RESEARCH PAPER Seismic Optimum Design of Steel Structures Using Gradient- Based and Genetic Algorithm Methods Jalal Akbari 1 • Mohammad Sadegh Ayubirad 1 Received: 23 September 2015 / Revised: 24 November 2015 / Accepted: 10 May 2016 Ó Iran University of Science and Technology 2016 Abstract Optimum design of structures under time-vari- able loadings is a difficult task. Time-dependent behavior of constraints and cost of gradients calculations could be mentioned when applying time history loadings in the optimization problems. To overcome these difficulties, the response spectra as a seismic demand are used instead of using time history acceleration in the structural modeling. In this paper, the P-Delta effects are considered in the finite-element modeling of the frames. Furthermore, many practical constraints are included in the optimization for- mulation according to the Iranian national building code (Standard N. 2800). The developed MATLAB-based computer program is utilized for optimization of the low, intermediate- and relatively high-rise braced and un-braced steel frames. The obtained results of sequential quadratic programing (SQP) method are compared with the results of genetic algorithm (GA) technique for guarantying the global optimal designs. Because of the inexpensive costs of SQP method in comparison with genetic algorithm tech- nique, SQP method could be confidently applied for obtaining the global optimum designs of the steel frames. Keywords Seismic optimum design  Steel frames  Response spectrum analysis  Sequential quadratic programming (SQP)  Genetic algorithm (GA) 1 Introduction The optimum designs of steel frames are often cost mini- mization with performance and construction criteria. Optimization techniques in structural engineering could be divided generally into three distinct methods: (1) mathe- matical/gradient-based methods, (2) optimality criteria methods and (3) stochastic search algorithms. Mathematical techniques are based on the gradients of functions in the solution space. Therefore, the algorithms need continuous functions representing the objective and constraint(s). Numerous researches have been conducted using the mathematical optimization methods [1–5]. Memari and Madhkhan [6] applied the feasible directions method to optimize the braced and un-braced steel frames using equivalent static loading. They concluded that braced frames are more economical than un-braced ones. Akbari and Sadoughi [7] employed SQP method for finding the optimum design of the structures under time history acceleration. They transformed acceleration time histories into the equivalent static loads (ESLs). The optimality criteria (OC) method is based on the combination of indirect Kuhn–Tucker conditions of non- linear mathematical programming with Lagrangian multi- pliers. The OC approach has been the subject of many studies [8]. H.Moharrami and S.A.Alavinasab [9] proposed an improved optimality criteria method for optimum design of steel frames. Due to the rapid development of computer facilities, new techniques such as genetic algorithms (GA) have been suggested in the field of structural optimization. One of the most important advantages of GA in optimal design of steel frames is using the discrete design variables and its capa- bilities for finding the global optimums. Optimization using GA has been successfully applied to structural optimization & Jalal Akbari akbari@malayeru.ac.ir; jalal.akbari@gmail.com Mohammad Sadegh Ayubirad m.s.ayubirad@gmail.com 1 Department of Civil Engineering, Malayer University, Malayer, Iran 123 Int J Civ Eng DOI 10.1007/s40999-016-0088-0 Author's personal copy