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Adaptive nested Monte Carlo approach for multi-objective efficient global optimization

Author

Listed:
  • Shengguan Xu

    (Nanjing Tech University)

  • Jianfeng Tan

    (Nanjing Tech University)

  • Jiale Zhang

    (Xiamen University)

  • Hongquan Chen

    (Nanjing University of Aeronautics and Astronautics)

  • Yisheng Gao

    (Nanjing University of Aeronautics and Astronautics)

Abstract

This paper presents a novel algorithm, namely the adaptive nested Monte Carlo based multi-objective Efficient Global Optimization (ANMC-MOEGO), which aims to enhance efficiency and accuracy while minimizing programming complexity in contrast to traditional multi-objective Efficient Global Optimization (MOEGO). In this algorithm, the programming complexity is streamlined by employing Monte Carlo simulation for both hypervolume improvement (HVI) and expected hypervolume improvement (EHVI) calculations. Furthermore, the efficiency and accuracy of HVI and EHVI calculations are improved through the utilization of a novel technique called adaptive Monte Carlo hypercube boundaries (AMCHB), which is based on the bisection method. The algorithm is validated via a set of test functions from the open literature. The numerical results demonstrate that the ANMC-MOEGO algorithm produces solutions closer to the theoretical results, with improved distributions on the corresponding Pareto fronts compared to the algorithm without AMCHB technique. Moreover, when obtaining a better Pareto front, the proposed algorithm is found to be more time-efficient, achieving speedups of up to 22.57 times.

Suggested Citation

  • Shengguan Xu & Jianfeng Tan & Jiale Zhang & Hongquan Chen & Yisheng Gao, 2025. "Adaptive nested Monte Carlo approach for multi-objective efficient global optimization," Journal of Global Optimization, Springer, vol. 91(3), pages 647-676, March.
    • Handle: RePEc:spr:jglopt:v:91:y:2025:i:3:d:10.1007_s10898-024-01442-9
    DOI: 10.1007/s10898-024-01442-9
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    References listed on IDEAS

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    1. Evans, Michael & Swartz, Timothy, 2000. "Approximating Integrals via Monte Carlo and Deterministic Methods," OUP Catalogue, Oxford University Press, number 9780198502784, Decembrie.
    2. Shengguan Xu & Hongquan Chen, 2018. "Nash game based efficient global optimization for large-scale design problems," Journal of Global Optimization, Springer, vol. 71(2), pages 361-381, June.
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