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In this work, a volume and longitudinal stability-constrained multiobjective aerodynamic shape optimization is conducted. The aerodynamic shapes of lifting bodies are parameterized by using class function/shape function transformation parameterization method for maximum design flexibility. Hypersonic aerodynamic objectives and constraints are analyzed by solving the Reynolds-averaged Navier–Stokes equations in conjunction with a two-equation turbulence model. The Kriging technique is adopted to construct surrogate models aiming at reducing the computational cost. A two-stage method of infill sampling combined with multiobjective optimization is proposed to improve the performance of the surrogate models. Multiobjective evolutionary algorithm based on decomposition (MOEA/D) combined with penalty function method is employed to handle the multiobjective optimization problem with nonlinear constraints. The optimization results reveal that the two-stage method based on surrogates can reduce the computational cost significantly, and the accuracy of the surrogates around the Pareto front is sufficient. The two objectives are competing such that a set of Pareto optimal solutions are obtained, which are the best tradeoffs among the objectives. The unconstrained multiobjective optimization problem is also investigated with MOEA/D and nondominated sorting genetic algorithm II (NSGA-II) respectively to make a further comparison. The results show that the Pareto sets based on MOEA/D are more excellent and distribute more evenly than that obtained by NSGA-II. The computational efficiency of MOEA/D is about six times faster than that of NSGA-II. Lastly, aerodynamic characters of typical shape of Pareto front are analyzed under different flight conditions, and the results reveal favorable robustness of this shape.
Ma et al. (Wed,) studied this question.