在GOMEA中引入连接核求解多结构问题
Solving Multi-Structured Problems by Introducing Linkage Kernels into GOMEA
摘要：
基于模型的进化算法（MBEA）可以通过链接（或变量交互）学习高度可扩展。然而，这要求链接模型能够捕捉到问题的可利用结构。通常，尝试使用诸如链接树的模型来捕获单一类型的链接结构。然而，在实践中，问题可能表现出多个链接结构。例如，当目标具有不同的链接结构时，在多目标优化中就是这种情况。当使用旨在捕获单一类型的链接结构的链接模型时，这不能充分建模，从而恶化了MBEA带来的优势。因此，在这里，我们引入了链接内核，从而为每个解决方案在其局部邻域上学习链接结构。我们实现链接内核到MBEA称为GOMEA，以前被发现是高度可扩展的解决各种问题时。我们进一步介绍了一种新的基准函数称为最佳陷阱（BoT），具有不同的连接结构的可调程度。在BoT和众所周知的MaxCut问题的基于最坏情况场景的变体上，我们通过实验发现，与具有单个链接树以及称为DSMGA-II的MBEA的GOMEA相比，链接内核GOMEA的性能有了巨大的改进。
英文摘要：
Model-Based Evolutionary Algorithms (MBEAs) can be highly scalable by virtue of linkage (or variable interaction) learning. This requires, however, that the linkage model can capture the exploitable structure of a problem. Usually, a single type of linkage structure is attempted to be captured using models such as a linkage tree. However, in practice, problems may exhibit multiple linkage structures. This is for instance the case in multi-objective optimization when the objectives have different linkage structures. This cannot be modelled sufficiently well when using linkage models that aim at capturing a single type of linkage structure, deteriorating the advantages brought by MBEAs. Therefore, here, we introduce linkage kernels, whereby a linkage structure is learned for each solution over its local neighborhood. We implement linkage kernels into the MBEA known as GOMEA that was previously found to be highly scalable when solving various problems. We further introduce a novel benchmark function called Best-of-Traps (BoT) that has an adjustable degree of different linkage structures. On both BoT and a worst-case scenario-based variant of the well-known MaxCut problem, we experimentally find a vast performance improvement of linkage-kernel GOMEA over GOMEA with a single linkage tree as well as the MBEA known as DSMGA-II.
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