KT-EGO: A Knowledge Transfer Assisted Efficient Global Optimization Algorithm for Solving High-Dimensional Expensive Black-Box Problems

Qineng Wang; Liming Song; Yun Chen; Guangjian Ma; Zhendong Guo; Jun Li

cs.CESep 28, 2026

KT-EGO: A Knowledge Transfer Assisted Efficient Global Optimization Algorithm for Solving High-Dimensional Expensive Black-Box Problems

Authors: Qineng Wang, Liming Song, Yun Chen, Guangjian Ma, Zhendong Guo, Jun Li

Organizations: Institute of Turbomachinery, Xi’an Jiaotong University,Xi’an,Shaan Xi, China · AVIC Shenyang Engine Design Institute, Shenyang, Liao Ning, China

Abstract

Many engineering problems involve optimizing a high-dimensional expensive black-box (HEB) design space. To solve such problems efficiently, we propose a knowledge transfer assisted efficient global optimization (EGO) algorithm, labeled as 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, we propose a surrogate-based data fusion strategy in 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 our proposed algorithm, it is compared against the state-of-the-art algorithms over 12 benchmark functions and a 28-dimensional engineering optimization for the design of compressor blade, which fully validates the effectiveness of the KT-EGO for solving HEB problems.

Figures & tables

Figure 1: Decomposition and combination strategy in one cycle of the Nash-EGO algorithm

Figure 2: The framework of the KT-EGO algorithm

Figure 3: Surrogate-based data fusion strategy and related subset design space optimization process

Figure 4: Comparison of PCE with low-order polynomials and kriging surrogate

Panel of Figure 5 — Figure 5: The average convergence curves of 7 algorithms on 30-D benchmark functions

Panel of Figure 6 — Figure 6: The average convergence curves of 7 algorithms on 60-D benchmark functions

Panel of Figure 7 — Figure 7: The average convergence curves of the KT-EGO algorithm and its 2 variants algorithms.

Geometric definition	variable index
control coefficient in 0% span	$x_{1},\cdots,x_{5}$
control coefficient in 25% span	$x_{6},\cdots,x_{10}$
control coefficient in 50% span	$x_{11},\cdots,x_{15}$
control coefficient in 75% span	$x_{16},\cdots,x_{20}$
control coefficient in 100% span	$x_{21},\cdots,x_{25}$
circumferential translation parameter	$x_{27}$

Table 1: Design variables in engineering test case

Figure 8: The sketch map of the 3D parameterization method

Condition name	Value
equivalent rotational speed[rpm]	17188.7
number of rotor blades	36
rotor blade aspect ratio	1.19
tip clearance gap[mm]	0.356
inlet total temperature[K]	288.15
inlet total pressure[Pa]	101325

Table 2: Design conditions

Figure 9: The mesh of Rotor 37 blade with $4\times{10^{6}}$ nodes

Figure 10: The optimization convergence curves of the engineering test case.

Panel of Figure 11 — Figure 11: The comparison of feature curves of optimization results of different algorithms and the baseline design

Panel of Figure 12 — Figure 12: The limit streamlines the suction surface of the optimal designs with different algorithms and the baseline design.

Black-Box Optimization

Black-box optimization finds high-quality solutions when objectives can only be queried, not directly analyzed or differentiated.

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Lawrence Livermore National Laboratory, CA, USA · National University of Singapore, Singapore · National Laboratory of the Rockies, CO, USA

Sep 13, 2026J/K move · Enter open · S save

A Dynamic Aggregation Strategy Enhanced Efficient Global Optimization Algorithm for Solving High-Dimensional Turbomachinery Design Problems

Qineng Wang, Zhendong Guo, Yun Chen, Guangjian Ma+2

Institute of Turbomachinery, Xi’an Jiaotong University, No.28, West Xianning Road, 710049, Xi’an, China · AVIC Shenyang Engine Design Institute, Fangjialan Road, Wanlian Street, 110066, Shenyang, China

Surrogate-Assisted Optimization Bayesian Optimization

Open paper AskPDF arXiv

In order to solve the high-dimensional (

d \geq 30

) expensive black-box problems within budget, an efficient global optimization (EGO) algorithm with a dynamic aggregation strategy is proposed, labeled as DA-EGO. Specifically, the DA-EGO decomposes the original high-dimensional design space into a set of low-dimensional subspaces for efficient surrogate-based optimization search, and the optimal solutions of subspaces are combined as an elite point for the global search. Most importantly, the subspaces are not fixed. Instead, the subspace variables are updated in each iteration, according to the variable interaction analyses in the sub- and full-spaces. The perturbation method and the analysis of variance are used to detect variable interactions. To further accelerate the optimization progress, the searching ranges of subspaces are also adaptively adjusted according to the analyses of subspace optimization results of the previous iteration. Tests on 21 benchmark instances, comprising seven functions at 30, 60, and 90 dimensions, show that DA-EGO is effective on separable and partially separable problems under a budget of 1500 function evaluations. Its advantage is case-dependent: on the non-separable shifted Rosenbrock function, GSGA performs better at 60 and 90 dimensions, while the 30-dimensional results are statistically comparable to IKAEA and GSGA. Moreover, the advantage of DA-EGO is also seen in the aerodynamic optimization of a transonic rotor blade with 28 variables as well as the compressor stage optimization with 60 variables. With the above, the effectiveness of the proposed DA-EGO has been well demonstrated.

Abstract

Black-Box Optimization

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