Non-linear Dimensionality Reduction Procedures for Certain Large-Dimensional Multi-objective Optimization Problems: Employing Correntropy and a Novel Maximum Variance Unfolding
Non-linear Dimensionality Reduction Procedures for Certain Large-Dimensional Multi-objective Optimization Problems: Employing Correntropy and a Novel Maximum Variance Unfolding
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DOI：
10.1007/978-3-540-70928-2_58
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发表时间：
2007-03
期刊：
影响因子：
8.8
通讯作者：
D. Saxena;K. Deb
中科院分区：
文献类型：
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作者：
D. Saxena;K. Deb
在我们最近的出版物[1]中，我们开始理解多目标优化的许多现实应用涉及大量（10个或更多）目标，但随后，现有的进化多目标优化（EMO）方法主要应用于具有较少数量目标（5个或更少）的问题。在强调了处理大量目标的主要障碍后，我们提出了一种基于主成分分析（PCA）的EMO过程，用于降维，其有效性通过解决多达50个目标的优化问题来证明。在这里，我们要解决的事实是，当数据点生活在一个非线性流形上或数据结构是非高斯的，PCA产生一个较小的维度的“线性”子空间可能是无效的揭示潜在的维度。为了克服这一问题，我们提出了两个新的非线性降维算法的进化多目标优化，即C-PCA-NSGA-II和MVU-PCA-NSGA-II。前者基于新引入的相关熵PCA [2]，后者以新的方式实现了最大方差展开原理[3，4，5]。我们还建立了这些新的EMO程序的优越性，较早的PCA为基础的程序，无论是在精度和计算时间，通过解决多达50个目标的优化问题。
In our recent publication [1], we began with an understanding that many real-world applications of multi-objective optimization involve a large number (10 or more) of objectives but then, existing evolutionary multi-objective optimization (EMO) methods have primarily been applied to problems having smaller number of objectives (5 or less). After highlighting the major impediments in handling large number of objectives, we proposed a principal component analysis (PCA) based EMO procedure, for dimensionality reduction, whose efficacy was demonstrated by solving upto 50-objective optimization problems. Here, we are addressing the fact that, when the data points live on a non-linear manifold or that the data structure is non-gaussian, PCA which yields a smaller dimensional ’linear’ subspace may be ineffective in revealing the underlying dimensionality. To overcome this, we propose two new non-linear dimensionality reduction algorithms for evolutionary multi-objective optimization, namely C-PCA-NSGA-II and MVU-PCA-NSGA-II. While the former is based on the newly introduced correntropy PCA [2], the later implements maximum variance unfolding principle [3,4,5] in a novel way. We also establish the superiority of these new EMO procedures over the earlier PCA-based procedure, both in terms of accuracy and computational time, by solving upto 50-objective optimization problems.