On Controlling the Extent of Robust Solution in Uncertain Environment in Multiobjective Optimization

In design and optimization problems, a solution which is stable enough in its variability in presence of the perturbation of the parameters/variables of the model is called robust. In engineering design optimization, the designer may sacrifice the optimal solution for the robust one in order to set a stable system design. Although in literature there are methods for capturing such solution, they do not provide the designer with a direct and system-atic control over the level of the required robustness. In this paper a new robust design methodology is introduced in the context of the multiobjective optimization problem. The proposed approach not only is able to capture the robust design but also can introduce a manipulation for controlling the extent of the design’s robustness based on the designer preferences while dealing with the fuzzy and interval values uncertainty. The presented method is different form its other counterparts as it does not average the vicinity of the current design nor change/add any new constraint to keep the feasibility of the design de-spite of variation. On the contrary, only a special tunable objective function is constructed to incorporate the preference of the designer on the extent of the demanded robustness efficiently. The benefits of the new approach are discussed and, to show its effectiveness, it is tested on a well known engineering design problem and the results are presented. The proposed approach is of immediate use for any engineering design, where the designer would like to study a set of robust solution with different levels and to choose the most appropriate ones amongst. I