Overall design procedure

Fig. 2 shows the flowchart of the hybrid OC-GA method. The framework of a simple GA is adopted and an OC operator is added after the crossover and mutation operations. An initial population of designs is randomly generated to commence the design process. Structural analysis using SAP2000 (CSI, 2001) is then carried out on each individual design to determine the response performances. Once internal element forces and the drift responses of each individual design within a generation are found, fitness evaluations according to the design problem formulation Eq. (1) are conducted. In the fitness evaluation process, a penalty-based modified objective function is used. Any constraint violation found will reduce the fitness of a design and is reflected by a penalty function which is imposed on the objective function. The selection operator will determine survival candidate designs from the current generation and pass them to the next generation. The tournament selection with elitism mechanism is implemented in this hybrid method. If the convergence criteria are not satisfied, the genetic crossover and mutation operators together with the OC operation will then be applied to produce new designs. The hybrid OC-GA process can be repeated until the optimum solution is found.