Hierarchical Genetic Algorithms

Current Genetic Algorithms can efficiently address order-k separable problems, in which the order of the linkage is restricted to a low value k. Outside this class, there exist hierarchical problems that cannot be addressed by current genetic algorithms, yet can be addressed efficiently in principle by exploiting hierarchy. We delineate the class of hierarchical problems, and describe a framework for Hierarchical Genetic Algorithms. Based on this outline for algorithms, we investigate under what conditions hierarchical problems may be solved efficiently. Sufficient conditions are provided under which hierarchical problems can be addressed in polynomial time. The analysis points to the importance of efficient sampling techniques that assess the quality of module settings.