Journal of Constructional Steel Research 65 (2009) 36–43 www.elsevier.com/locate/jcsr Optimum design of steel sway frames to BS5950 using harmony search algorithm M.P. Saka ∗ Middle East Technical University, Engineering Sciences Department, 06531 Ankara, Turkey Received 14 June 2007; accepted 22 February 2008 Abstract Harmony search method based optimum design algorithm is presented for the steel sway frames. The harmony search method is a numerical optimization technique developed recently that imitates the musical performance process which takes place when a musician searches for a better state of harmony. Jazz improvisation seeks to find musically pleasing harmony similar to the optimum design process which seeks to find the optimum solution. The optimum design algorithm developed imposes the behavioral and performance constraints in accordance with BS5950. The member grouping is allowed so that the same section can be adopted for each group. The combined strength constraints considered for a beam–column take into account the lateral torsional buckling of the member. The algorithm presented selects the appropriate sections for beams and columns of the steel frame from the list of 64 Universal Beam sections and 32 Universal Column sections of the British Code. This selection is carried out so that the design limitations are satisfied and the weight of steel frame is the minimum. The number of design examples considered to demonstrate the efficiency of the algorithm is presented. c  2008 Elsevier Ltd. All rights reserved. Keywords: Optimum structural design; Combinatorial optimization; Stochastic search technique; Harmony search algorithm; Minimum weight; Steel frame 1. Introduction Structural design optimization of steel frames generally requires selection of steel sections for its beams and columns from a discrete set of practically available steel section tables. This selection should be carried out in such a way that the steel frame has the minimum weight or cost while the behavior and performance of the structure is within the limitations described by the code of practice. Such problems fall into the subject of discrete optimization in which finding the optimum solution is a difficult task. Early optimum design algorithms based on a wide range of powerful mathematical programming methods have failed to satisfy the needs of practicing engineers. One of the reasons for this was that most of the mathematical programming techniques developed are based on the assumption of continuous design variables while in reality most of the structural optimization design variables are discrete in nature. Although some mathematical programming based methods have been developed for discrete optimum design ∗ Tel.: +90 312 210 2382; fax: +90 312 210 4462. E-mail address: mpsaka@metu.edu.tr. problems they are not very efficient for obtaining the optimum solution of the large size practical design problems [1,2]. In recent years, structural optimization witnessed the emergence of novel and innovative design techniques. These stochastic search techniques make use of the ideas taken from nature and do not suffer the discrepancies of mathematical programming based optimum design methods. The basic idea behind these techniques is to simulate the natural phenomena such as survival of the fittest, immune system, swarm intelligence and the cooling process of molten metals into a numerical algorithm. These methods are non-traditional search and optimization methods and they are very suitable and powerful in obtaining the solution of combinatorial optimization problems [3–22]. They do not require the derivatives of the objective function and constraints and they use probabilistic transition rules not deterministic rules. A large number of optimum structural design algorithms have been developed in recent years which are based on these effective, powerful and novel techniques [22–42]. One recent addition to these techniques is the harmony search algorithm [41–47]. This approach is based on the musical performance process that takes place when a musician 0143-974X/$ - see front matter c  2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2008.02.005