Hierarchical Problem Solving with the Linkage Tree Genetic Algorithm

Hierarchical problems represent an important class of nearly decomposable problems. The concept of near decomposability is central to the study of complex systems. When little a priori information is available, a black box problem solver is needed to optimize these hierarchical problems. The solver should be able to learn linkage information, and to preserve and test partial solutions at different levels in the hierarchy. Two well known benchmark functions - shuffled Hierarchical If-And-Only-If (HIFF) and shuffled Hierarchical Trap (HTRAP) functions - exemplify the challenges posed by hierarchical problems. Standard genetic algorithms are unable to solve these problems, and specific methods, like SEAM and hBOA, have been designed to address them. In this paper, we investigate how the recently developed Linkage Tree Genetic Algorithm (LTGA) performs on these hierarchical problems. We compare LTGA with SEAM and hBOA on HIFF and HTRAP functions. Results show that, although LTGA is a simple algorithm compared to SEAM and hBOA, it nevertheless is a very efficient, reliable, and scalable algorithm for solving the randomly shuffled versions of HIFF and HTRAP, two hard, hierarchical problems.