Experimental Design

1.1. Structural Systems in Tall Buildings

Computational experiments with MAs were conducted for two classes of complex structural design problems: design of a wind bracing system (Problem I) and design of an entire steel structural system in a tall building (Problem II). They are illustrated in Figure 2. In Problem I, an optimal configuration of wind bracing elements was sought while keeping the configurations of all other members the same, i. e., all beams, columns, and supports had the same topological configurations in all experiments. On the other hand, an optimal configuration of all structural members of the steel structure in a tall building was sought in Problem II (see Figure 2b). Furthermore, the first problem was further subdivided into the following 3 subproblems:

• Problem Ia – design of a wind bracing system composed of simple X bracings and no bracings (empty cells) only.

• Problem Ib – design of a wind bracing system composed of K bracings and no bracings (empty cells) only.

• Problem Ic – design of a wind bracing system composed of all 7 types of wind bracing elements shown in Figure 3a.

This was motivated by the fact that high-performance solutions for each of these subproblems are not only qualitatively but also quantitatively different (Kicinger, 2004). The impact of these differences on the performance of MAs was investigated. Figure 3b-c represent types of beam and support elements in conducted experiments, respectively. Columns were assumed the same (fixed joints) in all design experiments reported in this paper (for Problems I and II). Hence, there were not evolved by evolutionary algorithms but their cross-sections were optimized by the local search. The optimal cross­sections of structural members were selected from the catalog of standard shapes specified in (American Institute of Steel Construction, 1989).

a) Wind bracing design b) Entire steel structural system design

The parameters of the design problems and their values are presented in Table 1. It shows that 30- story buildings with 5 bays were considered. The 1st order structural analysis and the local optimization of cross-sections of members were conducted by SODA (Grierson, 1989). SODA is a commercial computer system developed for the analysis, design, and optimization of steel structural systems. Table 2 shows the magnitudes of dead, live, and wind loads assumed in these calculations.

Table 1: Parameters of the design problems Table 2: Magnitudes of dead, live, and wind loads