提出了一种可在1000次性能评估以内高效求解100维及以上多目标设计问题的高效优化算法MO-GSGA/D，并以之为基础开展了向心涡轮多学科优化设计研究。首先，针对向心涡轮设计所面临的昂贵、高维、多目标设计瓶颈，提出的MO-GSGA/D采用基于权重的分解策略将复杂多目标问题转化为一系列动态单目标子问题；并引入径向基函数代理模型辅助进化过程，通过局部搜索与个体预筛选策略，大幅减少了昂贵的真实CFD评估次数；同时，结合非支配排序与拥挤度距离机制更新种群，以保证Pareto解集分布的均匀性。通过100维的ZDT2和DTLZ2标准测试函数进行收敛性测试，结果表明MO-GSGA/D算法相比MOEA/D、NSGA-II等经典多目标优化算法具有更快的收敛速度。以MO-GSGA/D算法为核心，结合叶型三维参数化造型方法对向心涡轮进行参数化，开展了包含16个变量的等熵总总效率最大/叶根最大应力最小的多目标设计优化。优化后，所获得的最优方案等熵总总效率提高了1.12%，叶根最大应力降低了17%。在显著提升向心涡轮气动性能的同时有效提升了向心涡轮的强度性能。由此，验证了所提出的向心涡轮多学科优化设计方法的有效性。
An efficient multi-objective optimization algorithm, MO-GSGA/D(Multi-objective Generalized Surrogate-assisted Genetic Algorithm based on Decomposition), is proposed to effectively solve high-dimensional (100 dimensions and above) multi-objective design problems within a limited budget of 1,000 performance evaluations. Based on this algorithm, a multidisciplinary design optimization (MDO) study for radial inflow turbines was conducted. First, to address the bottlenecks of expensive, high-dimensional, and multi-objective design in radial inflow turbines, the proposed MO-GSGA/D utilizes a weight-based decomposition strategy to transform complex multi-objective problems into a series of dynamic single-objective subproblems. A Radial Basis Function (RBF) surrogate model is introduced to assist the evolutionary process. By implementing local search and individual pre-screening strategies, the number of computationally expensive high-fidelity CFD evaluations is significantly reduced. Meanwhile, non-dominated sorting and crowding distance mechanisms are incorporated to update the population, ensuring the uniformity of the Pareto front distribution. Convergence tests on 100-dimensional ZDT2 and DTLZ2 benchmark functions demonstrate that MO-GSGA/D achieves faster convergence compared to classical algorithms such as MOEA/D and NSGA-II. Subsequently, taking MO-GSGA/D as the core and integrating it with a 3D blade parametric modeling method, a multi-objective optimization with 16 design variables was performed to maximize isentropic total-to-total efficiency and minimize maximum root stress. The optimized results show an increase of 1.12% in isentropic total-to-total efficiency and a 17% reduction in maximum root stress. This study effectively enhances the structural strength of the radial turbine while significantly improving its aerodynamic performance, thereby validating the effectiveness of the proposed multidisciplinary optimization design method for radial inflow turbines.
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