Advanced optimization techniques with applications to organizational design and graph-based inference

This dissertation is divided into two parts: (i) modeling and the concomitant optimization algorithms for designing Command & Control ( C2) organizations; and (ii) disease diagnosis and discovering organizational networks and their processes from noisy observations (i.e., negative /positive findings, or uncertain message data) using inference techniques from graphical models. In the first part, we seek to design organizational (C2) structures with the ability to conduct dynamic action synchronization, achieve organization agility, and increase speed of command over a robust, decentralized architecture. The key components to design and evaluation of C2 organizational structure are: (i) mathematical modeling of the mission and organization and explicitly formulating the design optimization problem; (ii) develop algorithms for finding the optimal or near-optimal design. The search space of the optimization problem is very high-dimensional with discrete and continuous attributes. The shape of the high-dimensional surface that corresponds to the optimized function is usually very complex. The focus of this part of the dissertation is to provide mathematical modeling of missions and organizations, and to develop systematic procedures based on evolutionary algorithm (EA), specifically nested genetic algorithm (GA) and multi-objective EA, for designing organizations. The following three topics will be addressed: (1) explore various command & control organization models, i.e., hierarchy, heterarchy, and holarchy; (2) obtain congruent heterarchical organizational structures by applying concepts from group technology; (3) achieve flexibility of holonic structure and the concomitant distributed scheduling scheme by employing multiple objective optimization techniques. ^ In the second part of the thesis, we extend our optimization techniques to inference in network models. The networks include a QMR-DT (Quick Medical Reference-Decision Theoretic) network,1 where identifying the correct diagnoses is hard due to its large and loopy structure. A computationally efficient algorithm is developed to achieve fast inference in a QMR-DT network. Probabilistic graphical models and computationally efficient solution methods are also developed to discover C 2 organizational structures from noisy observations that include activities, communications and command decisions. The contributions of this part of the thesis are the following: (a) Lagrangian Relaxation Algorithm ( LRA) generates an upper bound for the objective function by relaxing the original problem via a set of Lagrange multipliers. The near-optimal diagnosis (configuration) is found by minimizing the duality gap via a subgradient method. (b) Approximate belief revision (ABR) algorithm, incorporating mean field theory and a novel message-passing mechanism, estimates the beliefs (pseudo marginal posterior probabilities) for each disease of interest; (c) A Hidden Markov Random Field (HMRF) model and a graph matching algorithm are employed to discover the attributes of and relationships among organizational members, assets, environment areas, and mission tasks. The focus is on identifying the mapping between a set of hypothesized networks and the observed data, and selecting the maximum a posteriori hypothesis as the matching network. ^ 1The QMR-DT network [82] is a large two-level (or bi-partite) graph model based on expert and statistical knowledge in internal medicine.