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.
翻译:模型化进化算法(MBEAs)可以通过联系(或可变互动)学习而高度可扩展。然而,这要求联系模式能够捕捉问题的可利用结构。通常,试图用链接树等模型来捕捉单一类型的联系结构。然而,在实践中,问题可能表现出多重联系结构。例如,在目标有不同联系结构的情况下,多目标优化就是这种情况。在使用旨在捕捉单一类型的联系结构、使MBEAs带来的优势恶化的链接模型时,这不可能做得足够好的模式模型。因此,在这里,我们采用链接内核,从而在每一个解决方案的本地邻居中学习一个链接结构。我们将连接内核圈引入MBEA,即以前发现在解决各种问题时高度可伸缩的GOMEA。我们还引入了一个新的基准功能,即“最佳陷阱”(Bot-The-Lest-Tracs),它具有可调整的不同联系结构的程度。关于BOT和基于最坏情况的设想变式的内核-MA公司作为已知的单一GA-GA联系的一个实验性改进问题,我们发现一个已知的GA-GA-GA-GA-GA-GA-D-GA-D-G-GA-D-G-G-G-GA-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-G-