The global optimization method with selective averaging of the discrete decision variables

Abstract

In the paper, the functional of selective averaging of discrete decision variables is proposed. The positive selectivity coefficient is entered into a positive decreasing kernel of functional and with growth of selectivity coefficient the mean gives optimum values (in a limit) of decision discrete variables in a problem of global optimization. Based on the estimate of the selective averaging functional, a basic global optimization algorithm is synthesized on a set of discrete variables with ordered possible values under inequality constraints. The basis is a computational scheme for optimizing continuous variables and its transformation for optimization with respect to discrete variables. On a test example the high convergence rate and a noise stability of base algorithm are shown. Simulations have shown that the estimate of the probability of making a true decision reaches unit.