Multi-objective Optimization of Steel Frames with Added Viscous Dampers using Imperialist Competitive Algorithm

Document Type : Original Article


Department of Civil Engineering, Faculty of Engineering, University of Zanjan, Zanjan, Iran


Optimization is a big challenging task for engineers and designers. In practice, almost all of the engineering problems have more than one objective function, criterion to be optimized, therefore, multi-objective optimization procedure is necessary for many optimization problems. In this study, we presented the development of the Imperialistic Competitive Algorithm (ICA) to multi-objective optimal design of steel frames with dampers. Semi-active liquid viscous dampers are added to the steel frames to reduce the seismic response of structures subjected to earthquake loadings. The number and position of the dampers are considered as the design variables and the structural responses such as the acceleration of each floors, the maximum displacement of the top roof and the maximum relative displacement of the floors are the objective functions to be minimized simultaneously. A seven-story and a twelve-story 3D buildings are selected as the numerical examples to test the developed algorithm. The resultant Pareto-front sets are reported and discussed for the numerical examples. The obtained trade-offs demonstrate very smooth and reliable sets for all case studies. Meanwhile, the results indicate that the position of the dampers directly influences their effectiveness in decreasing the seismic response of structures. The maximum top floor displacement, the maximum story drifts and the maximum acceleration of each story have reduced in comparison to the uncontrolled condition, by respective values of 44.9%, 43.2% and 11.8%, for seven-story case study.


  • Imperialistic Competitive Algorithm (ICA) developed to multi-objective optimal design of steel frames with dampers.
  • Trade-off between objective functions (displacement-acceleration and drift-acceleration) are illustrated for case studies.
  • The optimal number and location of the dampers are obtained for the numerical examples.


Main Subjects

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  • Receive Date: 02 June 2022
  • Revise Date: 13 July 2022
  • Accept Date: 14 July 2022
  • First Publish Date: 14 July 2022