Simpleksinės paieškos statistinių charakteristikų tyrimas

Abstract

The analysis of searching optimization tasks and methods at work have been performed, rules of constructing simplex, its motion rules have been presented. The methods of simplex search analysis have been investigated; simplex search methods compared to other optimization methods. The analysis of statistical characteristics of rectangular simplex search was made using multiple Markov chains. Double Markov chains describing properties of rectangular simplex search in the climbing stage were designed, simplex search statistical characteristics calculating methodic was created. Theoretical statistical characteristics – probabilities of search steps, mathematical expectancy of shift of the simplex center towards the aim – which let us evaluate the velocity of rectangular simplex search in the climbing stage and reveal its features were obtained. Rectangular simplex search with two and three controlled variables was analyzed experimentally. Theoretical characteristics are confirmed by the results of modeling the search. The task of filter structure synthesis was solved using simplex search method. The results and conclusions of the research can be used in creating new algorithms of simplex search.