Optimal design of single-story steel building structures based on parametric MINLP optimization Stojan Kravanja a, ⁎, Goran Turkalj b , Simon Šilih a , TomažŽula a a Faculty of Civil Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia b Faculty of Engineering, University of Rijeka, Vukovarska 58, 51000 Rijeka, Croatia abstract article info Article history: Received 22 April 2011 Accepted 13 November 2012 Available online 12 December 2012 Keywords: Optimization Topology optimization Discrete sizing optimization Mixed-integer non-linear programming MINLP Single-story industrial steel building The paper presents an optimal design of single-story industrial steel building structures based on the parametric mixed-integer non-linear programming (MINLP) optimization approach and Eurocode specifica- tions. The optimal design of the structures was investigated for factors which have significant influence on the structure mass: vertical variable load on the structure, horizontal variable load, structure span, structure height, type of standard cross-sections and strength of structural steel. For this purpose, parametric MINLP optimization was performed for a number of combinations between dif- ferent parameters, i.e. different values of the mentioned influence factors. The single-story steel building superstructure was generated and the MINLP optimization model developed. The objective function of the structure's mass was defined. The modified outer-approximation/equality-relaxation (OA/ER) algorithm and the three-phase MINLP strategy were used to perform the optimization. The minimal possible structure mass, the optimal topology and the optimal standard cross-sections were obtained through each individual MINLP optimization. Based on the obtained optimal results, the recommended optimal design for single-story/single-bay structures and the comparative mass diagrams were developed. © 2012 Elsevier Ltd. All rights reserved. 1. Introduction The paper discusses an optimal design of single-story industrial steel building structures based on the mathematical programming approach. Single-bay structures are considered here, composed from equal main frames with pitched roof beams, and mutually connected with purlins and rails. The structures investigated in the paper are built up from hot rolled I sections. The optimization of this simple type of steel structures has fre- quently been investigated in the past because of their wide use in engi- neering practice. The first two references, referred to the optimization of frame structures by Maxwell [1] in year 1869 and Michell [2] in 1904, be- long to the first references ever referred in the area of optimization. Due to significant developments in computing and computer hardware in the last four decades, a variety of optimization techniques and efficient algorithms has been developed and applied. Recently, O'Brien and Dixon [3] have proposed linear programming for the optimal design of pitched roof frames, Guerlement et al. [4] have introduced a discrete minimum weight design for single-story steel structures by using a DSO algorithm and Kamal et al. [5] have presented a modified method of feasible directions for the optimization of one-bay portal steel frames. Several authors have searched for an optimal design of steel frames by using different algorithms: Saka [6,7] used a genetic algorithm and a har- mony search algorithm, Toropov et al. [8] used a genetic algorithm, Foley et al. [9] used the advanced analysis and object-oriented evolutionary computation algorithm and Liu et al. [10] used the genetic evolutionary structural optimization algorithm. Hernández et al. [11] have considered the minimal weight design of steel portal frames with software devel- oped for structural optimization, and Farkas and Jarmai [12] have presented a volume and cost optimization of frames with the help of Rosenbrock's Hillclimb algorithm. Sobieszczanski-Sobieski [13] and Lesniak [14] have presented the optimization of cross-sections in steel structures by using a linear decomposition method. Burns et al. [15] have applied a single termed monomial method to structural design ap- plications. Issa et al. [16] have used a distributed genetic algorithm to perform optimization of haunched rafter pitched roof steel portal frames. It should be noted that all the mentioned authors dealt with dis- crete sizing optimization at fixed structural topologies. One of the latest studies in this field is the work reported by Žula et al. [17] and Kravanja and Žula [18], which introduces simultaneous topology and standard sizing optimization of single-story steel building structures, performed by the mixed-integer non-linear programming approach. The latter two references consider steel structures with main frames and purlins only. While Ref. [17] handles the mass optimization of the structure, Ref. [18] deals with the cost optimization. Journal of Constructional Steel Research 81 (2013) 86–103 ⁎ Corresponding author at: Faculty of Civil Engineering, University of Maribor, Smetanova 17, SI-2000 Maribor, Slovenia. Tel.: +386 2 2294 300; fax: +386 2 2524 179. E-mail address: stojan.kravanja@um.si (S. Kravanja). 0143-974X/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jcsr.2012.11.008 Contents lists available at SciVerse ScienceDirect Journal of Constructional Steel Research