Robust Constrained Multi-objective Evolutionary Algorithm based on Polynomial Chaos Expansion for Trajectory Optimization

TL;DR

This paper introduces a robust multi-objective evolutionary algorithm that integrates polynomial chaos expansion to effectively handle probabilistic and dynamic constraints in trajectory optimization problems, demonstrated through supersonic transport landing scenarios.

Contribution

It presents a novel integrated method combining MOEA and PCE to solve robust constrained multi-objective problems with probabilistic constraints under dynamic conditions.

Findings

Successfully optimized SST landing trajectories under wind uncertainty.

Quantified the impact of probabilistic constraints on solution robustness.

Proposed robust flight control strategies based on optimized trajectories.

Abstract

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.