A bi-stage surrogate-assisted hybrid algorithm for expensive optimization problems

Zhihai Ren,Ying Tan,Chaoli Sun,Shufen Qin,Guochen Zhang

doi:10.1007/s40747-021-00277-1

Zhihai Ren, Ying Tan + Show 3 more

Open Access

https://doi.org/10.1007/s40747-021-00277-1

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Abstract

Surrogate-assisted meta-heuristic algorithms have shown good performance to solve the computationally expensive problems within a limited computational resource. Compared to the method that only one surrogate model is utilized, the surrogate ensembles have shown more efficiency to get a good optimal solution. In this paper, we propose a bi-stage surrogate-assisted hybrid algorithm to solve the expensive optimization problems. The framework of the proposed method is composed of two stages. In the first stage, a number of global searches will be conducted in sequence to explore different sub-spaces of the decision space, and the solution with the maximum uncertainty in the final generation of each global search will be evaluated using the exact expensive problems to improve the accuracy of the approximation on corresponding sub-space. In the second stage, the local search is added to exploit the sub-space, where the best position found so far locates, to find a better solution for real expensive evaluation. Furthermore, the local and global searches in the second stage take turns to be conducted to balance the trade-off of the exploration and exploitation. Two different meta-heuristic algorithms are, respectively, utilized for the global and local search. To evaluate the performance of our proposed method, we conduct the experiments on seven benchmark problems, the Lennard–Jones potential problem and a constrained test problem, respectively, and compare with five state-of-the-art methods proposed for solving expensive problems. The experimental results show that our proposed method can obtain better results, especially on high-dimensional problems.

Highlights

Many real-world optimization problems, such as aircraft design [25], rainfall prediction [13], and drug design [16], often require minutes, hours or days to take one performance evaluation on the designed parameters [12], which are called computationally expensive or time-consuming optimization problems
We propose a bi-stage surrogate-assisted hybrid algorithm for solving the computationally expensive problems, in which the social learning particle swarm optimization (SL-PSO), a PSO variant proposed by Cheng and Jin [2], is utilized to search for the optimal solution of the surrogate ensemble in the first stage
In this paper, we propose a bi-stage surrogate-assisted hybrid algorithm, called BiS-SAHA, in which a number of global searches will be conducted in sequence in the first stage by a surrogate ensemble assisted SL-PSO to explore different regions of decision space, while in the second stage, a local search using an radial basis function (RBF)-assisted differential evolution algorithm will be conducted after each global search to improve the exploitation capability to speed up finding an optimal solution

Summary

Introduction

Many real-world optimization problems, such as aircraft design [25], rainfall prediction [13], and drug design [16], often require minutes, hours or days to take one performance evaluation on the designed parameters [12], which are called computationally expensive or time-consuming optimization problems. In this paper, we propose a bi-stage surrogate-assisted hybrid algorithm, called BiS-SAHA, in which a number of global searches will be conducted in sequence in the first stage by a surrogate ensemble assisted SL-PSO to explore different regions of decision space, while in the second stage, a local search using an RBF-assisted differential evolution algorithm will be conducted after each global search to improve the exploitation capability to speed up finding an optimal solution. Note that the surrogate models used in every global search are different to each other because one solution in the population with the maximum uncertainty on the approximated value would be evaluated using the expensive problem and be used to update the model.

13: Output popg

Experimental study

Experimental results in different strategies

Conclusion

Compliance with ethical standards