The fruit fly optimization algorithm (FOA) is a newly developed bio-inspired algorithm that has exhibited enormous values in engineering optimization. In this study, an effective multi-objective fruit fly optimization algorithm (MOFOA) incorporated with the Pareto dominance is investigated and applied to robust aerodynamic shape optimization considering uncertainties in the design process. In the MOFOA, the fruit flies are required to perform solution explorations within an adaptive search scope by flying around the Pareto non-dominated solutions. An enhanced clustering evolution mechanism of combining the cooperative local search and differential evolution operator is elaborately designed to enrich the exploratory capacities for complex optimization. Paired with the search strategy, the non-dominated sorting technique considering the quality as well as uniform distribution of Pareto solutions is adopted to deal with the multiple objectives. To generate high-quality and uniformly spread-out Pareto non-dominated solutions, the roulette wheel selection (RWS) operator based on crowding distance is employed to guide the selection processes of individuals throughout various stages of the MOFOA. The effectiveness and superiority of MOFOA are demonstrated by the comparative studies on several benchmark functions. Finally, a robust aerodynamic design system for combining the MOFOA optimizer with a Kriging-based surrogate model and full Navier–Stokes computation is advantageously implemented to perform shape optimization on a transonic airfoil using the Taguchi robust design methodology that emphasizes the inherent variability while improving engineering productivity. The design results show that the robust design, compared with the single-point design, is capable of producing a set of robust solutions that are significantly less sensitive to input variations by capturing the Pareto-optimal front with respect to the criteria of aerodynamic performance and its stability.

果蝇优化算法（FOA）是一种新开发的生物启发算法，在工程优化中具有巨大的价值。在这项研究中，研究了结合帕累托优势的有效多目标果蝇优化算法（MOFOA），并将其应用于考虑设计过程中不确定性的鲁棒空气动力学形状优化。在MOFOA中，需要果蝇通过在Pareto非主导解决方案周围飞行来在自适应搜索范围内执行解决方案探索。精心设计了一种将协同局部搜索和差分进化算子相结合的增强聚类进化机制，以丰富复杂优化的探索能力。结合搜索策略，考虑质量和帕累托解决方案的均匀分布的非支配排序技术被用来处理多个目标。为了生成高质量且均匀分布的帕累托非支配解决方案，基于拥挤距离的轮盘赌选择（RWS）运算符用于指导MOFOA各个阶段的个人选择过程。MOFOA的有效性和优越性通过对几个基准功能的比较研究得到证明。最后，使用Taguchi稳健的设计方法，强调了固有的可变性，同时提高了工程效率，因此可以实现将MOFOA优化器与基于Kriging的替代模型和完整的Navier–Stokes计算相结合的稳健的空气动力学设计系统，从而对跨音速翼型进行形状优化。设计结果表明，与单点设计相比，该鲁棒性设计能够通过捕获有关空气动力学性能和性能的帕累托最优前沿来产生一组鲁棒性解决方案，这些解决方案对输入变化的敏感性大大降低。其稳定性。