Keywords: genetic algorithm, optimization, multi-objective optimization, reinforced concrete, frame, design,.

An attempt to create an effective design procedure for reinforced concrete structures design goes through the history of Civil Engineering. We limit our attention to frame structures, which are the major part in this field as one of the basic building blocks of various construction systems.

It would be highly desirable to solve the whole design problem as one optimization task but the number of all possible solutions is too high for realistic frame structures. Therefore, it appears to be inevitable to split the process of structural design into two parts - the detailing of a reinforced concrete cross-section and the optimization of a whole structure in terms of basic structural characteristics like types of materials, dimensions of elements or profiles of steel bars.

The main goal of the first part is to fit an interaction diagram of a RC cross-section to a given combination of load cases. Efficient procedures for fast evaluation of internal forces for a general cross-section and stress-strain relationship were proposed in [1]. This task, for a given reinforcing bar diameter, thus reduces to a mere checking of admissible combinations of reinforcements.

The second part of a frame design focuses on the proportioning of building blocks. The goal is to find the best combination of discrete inputs that is, in an appropriate sense, optimal from the point of view of the total cost of the structure as well as maximum deflection of structural members.

For the single objective case, our experience [2,3] shows that a modified version of the genetic algorithm based procedure called Augmented Simulated Annealing method is capable of solving this combinatorial task. In this contribution, the multi-objective approach [4] is introduced to tackle several conflicting objectives. The Strength Pareto Approach algorithm [5] is used for the determination of trade-off surfaces for these two criteria.

The proposed procedure is applied to two model design problems. It is demonstrated that even for these rather elementary design tasks, both Pareto-optimal fronts are non-convex and non-smooth due to discrete nature of the optimization problem. This justifies the choice of the selected optimization strategy and suggests its applicability to more complex structural design problems.

1

R. Vondrácek and Z. Bittnar, " Area Integral of a Stress Function over a Beam Cross-Section, in " Proceedings of The Sixth International Conference on Computational Structures Technology", Civil-Comp Press, 2002. doi:10.4203/ccp.75.3

2

O. Hrstka, A. Kucerová, M. Leps and J. Zeman, " A competitive comparison of different types of evolutionary algorithms", in " Proceedings of the Sixth International Conference of Artificial Intelligence to Civil and Structural Engineering", Civil-Comp Press, 2001. doi:10.4203/ccp.74.37

3

K. Matous, M. Leps, J. Zeman and M. Sejnoha, " Applying genetic algorithms to selected topics commonly encountered in engineering practice", Computer Methods in Applied Mechanics and Engineering, 190, Vol. 13-14, 1629-1650, 2000. doi:10.1016/S0045-7825(00)00192-4

4

K. Deb, " Multi-Objective Optimization Using Evolutionary Algorithms", John Wiley & Sons, 2001.

5

E. Zitzler and L. Thiele, " Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach", IEEE Transactions on Evolutionary Computation, Vol. 3, No. 4, 257-271, 1999. doi:10.1109/4235.797969

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