The MINLP optimization approach to structural synthesis. Part II: Simultaneous topology, parameter and standard dimension optimization by the use of the linked two-phase MINLP strategy

Part II describes the Mixed-Integer Non-linear Programming (MINLP) approach to structural synthesis where standard dimensions are added to simultaneous topology and parameter optimization. For this purpose, the mechanical superstructure has been enhanced and a special MINLP-MS model formulation for mechanical superstructures from Part I adapted to standard dimension alternatives, which give rise to complex MINLP problems that are di¦cult to solve. A Linked Two-Phase MINLP Strategy has been developed to e¦ciently accelerate the solutions of highly combinatorial MINLP problems, performed by the ModiÞed OA/ER algorithm. In the Þrst phase, the strategy uses only continuous dimensions making it easier to Þnd an optimal topology. Based on the obtained global linear approximation of the superstructure, the proposed strategy in the second phase continues to perform an overall simultaneous optimization, where standard dimensions are added as additional discrete optimization alternatives. Thus, simultaneous topology, parameter and standard dimension optimization is now performed in the second phase. The synthesis of a multiple cantilever beam, introduced in Part I, was performed in accordance with the steps proposed by the MINLP optimization approach. This approach enables the obtaining of additional savings when compared to the one in Part I.