Stochastic iterated genetic hillclimbing

In the "black box function optimization" problem, a search strategy is required to find an extremal point of a function without knowing the structure of the function or the range of possible function values. Solving such problems efficiently requires two abilities. On the one hand, a strategy must be capable of learning while searching: It must gather global information about the space and concentrate the search in the most promising regions. On the other hand, a strategy must be capable of sustained exploration: If a search of the most promising region does not uncover a satisfactory point, the strategy must redirect its efforts into other regions of the space. This dissertation describes a connectionist learning machine that produces a search strategy called stochastic iterated genetic hillclimbing (SIGH). Viewed over a short period of time, SIGH displays a coarse-to-fine searching strategy, like simulated annealing and genetic algorithms. However, in SIGH the convergence process is reversible. The connectionist implementation makes it possible to diverge the search after it has converged, and to recover coarse-grained information about the space that was suppressed during convergence. The successful optimization of a complex function by SIGH usually involves a series of such converge/diverge cycles. SIGH can be viewed as a generalization of a genetic algorithm and a stochastic hillclimbing algorithm, in which genetic search discovers starting points for subsequent hillclimbing, and hillclimbing biases the population for subsequent genetic search. Several search stratgies--including SIGH, hillclimbers, genetic algorithms, and simulated annealing--are tested on a set of illustrative functions and on a series of graph partitioning problems. SIGH is competitive with genetic algorithms and simulated annealing in most cases, and markedly superior in a function where the uphill directions usually lead away from the global maximum. In that case, SIGH's ability to pass information from one coarse-to-fine search to the next is crucial. Combinations of genetic and hillclimbing techniques can offer dramatic performance improvements over either technique alone.