Application of Self-Adaptive Population Rao Algorithms to Optimization of Steel Grillage Structures

  • Maksym Grzywiński Faculty of Civil Engineering, Czestochowa University of Technology, Czestochowa, Poland
  • Tayfun Dede Department of Civil Engineering, Karadeniz Technical University, Trabzon, Turkey
  • Barbaros Atmaca Department of Civil Engineering, Karadeniz Technical University, Trabzon, Turkey


The self-adaptive population Rao algorithms (SAP-Rao) are employed in this study to produce the optimal designs for steel grillage structures. The size variables in the optimization problem consist of the cross-sectional area of the discrete W-shapes of these beams. The LRFD-AISC design code was used to optimize the constrained size of this kind of structure. The solved problem’s primary goal is to determine the grillage structure’s minimum weight. As constraints, it is decided to use the maximum stress ratio and the maximum displacement at the inner point of the steel grillage structure. The finite element method (FEM) was employed to compute the moment and shear force of each member, as well as the joint displacement. A computer program for the study and design of grillage structures, as well as the optimization technique for SAP-Rao, was created in MATLAB. The outcomes of this study are compared to earlier efforts on grillage structures. The findings demonstrate that the optimal design of grillage structures can be successfully accomplished using the SAP-Rao method described in this paper.


Minimum weight, Grillage structures, Layout and size optimization, Discrete variables, SAP-Rao algorithms, MATLAB,


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Nov 7, 2023
How to Cite
GRZYWIŃSKI, Maksym; DEDE, Tayfun; ATMACA, Barbaros. Application of Self-Adaptive Population Rao Algorithms to Optimization of Steel Grillage Structures. Computer Assisted Methods in Engineering and Science, [S.l.], v. 30, n. 4, p. 505–520, nov. 2023. ISSN 2956-5839. Available at: <>. Date accessed: 23 june 2024. doi:
CMM-SolMech 2022