Asian Journal of Civil Engineering

, Volume 19, Issue 7, pp 877–891 | Cite as

Optimal seismic design of steel moment frames by un-damped multi-objective vibrating particles system

  • Mohsen ShahrouziEmail author
  • Hamed Farah-Abadi
Original Paper


Structural design usually comes up with objectives that compete with each other. The present optimization problem is formulated by applying minimal weight and drift ratio in spectral analysis of steel frames. It is further solved introducing an undamped multi-objective vibrating particle search. It not only takes benefit of VPS walks but also utilizes special evolutionary and multi-objective operators such as mutation and non-dominated sorting to update an auxiliary memory of the best solutions. A variety of frame examples with 2–24 stories and 3–6 bays are treated to cover a practical range of aspect ratios. Performance of the proposed MOVPS is further evaluated in the treated examples via comparison with two popular multi-objective methods: NSGA-II and MOPSO. In this regard, some metrics are traced for multi-objective optimization in addition to generating boxplots of the C-function to compare relative dominance priority between each pair of methods. According to the present study, Pareto fronts are similar for low-rise frames as the latter two metrics converge with iterations; however, in taller frames, either Pareto front or performance metrics exhibit more difference. Consequently, the most extended, the utopia–closest and the fastest optimal results were obtained by MOVPS, NSGA-II and MOPSO, respectively.


Multi-objective vibrating particles search Spectral design Steel buildings Moment frames Performance metrics Pareto optimization 


Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Civil Engineering, Faculty of EngineeringKharazmi UniversityTehranIran

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