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

Abstract

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 difficult to solve. A Linked Two-Phase MINLP Strategy has been developed to efficiently accelerate the solutions of highly combinatorial MINLP problems, performed by the Modified OA/ER algorithm. In the first phase, the strategy uses only continuous dimensions making it easier to find 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.

MINLP Optimization of Mechanical Structures

“…The first one introduces the topology, shape and sizing optimization of an aluminium truss cantilever, the second example shows the topology and discrete/standard sizing optimization of a 40 m long steel truss and the last one presents the topology and discrete/standard sizing optimization of a single-storey industrial steel building. The optimization of the structures is proposed to be carried out by a user-friendly version of the MINLP computer package MIPSYN, the successor of PROSYN [1] and TOP [2][3][4]16] . MIPSYN is the implementation of many advanced optimization techniques, most important of which are the Modified OA/ER algorithm and MINLP strategies.…”

“…These constraints describe relations between binary variables and define the structure's topology, materials and standard dimensions. It should be noted, that the comprehensive MINLP model formulation for mechanical structures may be found elsewhere [3,5] .…”

“…A two-phase MINLP optimization is proposed to accelerate the convergence of the mentioned algorithm. The optimizations are carried out by the MINLP computer package MIPSYN, the successor of PROSYN [1] and TOP [2][3][4] . Three examples are presented at the end of the paper.…”

Minlp Optimization of Steel Frames

“…Kravanja et al [27] have presented a general view of the MINLP approach to simultaneous topology and continuous parameter optimization. The development of suitable strategies to solve comprehensive, non-convex and highly combinatorial MINLP problems for the simultaneous topology, material, standard and rounded dimension optimization was introduced by Kravanja et al [28,29]. The applicability of the proposed MINLP optimization approach was supported by the examples such as the MINLP optimization of roller hydraulic steel gate Intake Gate of Aswan II for Egypt by Kravanja et al [30], the optimization of steel gates for Sultartangi project in Iceland [31] as well as the MINLP optimization of steel trusses and composite I beams by Kravanja et al [29].…”

“…The Modified Outer-Approximation/Equality-Relaxation algorithm is applied to carry out the structural optimization, Kravanja and Grossmann [32], Kravanja et al [28,29]. A two-phase MINLP optimization approach is proposed.…”