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Model-Based Evolutionary Algorithms (MBEAs) can be highly scalable by virtueof linkage (or variable interaction) learning. This requires, however, that thelinkage model can capture the exploitable structure of a problem. Usually, asingle type of linkage structure is attempted to be captured using models suchas a linkage tree. However, in practice, problems may exhibit multiple linkagestructures. This is for instance the case in multi-objective optimization whenthe objectives have different linkage structures. This cannot be modelledsufficiently well when using linkage models that aim at capturing a single typeof linkage structure, deteriorating the advantages brought by MBEAs. Therefore,here, we introduce linkage kernels, whereby a linkage structure is learned foreach solution over its local neighborhood. We implement linkage kernels intothe MBEA known as GOMEA that was previously found to be highly scalable whensolving various problems. We further introduce a novel benchmark functioncalled Best-of-Traps (BoT) that has an adjustable degree of different linkagestructures. On both BoT and a worst-case scenario-based variant of thewell-known MaxCut problem, we experimentally find a vast performanceimprovement of linkage-kernel GOMEA over GOMEA with a single linkage tree aswell as the MBEA known as DSMGA-II.

Solving Multi-Structured Problems by Introducing Linkage Kernels into GOMEA