Keywords: reinforced concrete, design, frame, optimization, evolutionary algorithms, genetic algorithms, handling of constraints.

Nowadays rapid growth of computer performance enables and encourages new developments not only in Civil Engineering and related areas. Especially, within the field of structural mechanics, the modeling of individual materials and therefore the prediction of structural response is more accurate than in past decades. However, developments in the practical design of structures do not reflect the above mentioned progress. It should be emphasized that every design, as such, is actually an optimization task, where the designer, in agreement with his experience, constraints and principles given by standards or Codes of Practice, is choosing the most suitable solution.

Therefore, the main goal of the presented paper is to introduce and enhance the current state of the art within the design of reinforced concrete (RC) structures. In particular, as one of the most frequent type of structures, the design of reinforced concrete frame structures will be investigated in more detail.

For better understanding of presented procedures it is worthwhile to introduce the forms of structural optimization. In accordance with Prof. Steven [1], four different forms of structural optimization can be distinguished: topology optimization, shape optimization, size optimization and topography optimization. Also layout optimization, as a connection between the topology and sizing, can be seen as a stand-alone form. Each can be solved with distinct optimization strategy and each form can include a reinforced concrete structure as a particular case. Note that solving real problems typically calls for combination of these forms.

From the mathematical point of view, the design can be understood as a multi-objective, constrained and often mixed integer - continuous optimization problem (CMOP). The traditional ways of solving the CMOP are based on summations and/or different weighting methods, i.e. conversion of the CMOP into the single criterion optimization. For example, the author of this contribution in his previous research, e.g. [2] or [3], used the total price of a structure as the unifying variable among different antagonistic constraints. As an unfavorable result, however, the multi-modal response of the objective function is obtained and is very difficult to solve. Another problems cited in the literature for traditional solutions for CMOPs are the sensitivity to the shape of the Pareto optimal front or a requirement of some knowledge about solved problem [4].

In the last decades, evolutionary algorithms proved to be a proper solution strategy for the above mentioned problems. They can cover large domains and discover multiple trade-offs during one optimization run. Therefore the main part of the paper is devoted to a description of evolutionary algorithms and their enhancement for CMOPs.

The final part of this contribution mainly deals with applications of presented optimization methods to the design of reinforced concrete frames, that appear in the scientific literature during last few decades.

1

Steven, G. (2003). Product and system optimization in engineering simulation. FENet Newsletter, January, 2003.

2

Lepš, M., Zeman, J., Bittnar, Z., Hybrid optimization approach to design of reinforced concrete frames. In Topping, B. H. V. and Bittnar, Z., editors, Proceedings of The Third International Conference on Engineering Computational Technology, pages 177-178, Prague, Czech Republic. Civil-Comp Press, 2002. doi:10.4203/ccp.76.70

3

M. Lepš and M. Šejnoha. New approach to optimization of reinforced concrete beams. Computers & Structures, 81(18-19):1957-1966, August, 2003. doi:10.1016/S0045-7949(03)00215-3

4

Zitzler, E., Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. PhD thesis, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland, 1999.

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