Techniques for Construction of Pareto Frontier Approximations
Dhanesh Padmanabhan · 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference · 2005
The main aim of the work is to obtain Pareto frontier approximations that not only are good fits to the Pareto solutions but are also capable of predicting the feasibility of performance targets accurately. A standard least squares technique need not give intuitive and meaningful approximations because they need not satisfy certain derivative conditions that characterize a true trade-o or Pareto behavior for competing objectives. A constrained least square technique has been developed to address this issue. Moreover, for problems with discrete variables one can have multiple Pareto frontiers and hence an issue arises if a single approximation or multiple approximations (one for each discrete configuration) have to be used to characterize the Pareto frontiers. Feasibility assessment techniques have also been developed that use the Pareto frontier approximations to predict the feasibility of performance targets. Some of the feasibility assessment techniques also impose additional bound constraints to adequately capture the infeasible domains. Various approximation techniques were applied to Pareto solutions obtained from an analytic I-Beam problem and a preliminary vehicle design problem. Validation studies were also performed where various feasibility assessment techniques were used to predict the feasibility of benchmark points. For the implementation studies performed in this work, the constrained least squares technique gave better prediction accuracies than a traditional least squares when supplemented with additional bound constraints. Multiple approximations gave better R 2 values than single approximations.