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The robustness index of the objective function explored for robust optimization.The robustness of an objective function seeks an insensitive design although there are variations on design variables or parameters.Based on this viewpoint, a variety of robustness indices on the objective function have been developed.Nevertheless, the application of the index is not prevalent yet due to some limitations.Therefore, it is important to identify characteristics and drawbacks of the existing robustness indices.In this paper, a comparative study on the robustness index of an objective function is conducted to verify the characteristics and the limits.To reach the purpose, mathematical examples are utilized.The examples have both a deterministic optimum and a robust optimum.Then, evaluation and analysis of the robustness indices are conducted by using the examples.For the results, useful information about each index is obtained.Also, based on the comparison, some important issues for robustness of the objective function are discussed.