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A cooperative approach to efficient global optimization

Author

Listed:
  • Dawei Zhan

    (Southwest Jiaotong University)

  • Jintao Wu

    (Southwest Jiaotong University)

  • Huanlai Xing

    (Southwest Jiaotong University)

  • Tianrui Li

    (Southwest Jiaotong University)

Abstract

The efficient global optimization (EGO) algorithm is widely used for solving expensive optimization problems, but it has been frequently criticized for its incapability of solving high-dimensional problems, i.e., problems with 100 or more variables. Extending the EGO algorithm to high dimensions encounters two major challenges: the training time of the Kriging model goes up rapidly and the difficulty of solving the infill optimization problem increases exponentially as the dimension of the problem increases. In this work, we propose a simple and efficient cooperative framework to tackle these two problems simultaneously. In the proposed framework, we first randomly decompose the original high-dimensional problem into several sub-problems, and then train the Kriging model and solve the infill optimization problem for each sub-problem. Context vectors are used to link the sub-problems such that the Kriging models are trained and the infill optimization problems are solved in a cooperative way. Once all the sub-problems have been solved, we start another random decomposition again and repeat the divide-and-conquer process until the computational budget is reached. Experiment results show that the proposed cooperative approach can bring nearly linear speedup with respect to the number of sub-problems. The proposed approach also shows competitive optimization performance when compared with the standard EGO and six high-dimensional versions of EGO. This work provides an efficient and effective approach for high-dimensional expensive optimization.

Suggested Citation

  • Dawei Zhan & Jintao Wu & Huanlai Xing & Tianrui Li, 2024. "A cooperative approach to efficient global optimization," Journal of Global Optimization, Springer, vol. 88(2), pages 327-357, February.
  • Handle: RePEc:spr:jglopt:v:88:y:2024:i:2:d:10.1007_s10898-023-01316-6
    DOI: 10.1007/s10898-023-01316-6
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    References listed on IDEAS

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    1. D. Huang & T. Allen & W. Notz & N. Zeng, 2006. "Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models," Journal of Global Optimization, Springer, vol. 34(3), pages 441-466, March.
    2. Ivo Couckuyt & Dirk Deschrijver & Tom Dhaene, 2014. "Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization," Journal of Global Optimization, Springer, vol. 60(3), pages 575-594, November.
    3. Dawei Zhan & Huanlai Xing, 2020. "Expected improvement for expensive optimization: a review," Journal of Global Optimization, Springer, vol. 78(3), pages 507-544, November.
    4. Mickaël Binois & David Ginsbourger & Olivier Roustant, 2020. "On the choice of the low-dimensional domain for global optimization via random embeddings," Journal of Global Optimization, Springer, vol. 76(1), pages 69-90, January.
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