Improved Solution Search Performance of Constrained MOEA/D Hybridizing Directional Mating and Local Mating

In this study, we propose an improvement to the direct mating method, a constraint handling approach for multi-objective evolutionary algorithms, by hybridizing it with local mating. Local mating selects another parent from the feasible solution space around the initially selected parent. The direct mating method selects the other parent along the optimal direction in the objective space after the first parent is selected, even if it is infeasible. It shows better exploration performance for constraint optimization problems with coupling NSGA-II, but requires several individuals along the optimal direction. Due to the lack of better solutions dominated by the optimal direction from the first parent, direct mating becomes difficult as the generation proceeds. To address this issue, we propose a hybrid method that uses local mating to select another parent from the neighborhood of the first selected parent, maintaining diversity around good solutions and helping the direct mating process. We evaluate the proposed method on three mathematical problems with unique Pareto fronts and two real-world applications. We use the generation histories of the averages and standard deviations of the hypervolumes as the performance evaluation criteria. Our investigation results show that the proposed method can solve constraint multi-objective problems better than existing methods while maintaining high diversity.

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

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.