Optimization with constraints considering polymorphic uncertainties

In this contribution, a numerical design strategy for the optimization under polymorphic uncertainty is introduced and applied to a self-weight minimization of a framework structure. The polymorphic uncertainty, which affects the constraint function of the optimization problem, is thereby modeled in terms of stochastic variables, fuzzy sets, and intervals to account for variability, imprecision and insufficient information. The stochastic quantities are computed using polynomial chaos expansion resulting in a purely fuzzy-valued formulation of the constraint functions which can be computed using α-cut optimization. Afterward, the constraint function can be interpreted in a possibilistic manner, resulting in a flexible formulation to include expert knowledge and to achieve a robust design.