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Top1. Introduction
The dynamic behavior of an engineering structure mainly depends on their fundamental natural frequencies. Thus, limitations on the fundamental natural frequencies can minimize the destructive effect on the engineering structures. Also, engineering structures should be as light as possible. However, minimization of mass has an adverse effect with the frequency constraints and increases the further difficulty in structural optimization. Therefore, an efficient optimization method is desirable to design trusses subjected to frequency constraints, and continuous efforts are put by the researchers in this aspect.
Optimization of truss structure can be categorized into three types: size optimization, shape optimization, and topology optimization. Size optimization deals to set the best cross-sectional areas, while the nodal positions of the truss structure are assumed to design variables in shape optimization. Many scholars have been investigating simultaneous shape and size optimization of trusses subjected to multiple natural frequency constraints, yet this is an emerging field of research, and it remain not completely addressed so far. Bellagamba and Yang (1981) reported pioneering work in this field that addressed mass minimization of truss subjected to in frequency constraints. Similarly, Grandhi and Venkayya (1988) and Wang et al. (2004) investigated an optimality criterion (OC) based on the uniform Lagrangian density approach. A hybrid version of the simplex search method and genetic algorithm (GA) called a niche genetic hybrid algorithm (NGHA) used by Wei et al. (2005). Gomes (2011) utilized Particle swarm optimization (PSO). Kaveh and Zolghadr (2011) presented a charged system search (CSS) and enhanced CSS. Wei et al. (2011) proposed a parallel GA. Kaveh and Zolghadr (2012) proposed a hybrid version of CSS and big bang-big crunch (CSS-BBBC) with trap recognition ability. Miguel and Miguel (2012) presented a harmony search (HS) and firefly algorithm (FA). Gholizadeh and Barzegar (2013) proposed a sequential HS algorithm. A democratic particle swarm optimization (DPSO) employed by Kaveh and Zolghadr (2014a). Kaveh and Zolghadr (2014b) investigated nine optimization algorithms. Pholdee and Bureerat (2014) tested the performance of twenty-four optimization algorithms. Zuo et al. (2014) proposed a hybrid OC-GA. Khatibinia and Naseralavi (2014) used an orthogonal multi-gravitational search algorithm. Kaveh and Mahdavi (2014) and Kaveh and Mahdavi (2015) employed a colliding-bodies optimization (CBO) and two-dimensional CBO respectively. Kaveh and Ghazaan (2015a) proposed hybridized PSO algorithms. Kaveh and Ghazaan (2015b) employed enhanced colliding bodies optimization. Gonçalves et al. (2015) search group algorithm. Tejani et al. (2016a) proposed an adaptive symbiotic organisms search. In their second paper, Tejani et al. (2016b) proposed a modified sub-population teaching-learning-based optimization algorithm. Farshchin et al. (2016) presented multi-class teaching–learning-based optimization. On the other hand, optimization truss structures subjected to static and dynamic constraints has been studied by a few other scholars (Lin et al., 1982; Tong and Liu, 2001; Xu et al., 2003; Jin and De-yu, 2006; Noilublao and Bureerat, 2011; Kaveh and Zolghadr, 2013; Savsani et al., 2016a; 2016b).