Introducing Rough Set for Design Space Exploration and Optimization

Modern engineering design problems often involve computation-intensive analysis and simulation processes. Design optimization based on such processes is desired to be efficient, informative, and transparent. This work proposes a rough set based approach that can identify multiple subregions in a design space, within which all of the design points are expected to have a performance value equal to or less than a given level. The rough set method is applied iteratively on a growing sample set. A novel termination criterion is also developed to ensure a modest number of total expensive function evaluations to identify these sub-regions and search for the global optimum. The significances of the proposed method are two folds. First, it provides an intuitive method to establish the mapping from the performance space to the design space; given a performance level, its corresponding design region(s) can be identified. Such a mapping can be used to explore and visualize the entire design space. Second, it can be naturally extended to a global optimization method. It also bears potentials for more abroad applications to problems such as robust design optimization. The proposed method was tested with a number of test problems.