Design Space Reduction for Multi-Objective Optimization and Robust Design Optimization Problems

Modern engineering design often involves computation-intensive simulation processes and multiple objectives. Engineers prefer an efficient optimization method that can provide them insights into the problem, yield multiple good or optimal design solutions, and assist decision-making. This work proposed a rough-set based method that can systematically identify regions (or subspaces) from the original design space for multiple objectives. In the smaller regions, any design solution (point) very likely satisfies multiple design goals. Engineers can pick many design solutions from or continue to search in those regions. Robust design optimization (RDO) problems can be formulated as a biobjective optimization problem and thus in this work RDO is considered a special case of multi-objective optimization (MOO). Examples show that the regions can be efficiently identified. Pareto-optimal frontiers generated from the regions are identical with those generated from the original design space, which indicates that important design information can be captured by only these regions (subspaces). Advantages and limitations of the proposed method are discussed.