  An integrated optimization method based on the constrained multi-objective
evolutionary algorithm (MOEA) and non-intrusive polynomial chaos expansion
(PCE) is proposed, which solves robust multi-objective optimization problems
under time-series dynamics. The constraints in such problems are difficult to
handle, not only because the number of the dynamic constraints is multiplied by
the discretized time steps but also because each of them is probabilistic. The
proposed method rewrites a robust formulation into a deterministic problem via
the PCE, and then sequentially processes the generated constraints in
population generation, trajectory generation, and evaluation by the MOEA. As a
case study, the landing trajectory design of supersonic transport (SST) with
wind uncertainty is optimized. Results demonstrate the quantitative influence
of the constraint values over the optimized solution sets and corresponding
trajectories, proposing robust flight controls.
