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MINLP approach to the optimization of steel frames
Klanšek, Uroš ; Žula, Tomaž ; Kravanja, Stojan
The paper presents the discrete dimension optimization of unbraced rigid steel plane frames. The optimization of frames is performed using Mixed-Integer Non-linear Programming approach, MINLP. Since ...the MINLP denotes a combined discrete-continuous optimization technique, it performs the discrete optimization of discrete dimensions simultaneously with the continuous optimization of continuous parameters. The Modified Outer-Approximation/Equality-Relaxation algorithm is applied to execute the optimization. A two-phase MINLP optimization is proposed to start with the continuous optimization of the frame shape, while standard dimensions are relaxed temporary into continuous parameters. When the optimal shape is found, standard sizes of crosssections are re-established and the simultaneous shape and discrete dimension optimization is then continued until the optimal solution is found. The finite element equations are defined as the equality constraints for the secondorder elastic structural analysis. Design constraints for steel members are formulated accordingly to Eurocode 3. Besides the theoretical basis, an example of the optimization of a steel frame is presented at the end of the paper.
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