Study on structural optimum design based on qualitative sensitivities

An optimum design method is considered as a method whose results are the most reasonable from various standpoints in the prescribed mathematical formulation. However, its formulations present difficulties in choosing objective functions, setting allowances to constraints and so on, because they are greatly concerned with the results of optimization. In this study, we proposed concepts of qualitative sensitivities and qualitative optimality compared to quantitative concepts, as well as a general algorithm of the qualitative optimization method. We newly defined three kinds of fuzzy language, assigned fuzzy sets to each of them and assigned them to each candidate for discrete design variable. We proposed fuzzy reasoning rules by using these two kinds of fuzzy sets. We also extended the proposed algorithm to multi-objective optimization. Through the numerical example of a single-objective problem, we obtained almost the same solution as in quantitative methods, and efficiencies were confirmed for this case. Also through the example of a multiobjective problem, the new method was shown to have more flexibility in determining the preferred objective functions compared to the conventional method.