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A population-based incremental learning (PBIL) method is proposed to search for both robust and global optimal solutions of an inverse problem in which there are inevitable tolerances on the decision variables. To reduce the computational costs of the proposed algorithm, a methodology for evaluating the expectancy measures and a philosophy for worst-case solutions are proposed. Moreover, a novel mechanism for selecting the performance metrics is introduced to enable the algorithm to find both global and robust optimal solutions in a single run. Two numerical examples are reported to validate the proposed algorithm.