Keywords: genetic algorithm, simulated annealing, discrete optimization, reinforced concrete structures, automated frame design, parallel algorithms.

An attempt to create an effective design procedure of a reinforced concrete structure goes through the history of a mankind. In present times an emphasis is put on this problem due to widespread of RC structures in Civil Engineering especially in Eastern Europe. Frames are the major part in this field as one of the basic building block of various construction systems. Hence, our long-time effort is to prove the reliability and potency of a design tool capable of automated checking and optimization of RC beams and frames. In our previous works [2,3] many types of design procedures together with variety of genetic algorithm-based optimizers were tested. In this contribution, we present a combination of a parallel version of the augmented simulated annealing method [4] with one representative of deterministic methods.

It would be highly desirable to solve the whole problem as one optimization task but the number of all possible solutions is too high for realistic structures. From this point of view comes an idea to separate 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 an arbitrary stress-strain relationship were proposed in [5]. The task of designing the cross-section reinforcement for a given reinforcing bar diameter thus reduces to a mere checking of admissible combinations of reinforcement.

The second part of a frame design is devoted to the proportioning of building blocks. Mathematically, the goal is to find the best combination of discrete inputs but concurrently to pass certain conditions such as structural requirements, ultimate and serviceability constraints on one side or low price, workability and good appearance on the other side. Our experience shows that genetic algorithm-based strategies are capable of solving this combinatorial task. The modified version of the Augmented Simulated Annealing method together with differential operator outperformed many traditional methods [6]. The main principles of this method are the survival of the fittest strategy together with the simulated annealing principle, an integer coding, a differential cross-over and Gaussian mutation.

The disadvantage of all structural optimization problems is the computational complexity which is the result of both structural FEM analysis and optimization part. Our solution to this obstacle comes from the implicit parallelization of genetic algorithms [4]. The program is divided into an optimization and an analysis part and in this way is implemented in the cluster of PCs. Preliminary results outline the direction of future research.

1

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

2

M. Leps, K. Matous, and Z. Bittnar. Genetic algorithm in optimization of reinforced concrete beam. Acta Polytechnica, 39(2):145-155, 1999.

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(13-14), 1629-1650, 2000. doi:10.1016/S0045-7825(00)00192-4

4

S.W. Mahfoud and D. E. Goldberg. Parallel recombinative simulated annealing - A genetic algorithm. Parallel Computing, 21(1):1-28, 1995. doi:10.1016/0167-8191(94)00071-H

5

R. Vondrácek: Numerical methods in nonlinear concrete design. Diploma thesis, Czech Technical University in Prague, 2001

6

O. Hrstka, A. Kucerová, M. Leps, and J. Zeman. A competitive comparison of different types of evolutionary algorithms. In B.V.H. Topping and B. Kumar, editors, The Sixth International Conference on the Applications of Artificial Intelligence to Civil and Structural Engineering, pages 87-88. Civil-Comp Press, 2001. doi:10.4203/ccp.74.37

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