 
Summary: Equal Spacing of Pareto Points Using a Novel Method for CalculatEqual Spacing of Pareto Points Using a Novel Method for Calculating Derivativesing Derivatives
JeffreyJeffrey FikeFike
Aerospace Design LabAerospace Design Lab
Optimization applied to design is concerned with finding the "best" design.
There is usually more than one way of defining what is meant by "best". Multi
Objective optimization methods use these multiple competing definitions to find
designs that are Pareto optimal. A design is Pareto optimal if improvement with
respect to one objective requires a decrease in performance with respect to the
other objectives. These Pareto optimal points form a curve that is known as the
Pareto front.
The equal spacing procedure has been tested with objective functions of varying complexity. From
simple two variable analytic functions, to a more complex multivariable numerical example, to a
Supersonic Business Jet example. The results shown below are for the SSBJ case. The range
objective function uses preliminary design analysis routines. The sonic boom objective function
uses an initial pressure signature calculated using an aircraft shape factor. This initial pressure
signature is then propagated to the ground using the waveform parameter method. The figures below
show the results of the equal spacing procedure. Two different ways of defining equal spacing are
shown. Equal spacing defined in the design variable space and equal spacing defined in the
objective function space.
The method that has been developed produces N equally spaced Pareto optimal
