The multilevel MINLP optimization approach to structural synthesis: the simultaneous topology, material, standard and rounded dimension optimization

The paper describes the simultaneous topology, material, standard and rounded dimension optimization of mechanical structures, performed by the Mixed-Integer Non-linear Programming (MINLP) approach. Beside the generation of an MINLP mechanical superstructure, the development of a general multilevel MINLP formulation for a mechanical superstructure is presented. The consideration of the discrete materials as well as standard and particularly rounded dimensions in structural synthesis significantly increases the combinatorics of the discrete optimization, which as a result may become too difficult to solve. A Linked Multilevel Hierarchical Strategy (LMHS) has been introduced for the solving of such large combinatorial problems. In order to decrease the effect of non-convexities, the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm has been applied. Four numerical examples of different complexities are presented to illustrate the proposed multilevel MINLP optimization approach: the optimization of two steel trusses, a composite I beam and a hydraulic steel roller gate Intake gate, erected in Aswan II, Egypt.