| Goal optimization has long been a topic of great interest in computer science. The literature contains many thousands of papers that discuss methods for the search of optimal solutions to complex problems. In the case of multi-objective optimization, such a search yields iteratively improved approximations to the Pareto frontier, i.e. the set of best solutions contained along a trade-off curve of competing objectives.;To approximate the Pareto frontier, one method that is ubiquitous throughout the field of optimization is stochastic search. Stochastic search engines explore solution spaces by randomly mutating candidate guesses to generate new solutions. This mutation policy is employed by the most commonly used tools (e.g. NSGA-II, SPEA2, etc.), with the goal of a) avoiding local optima, and b) expand upon diversity in the set of generated approximations. Such "blind" mutation policies explore many sub-optimal solutions that are discarded when better solutions are found. Hence, this approach has two problems. Firstly, stochastic search can be unnecessarily computationally expensive due to evaluating an overwhelming number of candidates. Secondly, the generated approximations to the Pareto frontier are usually very large, and can be difficult to understand.;To solve these two problems, a more-directed, less-stochastic approach than standard search tools is necessary. This thesis presents GALE (Geometric Active Learning). GALE is an active learner that finds approximations to the Pareto frontier by spectrally clustering candidates using a near-linear time recursive descent algorithm that iteratively divides candidates into halves (called leaves at the bottom level). Active learning in GALE selects a minimally most-informative subset of candidates by only evaluating the two-most different candidates during each descending split; hence, GALE only requires at most, 2Log2(N) evaluations per generation. The candidates of each leaf are thereafter non-stochastically mutated in the most promising directions along each piece. Those leafs are piece-wise approximations to the Pareto frontier.;The experiments of this thesis lead to the following conclusion: a near-linear time recursive binary division of the decision space of candidates in a multi-objective optimization algorithm can find useful directions to mutate instances and find quality solutions much faster than traditional randomization approaches. Specifically, in comparative studies with standard methods (NSGA-II and SPEA2) applied to a variety of models, GALE required orders of magnitude fewer evaluations to find solutions. As a result, GALE can perform dramatically faster than the other methods, especially for realistic models. |
