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

Shengguan Xu (), Jianfeng Tan (), Jiale Zhang (), Hongquan Chen () and Yisheng Gao ()
Additional contact information
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

Journal of Global Optimization, 2025, vol. 91, issue 3, No 9, 647-676

Abstract: 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.

Keywords: Expected hypervolume improvement; Monte Carlo method; Efficient global optimization; Multi-objective optimization (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-024-01442-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:91:y:2025:i:3:d:10.1007_s10898-024-01442-9

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-024-01442-9

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().