Granular Linkage Blocks - the gates to the Granular Function Form

Solving complex problems with Evolutionary Algorithms (EAs) efficiently and effectively often requires linkagebased variation, where variables are dependent because they together have a non-linear influence on the optimized function and, therefore, should be processed jointly. In black-box optimization, dependencies must first be discovered and then used during variation. Traditional linkage-learning techniques focus on discovering whether any two variables are dependent. While already powerful, this has its limitations, particularly when subfunctions overlap, making it difficult to decide which subsets of variables (masks) to process jointly. Limiting masks only to variables relevant to the optimization process increases the chance of finding improvement by variation operators. Some irrelevant dependencies can be eliminated by concerning the nonmonotonical instead of the non-linear influence of variable pairs on function value. However, the generalized subfunction-based representations that consider the non-monotonical dependencies are unavailable. Therefore, we propose the granular form of a function, a new concept aiming at representing the optimized problem in a subfunction-based manner that is convenient when non-monotonical dependencies are considered. We also propose a new approach to identify the Granular Linkage Blocks (GLBs), the argument sets of the granular form subfunctions. Using GLBs, we develop new variation operators and incorporate them into a new parameter-less optimizer. The experiments considering a large suite of well-known benchmarks confirm that exploiting the concepts arising from granular form provides better results than other state-of-the-art linkage-learning EAs.