Observations on the Topology of Pareto Frontiers with Implications for Design Decision Making
Matthew J. Daskilewicz, Brian German · 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition · 2012
Optimization of an aggregate objective function can be used to automate the steps of a decision-based design process. This approach requires the designer to specify preferences, in the form of coecients or weights in the objective function, a priori, but many designers instead prefer to explore the feasible design space before nalizing their preferences. Multiobjective optimization allows a weaker form of a priori preference articulation, but unlike single objective optimization, it does not fully solve the decision making problem|it only generates alternatives and still leaves it to the designer to choose one. While many references the in engineering literature discuss the process of nding non-dominated designs, few techniques exist for interpreting the set of non-dominated designs to aid in formulating preferences. In this paper, we examine some interesting topological features of Pareto frontiers whose objective functions are dierentiable with emphasis on three features: the signicance of partial derivatives of non-dominated objective vectors, the local dimensionality of the Pareto frontier, and the uniqueness of non-dominated objective vectors. An example engineering design problem is presented that illustrates the emergence of these properties and their interpretation.