Dynamic Resource Management Algorithms for Complex Systems and Novel Approaches to Adaptive Kalman Filtering

This thesis considers three combinatorial optimization problems of substantial practical importance. First, a new approach to efficiently obtain a large number of ranked solutions to a 3-dimensional assignment problem is presented, and is applied to generate fuel assembly loading patterns. Second, we formulate the problem of dynamically scheduling maritime surveillance assets, and solve it using branch-and-cut and approximate dynamic programming (ADP) with rollout, and investigate the tradeoffs between the two. Third, a multi-objective ship routing problem is also investigated, where we propose a solution combining approximate dynamic programming techniques and clustering techniques to contain the computational and storage complexity. Lastly, this dissertation develops a seminal approach to adaptive Kalman filtering via the use of post-fit residuals given data samples -- an approach not yet discussed prior to this work.