Multi-objective optimization (MDO) and differential geometry controlled pareto front solution spacing

Multidisciplinary Design Optimization (MDO) deals with the optimization of complex but typically only single-objective design problems. However, Multi-Objective Optimization (MOO) is becoming more and more important; thus it would be valuable to connect it with MDO. Within MOO, Weighted Sums (WS) is a standard solution method, but it may not produce a good spacing of solution points along the Pareto front. Here, using differential geometry tools which we have previously developed for MDO problems, we present a technique for intelligently spacing out Pareto solutions produced with WS. We then demonstrate our technique on two different analytical problems, discuss its current limitations, and identify several directions for future inquiry in order to further develop and expand this technique