Binary-code genetic algorithms (BGA) have been used to obtain the optimum design for deep groove ball bearings, based on maximum fatigue life as an objective function. The problem has ten design variables and 20 constraint conditions. This method can find better basic dynamic loads rating than those listed in standard catalogues. However, the BGA algorithm requires a tremendous number of evaluations of the objective function per case to achieve convergence (e.g. about 5 200 000 for a representative case). To overcome this difficulty, a hybrid evolutionary algorithm by combining real-valued genetic algorithm (GA) with differential evolution (DE) is used together with the proper handling of constraints for this optimum design task. Findings show that the GA—DE algorithm can successfully find the better dynamic loads rating, about 1.3—11.1 per cent higher than those obtained using the traditional BGA. Moreover, the mean number of evaluations of the objective function required to achieve convergence is about 3011, using the GA—DE algorithm, as opposed to about 5 200 000 for a representative case using the BGA. Comparison shows the GA—DE algorithm to be much more effective and efficient than the BGA.
Optimum Design of Parallelogram Five-bar Manipulator for Dexterous Workspace by using ELEMAEF in Differential Evolution
