Smart Pareto filter: obtaining a minimal representation of multiobjective design space

Multiobjective optimization is a powerful tool for resolving conflicting objectives in engineering design and numerous other fields. One general approach to solving multiobjective optimization problems involves generating a set of Pareto optimal solutions, followed by selecting the most attractive solution from this set as the final design. The success of this approach critically depends on the designer's ability to obtain, manage, and interpret the Pareto set—importantly, the size and distribution of the Pareto set. The potentially significant difficulties associated with comparing a significantly large number of Pareto designs can be circumvented when the Pareto set: (i) is adequately small, (ii) represents the complete Pareto frontier, (iii) emphasizes the regions of the Pareto frontier that entail significant tradeoff, and (iv) de-emphasizes the regions corresponding to little tradeoff. We call a Pareto set that possesses these four important and desirable properties a smart Pareto set. Specifically, a smart Pareto set is one that is small and effectively represents the tradeoff properties of the complete Pareto frontier. This article presents a general method to obtain smart Pareto sets for problems of n objectives, given previously generated sets of Pareto solutions. Under the proposed method, the designer uses a smart Pareto filter to control the size of the Pareto set and the degree of tradeoff representation among objectives. Importantly, the smart Pareto filter yields a Pareto set comprising a minimal number of solutions needed to adequately characterize the problem's tradeoff properties. In this article, the smart Pareto filter is analytically developed, and mathematical and physical examples are presented to illustrate the filter's effectiveness.