A dynamic surrogate-assisted evolutionary algorithm framework for expensive structural optimization

  • Mingyuan Yu
  • Xia Li
  • Jing LiangEmail author
Research Paper


In the expensive structural optimization, the data-driven surrogate model has been proven to be an effective alternative to physical simulation (or experiment). However, the static surrogate-assisted evolutionary algorithm (SAEA) often becomes powerless and inefficient when dealing with different types of expensive optimization problems. Therefore, how to select high-reliability surrogates to assist an evolutionary algorithm (EA) has always been a challenging task. This study aimed to dynamically provide an optimal surrogate for EA by developing a brand-new SAEA framework. Firstly, an adaptive surrogate model (ASM) selection technology was proposed. In ASM, according to different integration criteria from the strategy pool, elite meta-models were recombined into multiple ensemble surrogates in each iteration. Afterward, a promising model was adaptively picked out from the model pool based on the minimum root of mean square error (RMSE). Secondly, we investigated a novel ASM-based EA framework, namely ASMEA, where the reliability of all models was updated in real-time by generating new samples online. Thirdly, to verify the performance of the ASMEA framework, two instantiation algorithms are widely compared with several state-of-the-art algorithms on a commonly used benchmark test set. Finally, a real-world antenna structural optimization problem was solved by the proposed algorithms. The results demonstrate that the proposed framework is able to provide a high-reliability surrogate to assist EA in solving expensive optimization problems.


Evolutionary algorithm Adaptive surrogate model Expensive optimization Reliability 




finite element analysis


computational fluid dynamics


evolutionary algorithm


surrogate-assisted evolutionary algorithm


adaptive surrogate model


ASM-based evolutionary algorithm


particle swarm optimization


differential evolution


particle swarm optimization based on ASM


differential evolution based on ASM


Gauss process model


Kriging model


polynomial response surface model


radial basis function model


Shepard model


artificial neural network


support vector machine


radial basis neural network


extreme learning machine


high-frequency simulation software


weighted average surrogate


optimum weight surrogate


design of experiment


Latin hypercube sampling


root of mean square error


absolute error


prediction residual error sum of square


successful run


value to reach



the number of meta-models


the number of elite meta-models


the number of variables


the size of the population


the size of the strategy pool


the train set in the database


the test set in the database

G or Gm

the evolutional generation or maximum G

FES or FESmax

the function evaluations or maximum FES

c1 and c2

learn rates in PSO


scale factor in DE


crossover rate in DE

xmin and xmax

variable space


evaluation function based on ASM


evaluation function based on simulation


global optimum


local optimum


the number of G-opt


the number of L-opt


the ASMPSO algorithm


the ASMDE algorithm


the number of sampling points


return less

L, W, h,

the length, width, height of the patch


edge distance

Greek symbols


scale factor in T1 and T2


inertia weight in PSO




Funding information

This research was supported by the National Natural Science Foundation of China (Grant Nos. 61803054 and 61876169) and the State Education Ministry and Fundamental Research Funds for the Central Universities (2019 CDJSK 04 XK 23).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.The School of AutomationChongqing UniversityChongqingChina
  2. 2.The School of the Third Affiliated HospitalZhengzhou UniversityZhengzhouChina
  3. 3.The School of Electrical EngineeringZhengzhou UniversityZhengzhouChina

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