Optimum design of structures with discrete variables using higher-order approximation
The paper deals with an introduction of some higher-order approximations during the optimization process with continuous and discrete design variables. Second- and third-order approximations are presented by employing only the diagonal terms of matrices of higher-order derivatives. To reduce the computational cost, these derivatives are estimated by using the first-order derivatives available from the previous design points. A hybrid form of the second- and third-order approximations is also presented for function approximation. It is observed that the hybrid form is more effective. To achieve the optimal discrete variables, a new penalty function is introduced. First, the continuous optimization is carried out by means the penalty function, and then the results are used as the starting point for discrete optimization. In both the continuous and discrete optimization, the idea of various function approximations is employed to decrease the computation time required by the design process. Examples are solved, and the effects of different proposed approximate techniques are discussed.
scientific article; zbMATH DE number 1741986