Design space optimization using a numerical design continuation method

Abstract

A generalized optimization problem in which the design space is also a design variable to be determined is defined and a numerical implementation method is proposed. In conventional optimization, only some of the structural parameters are designated as design variables while the remaining parameters related to the design space are often taken for granted. The number of design variables along with the layout or configuration specifies a design space. To solve this type of design space problem, a simple initial design space is selected and gradually improved while the usual design variables are being optimized. To make the design space evolve into a better one, the designer may increase the number of design variables, but in this transition, there are discontinuities in the objective and constraint functions. Accordingly, the sensitivity analysis methods based on continuity cannot be used in this discontinuous stage. To overcome this difficulty, a numerical continuation scheme is proposed. It is based on a new concept of a pivot phase design space. This is applicable only for the cases when new design variables are added. To find the set of new design cells to be added, first a set of potential cells to be possibly added are specified, for example, by including all the adjacent cells to the existing active cells. The directional derivatives based on the introduction of pivot phase space are calculated and then a portion of the set are selected using the ranking of the sensitivities. The selection ratio is chose by the user. It is noted that only one analysis is necessary for the sensitivity information, and this makes this process very efficient. In order to reduce computational cost and improve efficiency, however, it is necessary to include a process of removing design variables when the values remain constant over iterations, because in this case the design variables are not used for optimization. In the topology optimization of density approach, a cell whose ...