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

• Published in: Journal of global optimization Vol. 91; no. 3; pp. 647 - 676
• Main Authors: Xu, Shengguan, Tan, Jianfeng, Zhang, Jiale, Chen, Hongquan, Gao, Yisheng
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2025; Springer Nature B.V
• Subjects: Adaptive algorithms; Algorithms; Complexity; Computer Science; Global optimization; Hypercubes; Mathematical analysis; Mathematics; Mathematics and Statistics; Monte Carlo simulation; Multiple objective analysis; Operations Research/Decision Theory; Optimization; Real Functions; Expected hypervolume improvement; Monte Carlo method; Multi-objective optimization; Efficient global optimization
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-024-01442-9

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.