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The automated search techniques from the field of numerical optimization provide tools that enable optimal design of electronic packages in general, and solder joints in particular. However, there is considerable difficulty in using these procedures for solder joints since the estimation of fatigue life is computationally very expensive. In this paper, global approximation schemes based on designed experiments, linear regression models, and artificial neural network models are developed to approximate the fatigue life as a function of solder joint design parameters. Since these approximate surfaces are inexpensive to evaluate, their use with the numerical optimization techniques leads to a computationally efficient method for optimizing electronic packages. The developed techniques are demonstrated using the 225 I/0 Plastic Ball Grid Array (PBGA) package, manufactured by Motorola, Inc. An exact optimization of the solder joints (without approximations) is also carried out and used as a basis for comparing the accuracy and efficiency of the developed methods.