Robust Design of a Single Objective as Dual Sub-objectives Optimization

This chapter aims to develop a probabilistic approach of robust design with one objective, which is based on the probabilistic multi-objective optimization. In the treatment, the arithmetic mean value of performance utility indicator of the objective of an alternative is taken as one sub-objective, and the dispersion of performance utility indicator is taken as other sub-objective, the dual sub-objectives contribute their part of partial preferable probabilities to the alternative individually. Thus it becomes an optimization problem of dual sub-objectives simultaneously. Furthermore, three cases, i.e., the larger the better, the smaller the better and target the best, are formulated respectively. Moreover, ranking sequence of total preferable probabilities of alternatives is used to complete the optimization option. Subsequently, some application examples are given.