Discrete Structural Optimization Based on Multipoint Explicit Approximations

Abstract

Many real-life structural optimization problems have the following characteristic features: (i) some or all design variables can be defined as a set of discrete parameters, (ii) the objective function and constraints are implicit functions of design variables, (iii) to calculate values of these functions means to use some numerical response analysis technique which usually involves a large amount of computer time, (iv) the function values and (or) their derivatives often contain noise, i.e. can only be estimated with a finite accuracy. To cope with above problems, the multipoint approximation method has been developed. It is considered as a general iterative technique, which uses in each iteration simplified approximations of the original objective/constraint functions. They are obtained by the multiple regression analysis methods which can use information being more or less inaccurate. The technique allows to use in each iteration the information gained in several previous design points which are considered as a current design of numerical experiments defined on a given discrete set of parameters. It allows to consider instead of the initial discrete optimization problem a sequence of simpler mathematical programming problems and to reduce the total number of time-consuming numerical analyses. The obtained approximations are considered to be valid within a current subregion of the space of design variables defined by discrete values of move limits. This approach provides flexibility in choosing design variables and objective/constraint functions and allows the designer to use his experience and judgment in directing the optimization process.