Worst case deterministic feasibility and multiobjective robustness measures for engineering design optimisation

Nearly all real-world engineering design optimisation problems have parameters with uncontrollable variations. Such variations can significantly degrade the performance of optimum design solutions in terms of their feasibility and/or objective functions values, as obtained by multiobjective design optimisation methods. We present a deterministic feasibility and multiobjective optimisation approach, based on some worst case measures, for generating robustly non-dominated optimal solutions. Following this approach, for uncontrollable parameter variations, we can obtain a (1) feasibly robust design: for which no constraint is violated and (2) multiobjectively robust design: for which, with respect to a target and in a multiobjective sense, minimal distance between worst and best case points (or variability) and minimal distance of a worst case point from a target are obtained. We illustrate and verify the approach with a numerical and an engineering example.