Klaipėdos universitetas

The paper proposes a technology for mass optimization of two-dimensional body applying genetic algorithms. Main attention is focused on geometry of 2D body, i. e. search for optimal coordinates of body points. Direct analysis of 2D body – von Mises stress determination – is performed using original program based on finite element method. The set of design parameters contains the coordinates of body points in 2D space. The results of numerical experiments proved the proposed technology to be efficient tool for solution of 2D body mass optimization problem.

In this paper a stochastic adaptive method has been developed to solve stochastic linear problems by a finite sequence of Monte-Carlo sampling estimators. The method is based on the adaptive regulation of the size of Monte-Carlo samples and a statistical termination procedure taking into consideration statistical modelling accuracy. Our approach distinguishes itself by the treatment of accuracy of the solution in a statistical manner, testing the hypothesis of optimality according to statistical criteria, and estimating confidence intervals of the objective and constraint functions. To avoid “jamming” or “zigzagging” solving a constraint problem we implement the ε–feasible direction approach. The proposed adjustment of a sample size, when it is taken inversely proportional to the square of the norm of the Monte-Carlo estimate of the gradient, guarantees convergence a. s. at a linear rate. The numerical study and examples in practice corroborate theoretical conclusions and show that the developed procedures make it possible to solve stochastic problems with sufficient accuracy by the means of an acceptable size of computations.