en Applications Applications پژوهشي Research <span style="font-size:11pt"><span style="line-height:150%"><span style="font-family:Calibri,sans-serif"><span style="font-size:12.0pt"><span style="line-height:150%"><span new="" roman="" style="font-family:" times="">In order to evaluate the damage state, value, and position of structural members more accurately, a multi-objective optimization (MO) method is utilized that is based on changes in natural frequency. <span style="color:#1f1f1f">The multi-objective optimization dynamic-based damage detection method is first introduced. Two objective functions for optimization are then introduced in terms of changing the </span>natural frequencies and mode shapes<span style="color:#1f1f1f">. The multi-objective optimization problem (MOP) is formulated by using the two objective functions. Three considered MO</span> algorithms consist of Colliding Bodies Optimization<span style="color:#1f1f1f"> (MOCBO), Particle Swarm Optimization (MOPSO), and non-dominated sorting genetic algorithm (NSGA-II) to achieve the best structural damage detection. The proposed methods are then applied to three planar steel frame structures. Compared to the traditional optimization methods utilizing the single-objective optimization (SO) algorithms, the presented methods provide superior results.</span></span></span></span></span></span></span> Damage detection, Natural frequency, Optimization algorithms, Multi-objective optimizations, frame structures. 337 354 http://ijoce.iust.ac.ir/browse.php?a_code=A-10-6463-2&slc_lang=en&sid=1 V.R. Mahdavi 180031947532846002517 180031947532846002517 No Department of Civil and Geomechanics Engineering, Arak University of Technology, Arak, Iran A. Kaveh Alikaveh@iust.ac.ir 180031947532846002518 180031947532846002518 Yes School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran-16, Iran