Artificial Bee Colony (ABC) algorithm in the design optimization of RC continuous beams
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Artificial Bee Colony (ABC) algorithm in the design optimization of RC continuous beams M. M. Jahjouh · M. H. Arafa · M. A. Alqedra
Received: 19 May 2012 / Revised: 13 December 2012 / Accepted: 20 December 2012 / Published online: 2 March 2013 © Springer-Verlag Berlin Heidelberg 2013
Abstract The objective of this study is to obtain the optimum design for reinforced concrete continuous beams in terms of cross section dimensions and reinforcement details using a fine tuned Artificial Bee Colony (ABC) Algorithm while still satisfying the constraints of the ACI Code (2008). The ABC algorithm used in this paper has been slightly modified to include a Variable Changing Percentage (VCP) that further improves its performance when dealing with members consisted of multiple variables. The objective function is the total cost of the continuous beam which includes the cost of concrete, formwork and reinforcing steel bars. The design variables used are beam width, beam height, number and diameter of: bottom continuous reinforcing bars, bottom cutoff reinforcing bars, top continuous reinforcing bars and top cutoff reinforcing bars as well as the diameter of stirrups. Four RC beams of varying complexity are presented and optimized. The first three beams are used to fine tune the control parameters of the ABC algorithm, whereas the fourth beam was previously optimized by Arafa et al. (J Artif Intell 76–88, 2011) and is presented here to prove the superiority of this relatively new optimization algorithm. Keywords Optimization · RC · Beams · Artificial · Bee · Colony
M. M. Jahjouh () · M. H. Arafa · M. A. Alqedra Department of Civil Engineering, The Islamic University of Gaza, Gaza, Palestine e-mail: [email protected]
1 Introduction Material cost is an important issue in the design and construction of reinforced concrete structures. The main factors affecting cost are the amount of concrete and steel reinforcement required. It is, therefore, desirable to make reinforced concrete structures lighter, while still fulfilling serviceability and strength requirements. In addition to material cost, labor and formwork costs are significant (Wight and MacGregor 2008; Camp et al. 2003). Good engineers are those capable of designing low cost structures without compromising its function or violating structural constraints. The traditional approach to design reinforced concrete members does not fully optimize the use of materials. Most designs are based on the prior experience of the engineer, who selects cross-section dimensions and material grades by comparing past experience. This gives rise to fixed rulesof-thumb for preliminary designs (Paya-Zaforteza et al. 2009). This process is typically of high cost in terms of time, human effort and material usage, which makes structural optimization procedures using artificial intelligence a clear alternative to designs based on experience (Paya-Zaforteza et al. 2009; Coello et al. 1997). The optimum design of RC beams has been investigated by many researchers. For
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