A matrix approach for finding extrema: problems with modularity, hierarchy, and overlap

Unlike most simple textbook examples, the real world is full with complex systems, and researchers in many different fields are often confronted by problems arising from such systems. Simple heuristics or even enumeration works quite well on small and easy problems; however, to efficiently solve large and difficult problems, proper decomposition according to the complex system is the key. In this research project, investigating and analyzing interactions between components of complex systems shed some light on problem decomposition. By recognizing three bare-bone types of interactions---modularity, hierarchy, and overlap, theories and models are developed to dissect and inspect problem decomposition in the context of genetic algorithms. This dissertation presents a research project to develop a competent optimization method to solve boundedly difficult problems with modularity, hierarchy, and overlap by explicit problem decomposition. The proposed genetic algorithm design utilizes a matrix representation of an interaction graph to analyze and decompose the problem. The results from this thesis should benefit research both technically and scientifically. Technically, this thesis develops an automated dependency structure matrix clustering technique and utilizes it to design a competent black-box problem solver. Scientifically, the explicit interaction model better describes the problem structure and helps researchers gain important insights through the explicitness of the procedure.