High-dimensional Expensive Black-box Research Articles

A surrogate-assisted evolutionary algorithm with clustering-based sampling for high-dimensional expensive blackbox optimization

A surrogate-assisted evolutionary algorithm with clustering-based sampling for high-dimensional expensive blackbox optimization

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

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.

KT-EGO: a knowledge transfer assisted efficient global optimization algorithm for solving high-dimensional expensive black-box problems

Many engineering problems involve optimizing a high-dimensional expensive black-box (HEB) design space. To solve such problems efficiently, a knowledge transfer (KT) assisted efficient global optimization (EGO) algorithm is proposed, called the KT-EGO, which extends the EGO algorithm for solving problems over higher dimensions (i.e.d>20). Specifically, the original design space is divided into several low-dimensional subset design spaces. More importantly, in order to extract information from the subset design spaces to accelerate the progress of full optimization, a surrogate-based data fusion strategy is proposed in the KT-EGO. And further, a searching strategy with an adaptive variable range is devised to enhance the exploitation of promising areas. To show the effectiveness of the proposed algorithm, it is compared against state-of-the-art algorithms over 12 benchmark functions and a 28-dimensional engineering optimization for the design of a compressor blade, which fully validates the effectiveness of the KT-EGO for solving HEB problems.

CFD-driven symbolic identification of algebraic Reynolds-stress models

A CFD-driven deterministic symbolic identification algorithm for learning explicit algebraic Reynolds-stress models (EARSM) from high-fidelity data is developed building on the frozen-training SpaRTA algorithm of [1]. Corrections for the Reynolds stress tensor and the production of transported turbulent quantities of a baseline linear eddy viscosity model (LEVM) are expressed as functions of tensor polynomials selected from a library of candidate functions. The CFD-driven training consists in solving a blackbox optimization problem in which the fitness of candidate EARSM models is evaluated by running RANS simulations. The procedure enables training models against any target quantity of interest, computable as an output of the CFD model. Unlike the frozen-training approach, the proposed methodology is not restricted to data sets for which full fields of high-fidelity data, including second flow order statistics, are available. However, the solution of a high-dimensional expensive blackbox function optimization problem is required. Several steps are then undertaken to reduce the associated computational burden. First, a sensitivity analysis is used to identify the most influential terms and to reduce the dimensionality of the search space. Afterwards, the Constrained Optimization using Response Surface (CORS) algorithm, which approximates the black-box cost function using a response surface constructed from a limited number of CFD solves, is used to find the optimal model parameters. Model discovery and cross-validation is performed for three configurations of 2D turbulent separated flows in channels of variable section using different sets of training data to show the flexibility of the method. The discovered models are then applied to the prediction of an unseen 2D separated flow with higher Reynolds number and different geometry. The predictions of the discovered models for the new case are shown to be not only more accurate than the baseline LEVM, but also of a multi-purpose EARSM model derived from purely physical arguments. The proposed deterministic symbolic identification approach constitutes a promising candidate for building accurate and robust RANS models customized for a given class of flows at moderate computational cost.

Mode-Pursuing Sampling Method Using Discriminative Coordinate Perturbation for High-Dimensional Expensive Black-Box Optimization

Abstract This article presents a novel mode-pursuing sampling method using discriminative coordinate perturbation (MPS-DCP) to further improve the convergence performance of solving high-dimensional, expensive, and black-box (HEB) problems. In MPS-DCP, a discriminative coordinate perturbation strategy is integrated into the original mode-pursuing sampling (MPS) framework for sequential sampling. During optimization, the importance of variables is defined by approximated global sensitivities, while the perturbation probabilities of variables are dynamically adjusted according to the number of optimization stalling iterations. Expensive points considering both optimality and space-filling property are selected from cheap points generated by perturbing the current best point, which balances between global exploration and local exploitation. The convergence property of MPS-DCP is theoretically analyzed. The performance of MPS-DCP is tested on several numerical benchmarks and compared with state-of-the-art metamodel-based design optimization methods for HEB problems. The results indicate that MPS-DCP generally outperforms the competitive methods regarding convergence and robustness performances. Finally, the proposed MPS-DCP is applied to a stepped cantilever beam design optimization problem and an all-electric satellite multidisciplinary design optimization (MDO) problem. The results demonstrate that MPS-DCP can find better feasible optima with the same or less computational cost than the competitive methods, which demonstrates its effectiveness and practicality in solving real-world engineering problems.

Development of a metamodel assisted sampling approach to aerodynamic shape optimization problems

A new metamodel-assisted sampling search approach applied to the aerodynamic shape optimization of turbomachinery airfoils is presented in this paper. The proposed methodology integrates a non-uniform rational B-spline (NURBS) geometry representation, a twodimensional flow analysis, and an improved metamodel driven optimization algorithm named approximated promising region identifier (APRI), which represents a momentous advancement of the existing space exploration techniques specifically for the high-dimensional expensive black-box (HEB) problems. The novel optimization method prospects the whole design space by generating sample points, reporting evaluating information using a surrogate model, and then focusing the search in the most promising region by deploying more agents. Using the integration of these adaptive tools and methods, the optimization results are considerably promising in terms of computational efficiency and performance enhancement of the turbomachinery blade airfoil shape in both design and off-design conditions.