基于非支配排序的并行加点方法研究及应用

Research and application of parallel infill sampling method based on non-dominated sorting

代理优化方法可以大幅提升高精度数值优化的效率,而加点方法对于优化结果和效率非常重要。并行加点方法一次可以添加多个训练样本,从而可以充分发挥计算资源的利用率,并且提高效率。在包含子优化的紧密式代理优化框架上将预测值、预测方差和期望改善(EI)函数值两两结合作为子优化目标,构建3种多目标并行加点方法,提出基于非支配排序的并行加点样本的策略。以SC(six-hump camel back)函数和2维GN(Griewank)函数、5维Rosenbrock函数及10维HD1(high-dimension 1)函数作为无约束优化算例,以7维G9函数作为约束优化算例,将构建的3种多目标并行加点方法与混合并行加点方法进行对比分析,结果表明:多目标并行加点方法效果较好。采用多目标并行加点方法、混合并行加点方法及基于计算流体力学(CFD)的遗传算法开展了二维多段翼型起飞状态的升阻比优化。优化结果表明:在升力系数不减小的约束下,多目标并行加点方法经过少量CFD评估,得到的优化结果使升阻比提升了14%,证明多目标并行加点方法在工程问题中的适用性。

The surrogate-based optimization method can greatly improve the efficiency of high-precision numerical optimization,while the infill sampling method is very important for the optimization result and efficiency.Several training samples can be infilled using the parallel infill sampling approach in a single step,fully using computer resources and increasing efficiency.In this article,based on the surrogate-based optimization framework including sub-optimization,three multi-objective parallel infill methods are constructed,using the prediction value,prediction variance and expected improvement(EI)function value as sub-optimization objectives.Besides,a strategy for selecting samples based on non-dominated sorting is proposed.Next,take the six-hump camel back(SC)function,the 2-dimensional griewank(GN)function,the 5-dimensional Rosenbrock function and the 10-dimensional highdimension 1(HD1)function as unconstrained optimization examples,and the 7-dimensional G9 function as the constrained optimization example,the three multi-objective parallel infill sampling methods are compared with the hybrid parallel infill sampling methods.The outcomes demonstrate the superiority of the multi-objective parallel infill technique.Finally,the lift-drag ratio optimization of the two-dimensional multi-foil at take-off state was carried out by using the multi-objective infill sampling method,the hybrid parallel infill method and the genetic algorithm based on computational fluid dynamics(CFD).The optimization findings demonstrate the usefulness of the parallel infill sampling method in engineering issues by increasing the lift-to-drag ratio by 14%after a minimal amount of CFD evaluation under the constraint that the lift coefficient does not drop.