Quantifying tradeoffs to reduce the dimensionality of complex design optimization problems and expedite trade space exploration

Multi-objective optimization is increasingly being employed to solve complex design problems. However, multi-objective optimization problems might be formulated with extraneous objective functions that could be eliminated without affecting the final solution. Furthermore, as the number of objectives increases, the effort required to visualize and explore the resulting solution set, herein referred to as the trade space, increases. Although visual analytic techniques exist to facilitate analytical reasoning for exploring a high-dimensional trade space through graphical interfaces, existing techniques often rely upon exhaustive two-dimensional representations to identify all tradeoffs. Yet, the knowledge of the tradeoffs among competing objectives is important for decision-making because it fosters learning from the trade space and hence aids preference formation. In this paper, an index to quantify the tradeoff between any two objectives from multi-objective optimization is presented and incorporated into a visual analytic technique that can be used as a tool for reducing the dimensionality of the problem formulation. The tradeoff index reveals the conflicting and correlated objectives; hence, it can be used to expedite trade space exploration by focusing cognitive effort only on those objectives that have tradeoff. The utility and efficiency of the proposed technique is illustrated through application to a Pareto approximate solution set from a benchmark optimization problem with eight objectives. The results of this exercise are compared to the solutions obtained using other existing visual analytic techniques found in the literature.