Multiple criteria optimization for the robust design of quantitative parameters

This paper proposes a new method for optimizing multiple responses in robust design with quantitative parameters. A stochastic achievement function is developed based on the achievement function used in the reference point approach of multiple criteria optimization, and the Cholesky decomposition of the covariance matrix of the estimated responses. Nondominated solutions that are closest to the reference points specified by designers can be obtained by maximizing the stochastic achievement function. The new method guarantees the optimality of the solution for problems in which the measurements are embedded in noise. It is more flexible, and has a substantially lower computation cost than a previous approach for this problem. The proposed method is integrated into an interactive procedure that can assist the designer in finding the optimal solution that conforms to his/her preferences