Parallel Problem Solving from Nature - PPSN XVII - 17th International Conference, PPSN 2022, Dortmund, Germany, September 10-14, 2022, Proceedings, Part I
Parallel Problem Solving from Nature - PPSN XVII - 17th International Conference, PPSN 2022, Dortmund, Germany, September 10-14, 2022, Proceedings, Part I
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自然并行问题解决 - PPSN XVII - 第 17 届国际会议，PPSN 2022，德国多特蒙德，2022 年 9 月 10-14 日，会议记录，第一部分
DOI：
10.1007/978-3-031-14714-2_7
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Rahat A
中科院分区：
文献类型：
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作者：
Rahat A
最近提出了许多方法来执行多目标优化的计算昂贵的问题。通常，每个目标的概率代理是从初始数据集构建的。然后可以使用代理来为任何解决方案在目标空间中产生预测密度。使用预测密度，我们可以计算由于解决方案而产生的预期超体积改善（EHVI）。最大化EHVI，我们可以找到最有前途的解决方案，可能是昂贵的下一个评估。存在用于计算EHVI的封闭形式表达式，其在多变量预测密度上积分。然而，它们需要分割目标空间，对于三个以上的目标来说，这可能是非常昂贵的。此外，对于预测密度是依赖的问题，没有封闭形式的表达式，捕获目标之间的相关性。在这种情况下，使用蒙特卡罗近似，这是不便宜的。因此，仍然需要开发新的精确但更便宜的近似方法。在这里，我们研究了一种替代方法，接近EHVI使用高斯-厄米积分。我们表明，它可以是一个准确的替代Monte Carlo的独立和相关的预测密度与统计上显着的等级相关性的一系列流行的测试问题。
Many methods for performing multi-objective optimisation of computationally expensive problems have been proposed recently. Typically, a probabilistic surrogate for each objective is constructed from an initial dataset. The surrogates can then be used to produce predictive densities in the objective space for any solution. Using the predictive densities, we can compute the expected hypervolume improvement (EHVI) due to a solution. Maximising the EHVI, we can locate the most promising solution that may be expensively evaluated next. There are closed-form expressions for computing the EHVI, integrating over the multivariate predictive densities. However, they require partitioning of the objective space, which can be prohibitively expensive for more than three objectives. Furthermore, there are no closed-form expressions for a problem where the predictive densities are dependent, capturing the correlations between objectives. Monte Carlo approximation is used instead in such cases, which is not cheap. Hence, the need to develop new accurate but cheaper approximation methods remains. Here we investigate an alternative approach toward approximating the EHVI using Gauss-Hermite quadrature. We show that it can be an accurate alternative to Monte Carlo for both independent and correlated predictive densities with statistically significant rank correlations for a range of popular test problems.