” method requires mostly steps of calculating. In about 80 % of calculation the shortest interval of the search was using the “Powell” method of optimizing, in 20 % of calculation the shortest interval of the search was using the “Golden cut” method of optimization. After 30 steps of calculation the shortest interval was never get using “Half distribution” optimization method. Analysis of effectiveness of these optimization methods i. e. the number of calculating steps and the value of function minimum, the best is “Powell” optimization method. The advantage of this method is quadratic approximation, limitation – with some primary values the research could find the minimum that is not the principal researched point in the functions which have o few minimum points. Comparing “Golden cut” and “Half distribution” methods the better effectiveness has the “Golden cut” optimization method.