Marginal Distribution Density of Free Reflection Simplex Search Algorithm when Target Function is Square

Abstract

Search optimization of real objects is always carried under conditions of disturbances, which emerge because of imprecise measurement, influence of unknown factors on object functioning indicators, object characteristic change and other reasons. Random disturbances create step direction errors, false view of extreme position and so decrease the effectiveness of search. Because of that, when creating optimization algorithms, applied for solving stochastic problems, it is necessary to perform the search systems research working under disturbances conditions. In this work the marginal distribution density of free reflection simplex search algorithm was found when working under the condition of normally distributed disturbances, with square function target. Simplex state probabilities were calculated using Monte Carlo method. Il. 5, bibl. 5 (in English; summaries in English, Russian and Lithuanian).