Hybrid linkage learning for permutation optimization with Gene-pool optimal mixing evolutionary algorithms

Linkage learning techniques are employed to discover dependencies between problem variables. This knowledge can then be leveraged in an Evolutionary Algorithm (EA) to improve the optimization process. Of particular interest is the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) family, which has been shown to exploit linkage effectively. Recently, Empirical Linkage Learning (ELL) techniques were proposed for binary-encoded problems. While these techniques are computationally expensive, they have the benefit of never reporting spurious dependencies (false linkages), i.e., marking two independent variables as being dependent. However, previous research shows that despite this property, for some problems, it is more suitable to employ more commonly-used Statistical-based Linkage Learning (SLL) techniques. Therefore, we propose to use both ELL and SLL in the form of Hybrid Linkage Learning (HLL). We also propose (for the first time) a variant of ELL for permutation problems. Using a wide range of problems and different GOMEA variants, we find that also for permutation problems, in some cases, ELL is more advantageous to use while SLL is more advantageous in other cases. However, we also find that employing the proposed HLL leads to results that are better or equal than the results obtained with SLL for all the considered problems.