An efficient surrogate-assisted differential evolution algorithm for turbomachinery cascades optimization with more than 100 variables

Abstract

The CFD-based design optimization of turbomachinery cascades is a typical high-dimensional expensive black-box (HEB) problem. Specifically, to fully consider the interactions between vanes and stages and thus achieving desirable solutions, the cascades of two or more stages have to be optimized simultaneously. The number of variables can reach to more than 100 while the affordable CFD simulations within a design cycle can be only a few hundred or thousand. Hence, how to achieve the optimal design of turbomachinery cascades on budget is very challenging. To solve this problem, a generalized surrogate-assisted differential evolution (DE) algorithm is proposed, which is labeled as GSDE. In GSDE, radial basis function is incorporated into the population regeneration process, which helps to enhance the local exploitation in each iteration and thus achieving a good balance in between global and local search. By validating on benchmark functions ranging from 50 to 100 dimensions, the proposed GSDE algorithm is observed to obtain the true optimal solution with less than 1000 function calls and have far better convergence rate than other state-of-the-art algorithms. Furthermore, GSDE is then tested on the cascades design optimization of a 3.5-stage compressor with 126 variables. Within 1500 CFD evaluations, the total-to-total efficiency is increased by 1.104%. In contrast, classic DE algorithm achieves a similar efficiency gain with nearly 20,000 CFD evaluations. In other words, the computational cost of GSDE amount to only 1/13 of frequently-used evolutionary algorithms. Therefore, the efficiency of the proposed GSDE algorithm for solving high-dimensional turbomachinery optimization problems is well demonstrated.