RESEARCH PAPER An efficient method for reliability-based design optimization of nonlinear inelastic steel space frames V. H. Truong 1 & Seung-Eock Kim 1 Received: 4 September 2016 /Revised: 13 January 2017 /Accepted: 3 February 2017 # Springer-Verlag Berlin Heidelberg 2017 Abstract This paper proposes an effective numerical pro- cedure for reliability-based design optimization (RBDO) of nonlinear inelastic steel frames by integrating a harmo- ny search technique (HS) for optimization and a robust method for failure probability analysis. The practical ad- vanced analysis using the beam-column approach is used for capturing the nonlinear inelastic behaviors of frames, while a detail implement of HS for discrete optimization of steel frames is introduced. The failure probability of structures is evaluated by using the combination of the improved Latin Hypercube (IHS) and a new effective im- portance sampling (EIS). The efficiency and accuracy of the proposed procedure are demonstrated through three mathematical examples and five steel frames. The results obtained in this paper prove that the proposed procedure is computationally efficient and can be applied in practical design. Furthermore, it is shown that the use of nonlinear inelastic analysis in the optimization of steel frames yields more realistic results. Keywords Reliability-based optimization . Steel frame . Advanced analysis . Harmony search . Reliability analysis . Latin hypercube . Importance sampling 1 Introduction The optimization of steel frames has been attracting the interest of many researchers in recent years since this approach reduces costs and guarantees performance of structures. In optimiza- tion, the frame weight is minimized by selecting the lightest cross-sectional area from the standard lists of sections (e.g. AISC, Eurocode, etc.), while the performance requirements are still satisfied. The optimization of steel frames is hence a discrete optimization and requires metaheuristic algorithms for solving discrete variable spaces. Based on considering or ig- noring probabilistic constraints, the optimization of steel frames is divided into deterministic design optimization (DDO) and reliability-based design optimization (RBDO), respectively. Many researches concerning DDO of steel frames have been carried out in the literature with various algorithms and techniques being proposed (Hasançebi et al. 2009, 2010a, b; Kripakaran et al. 2011; Doğan and Saka 2012; Alberdi and Khandelwal 2015). In these researches, considerable effort has been used to improve and develop metaheuristic optimization algorithms since these techniques are accepted as the standard design optimization tools for the foreseeable future (Saka and Geem 2013). Some of the well-known metaheuristic optimi- zation algorithms are ant colony optimization (ACO) (Camp et al. 2005 ), genetic algorithm (GA) (Rajeev and Krishnamoorthy 1992), harmony search (HS) (Lee and Geem 2004), particle swarm optimization (PSO) (Perez and Behdinan 2007), simulated annealing (SA) (Balling 1991), Tabu search (TS) (Bland 1995 ), etc. The review of metaheuristic algorithms for steel frames is presented by Saka and Geem (2013). Although there has been significant improvement in the study of metaheuristic algorithms, most of their applications are limited to linear frames where the member-based design method is used for evaluating strength * Seung-Eock Kim sekim@sejong.ac.kr V. H. Truong truongviethung82@sju.ac.kr 1 Department of Civil and Environmental Engineering, Sejong University, 98 Gunja Dong, Gwangjin Gu Seoul 143-747, South Korea Struct Multidisc Optim DOI 10.1007/s00158-017-1667-7