Bayesian optimization algorithm: From single level to hierarchy

There are four primary goals of this dissertation. First, design a competent optimization algorithm capable of learning and exploiting appropriate problem decomposition by sampling and evaluating candidate solutions. Second, extend the proposed algorithm to enable the use of hierarchical decomposition as opposed to decomposition on only a single level. Third, design a class of difficult hierarchical problems that can be used to test the algorithms that attempt to exploit hierarchical decomposition. Fourth, test the developed algorithms on the designed class of problems and several real-world applications.; The dissertation proposes the Bayesian optimization algorithm (BOA), which uses Bayesian networks to model the promising solutions found so far and sample new candidate solutions. BOA is theoretically and empirically shown to be capable of both learning a proper decomposition of the problem and exploiting the learned decomposition to ensure robust and scalable search for the optimum across a wide range of problems. The dissertation then identifies important features that must be incorporated into the basic BOA to solve problems that are not decomposable on a single level, but that can still be solved by decomposition over multiple levels of difficulty. Hierarchical BOA extends BOA by incorporating those features for robust and scalable optimization of hierarchically decomposable problems. A class of problems called hierarchical traps is then proposed to test the ability of optimizers to learn and exploit hierarchical decomposition. Hierarchical BOA passes the test and is shown to solve hierarchical traps and other hierarchical problems in a scalable manner. Finally, the dissertation applies hierarchical BOA to two important classes of problems of statistical physics and artificial intelligence—Ising spin-glass systems and maximum satisfiability. Experiments show that even without requiring any prior problem-specific knowledge about the structure of the problem at hand or its properties, hierarchical BOA is capable of achieving comparable or better performance than other state-of-the-art methods specializing in solving the examined classes of problems.