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Mathematical Problems in Engineering
Volume 2013, Article ID 271031, 33 pages
Review Article

Mathematical and Metaheuristic Applications in Design Optimization of Steel Frame Structures: An Extensive Review

1Department of Civil Engineering, University of Bahrain, P.O. Box 32038, Isa Town, Bahrain
2Department of Energy and Information Technology, Gachon University, Seongnam 461-701, Republic of Korea

Received 28 September 2012; Accepted 4 December 2012

Academic Editor: Sheng-yong Chen

Copyright © 2013 Mehmet Polat Saka and Zong Woo Geem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The type of mathematical modeling selected for the optimum design problems of steel skeletal frames affects the size and mathematical complexity of the programming problem obtained. Survey on the structural optimization literature reveals that there are basically two types of design optimization formulation. In the first type only cross sectional properties of frame members are taken as design variables. In such formulation when the values of design variables change during design cycles, it becomes necessary to analyze the structure and update the response of steel frame to the external loading. Structural analysis in this type is a complementary part of the design process. In the second type joint coordinates are also treated as design variables in addition to the cross sectional properties of members. Such formulation eliminates the necessity of carrying out structural analysis in every design cycle. The values of the joint displacements are determined by the optimization techniques in addition to cross sectional properties. The structural optimization literature contains structural design algorithms that make use of both type of formulation. In this study a review is carried out on mathematical and metaheuristic algorithms where the effect of the mathematical modeling on the efficiency of these algorithms is discussed.