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An improved bagging ensemble surrogate-assisted evolutionary algorithm for expensive many-objective optimization

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Abstract

When the surrogate-assisted evolutionary algorithm is used to solve expensive many-objective optimization problems, the surrogate is used to approximate the expensive fitness functions. However, with the increase of the number of objectives, the approximate error of the surrogate will accumulate gradually, and the computational cost will also increase sharply. This paper proposes an improved bagging ensemble surrogate-assisted evolutionary algorithm (IBE-CSEA) to solve these problems. An ensemble classifier is used to classify the offspring instead of building the surrogate to approximate the fitness function of each objective. Firstly, a group of classification boundary individuals are selected one by one from the individuals evaluated by the expensive fitness function. All the individuals evaluated by the expensive fitness function are divided into two categories; Secondly, the individuals in these two categories are divided into the training set and the test set. The training set is used to train an improved bagging ensemble classifier. The test set is used to calculate the reliability of the classification; Finally, the classification results and the reliability are used to select the promising individuals for expensive fitness function evaluation. Compared with the current popular surrogate-assisted evolutionary algorithm, IBE-CSEA algorithm is more competitive.

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Data availability

The data used to support the findings of this study are available from the corresponding author upon request.

Abbreviations

ANN:

Artificial Neural Network

CPS-MOEA:

Classification and Pareto Domination based Multi-Objective Evolutionary Algorithm

CSEA:

Classification-based Surrogate-Assisted Evolutionary Algorithm

EA:

Evolutionary Algorithm

FE:

Fitness Evaluation

HV:

Hypervolume

IBE-CSEA:

Improved Bagging Ensemble Surrogate-Assisted Evolutionary Algorithm

IGD:

Inverse Generational Distance

K-RVEA:

Surrogate-Assisted Reference Vector Guided Evolutionary Algorithm

KTA2:

A Kriging-Assisted Two-Archive Evolutionary Algorithm

MAE:

Mean Absolute Error

MaOP:

Many-Objective Optimization Problem

MOEA/D-EGO:

Expensive Multi-Objective Optimization by MOEA/D with Gaussian Process Model

MOP:

Multi-Objective Optimization Problem

NSGA-III:

Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach

PF:

Pareto Front

RMSE:

Root Mean Squared Error

SAEA:

Surrogate-Assisted Evolutionary Algorithm

c :

Categories of solution.

C Pi :

Model prediction results.

d :

The number of the decision variables.

d i :

Deviation between the predicted value and the true value.

FE max :

Maximum number of evaluations.

K :

The number of the classification boundary solutions.

M :

The number of objectives.

N :

Population size.

P :

Population.

p m :

Mutation probability.

P R :

Classification boundary.

Q :

offspring population.

Q c :

The set of group c solutions.

rr :

Proportion of group A solutions.

S :

Training set.

S’ :

Test set.

T :

Model pool size.

Ω :

Realized non-dominated solution set.

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Acknowledgments

This work was supported by National Natural Science Foundation of China [No.51774228]; Natural Science Foundation of Shaanxi Province of China [2020JC-44]; National Natural Science Foundation of China [No.51974223]; National Natural Science Foundation of China [No.52074205].

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Author notes

  1. Xiaoyue Zhang contributed equally to this work.

Authors and Affiliations

  1. School of Management, Xi’an University of Architecture and Technology, Xi’an, China

    Qinghua Gu, Xiaoyue Zhang & Lu Chen

  2. Xi’an Key Laboratory for Intelligent Industrial Perception, Calculation and Decision, Xi’an University of Architecture and Technology, Xi’an, China

    Qinghua Gu, Xiaoyue Zhang & Lu Chen

  3. Department of Mathematics and Computer Science, Northeastern State University, Tahlequah, OK, USA

    Naixue Xiong

Authors
  1. Qinghua Gu
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  2. Xiaoyue Zhang
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  3. Lu Chen
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Correspondence to Qinghua Gu.

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Gu, ., Zhang, X., Chen, L. et al. An improved bagging ensemble surrogate-assisted evolutionary algorithm for expensive many-objective optimization. Appl Intell 52, 5949–5965 (2022). https://doi.org/10.1007/s10489-021-02709-4

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