On the usefulness of linkage processing for solving MAX-SAT

The linkage tree genetic algorithm (LTGA) learns, each generation, a linkage model by building a hierarchical cluster tree. The LTGA is an instance of the more general gene-pool optimal mixing evolutionary algorithm (GOMEA) that uses a family of subsets (FOS) linkage model. We compare the performance of the linkage model learning LTGA with several predetermined FOS linkage models applied by GOMEA. The predetermined models are matched to the underlying problem structure of four benchmark functions: onemax, deceptive trap functions, maximal overlapping nearest-neighbor NK-landscapes, and weighted MAXCUT problems. Although the a priori fixed models are specifically designed to capture the interactions between the problem variables, experimental results show that - for problems with intricate interaction structure - they are actually less efficient than LTGA that dynamically learns a hierarchical tree model. Some of these observations were unexpected and raise the question of what exactly is the optimal linkage structure for a given problem as used by GOMEA. In the case of the NK-problem a linkage model that is an accurate description of the underlying additively decomposable fitness structure is clearly not an optimal linkage model. Being able to rebuild the linkage model each generation has clear benefits above using fixed, predetermined linkage models.