Consensus occurs within a multi-agent system when every agent is in agreement about the value of some particular state. For example, the color of an LED, the position or magnitude of a vector, a rendezvous location, the most recent state of data within a database, or the identity of a leader are all states that agents might need to agree on in order to execute their tasking. The task of the decentralized consensus problem for multi-agent systems is to design an algorithm that enables agents to communicate and exchange information such that, in finite time, agents are able to form a consensus without the use of a centralized control mechanism. The primary goal of this research is to introduce and provide supporting evidence for Stochastic Local Observation/Gossip (SLOG) algorithms as a new class of solutions to the decentralized consensus problem for multi-agent systems that lack a centralized controller, with the additional constraints that agents act asynchronously, information is discrete, and all consensus options are equally preferable to all agents. Examples of where these constraints might apply include the spread of social norms and conventions in artificial populations, rendezvous among a set of specific locations, and task assignment. This goal is achieved through a combination of theory and experimentation. Information propagation process and an information propagation algorithm are derived by unifying the general structure of multiple existing solutions to the decentralized consensus problem. They are then used to define two classes of algorithms that spread information across a network and solve the decentralized consensus problem: buffered gossip algorithms and local observation algorithms. Buffered gossip algorithms generalize the behavior of many push-based solutions to the decentralized consensus problem. Local observation algorithms generalize the behavior of many pull-based solutions to the decentralized consensus problem. In the language of object oriented design, buffered gossip algorithms and local observation algorithms are abstract classes; information propagation processes are interfaces. SLOG algorithms combine the transmission mechanisms of buffered gossip algorithms and local observation algorithms into a single "hybrid" algorithm that is able to push and pull information within the local neighborhood. A common mathematical framework is constructed and used to determine the conditions under which each of these algorithms are guaranteed to produce a consensus, and thus solve the decentralized consensus problem. Finally, a series of simulation experiments are conducted to study the performance of SLOG algorithms. These experiments compare the average speed of consensus formation between buffered gossip algorithms, local observation algorithms, and SLOG algorithms over four distinct network topologies. Beyond the introduction of the SLOG algorithm, this research also contributes to the existing literature on the decentralized consensus problem by: specifying a theoretical framework that can be used to explore the consensus behavior of push-based and pull-based information propagation algorithms; using this framework to define buffered gossip algorithms and local observation algorithms as generalizations for existing solutions to the decentralized consensus problem; highlighting the similarities between consensus algorithms within control theory and opinion dynamics within computational sociology, and showing how these research areas can be successfully combined to create new and powerful algorithms; and providing an empirical comparison between multiple information propagation algorithms.

This dissertation develops mathematical models to efficiently manage the inland waterway port operations while minimizing the overall supply chain cost. In the first part, a capacitated, multi-commodity, multi-period mixed-integer linear programming model is proposed capturing diversified inland waterway transportation network related properties. We developed an accelerated Benders decomposition algorithm to solve this challenging NP-hard problem. The next study develops a two-stage stochastic mixed-integer nonlinear programming model to manage congestion in an inland waterway transportation network under stochastic commodity supply and water-level fluctuation scenarios. The model also jointly optimizes trip-wise towboat and barge assignment decisions and different supply chain decisions (e.g., inventory management, transportation decisions) in such a way that the overall system cost can be minimized. We develop a parallelized hybrid decomposition algorithm, combining Constraint Generation algorithm, Sample Average Approximation (SAA), and an enhanced variant of the L-shaped algorithm, to effectively solve our proposed optimization model in a timely fashion. While the first two parts develop models from the supply chain network design viewpoint, the next two parts propose mathematical models to emphasize the port and waterway transportation related operations. Two two-stage, stochastic, mixed-integer linear programming (MILP) models are proposed under stochastic commodity supply and water level fluctuations scenarios. The last one puts the specific focus in modeling perishable inventories. To solve the third model we propose to develop a highly customized parallelized hybrid decomposition algorithm that combines SAA with an enhanced Progressive Hedging and Nested Decomposition algorithm. Similarly, to solve the last mathematical model we propose a hybrid decomposition algorithm combining the enhanced Benders decomposition algorithm and SAA to solve the large size of test instances of this complex, NP-hard problem. Both proposed approaches are highly efficient in solving the real-life test instances of the model to desired quality within a reasonable time frame. All the four developed models are validated a real-life case study focusing on the inland waterway transportation network along the Mississippi River. A number of managerial insights are drawn for different key input parameters that impact port operations. These insights will essentially help decisions makers to effectively and efficiently manage an inland waterway-based transportation network.

Demonstrating strength and agility on virtual and real humanoids has been an important goal in computer graphics and robotics. However, developing physics- based controllers for various agile motor skills requires a tremendous amount of prior knowledge and manual labor due to complex mechanisms of the motor skills. The focus of the dissertation is to develop a set of computational tools to expedite the design process of physics-based controllers that can execute a variety of agile motor skills on virtual and real humanoids. Instead of designing directly controllers real humanoids, this dissertation takes an approach that develops appropriate theories and models in virtual simulation and systematically transfers the solutions to hardware systems. The algorithms and frameworks in this dissertation span various topics from spe- cific physics-based controllers to general learning frameworks. We first present an online algorithm for controlling falling and landing motions of virtual characters. The proposed algorithm is effective and efficient enough to generate falling motions for a wide range of arbitrary initial conditions in real-time. Next, we present a robust falling strategy for real humanoids that can manage a wide range of perturbations by planning the optimal contact sequences. We then introduce an iterative learning framework to easily design various agile motions, which is inspired by human learn- ing techniques. The proposed framework is followed by novel algorithms to efficiently optimize control parameters for the target tasks, especially when they have many constraints or parameterized goals. Finally, we introduce an iterative approach for exporting simulation-optimized control policies to hardware of robots to reduce the number of hardware experiments, that accompany expensive costs and labors.

The teaching and learning of Euclidean geometry in black South African schools is characterised by teachers' poor knowledge of Euclidean geometry and the use of traditional taaching methods that encourage rote learning. In the light of this, the study investigated the extent to which learners perform in Process-Based Instruction. Process-Based Instruction is charactarised by the gradual transfer of instruction from the teacher to the learner. In Process-Based Instruction learners are expected to communicate thought,form concepts and master theorems by drawing, 'showed with and used hands', talking and writing. Learners' performance is assessed by rubrics and is analysed using graphs. The findings of the empirical investigation revealed that learners of both grades 8 and 9 cannot communicate thought by any media (talking, writing, 'showed with and used hands' and drawing). A few learners formed a few concepts and mastered theorems. On the basis of the findings and the shortcomings of the study recommendations are made. / Educational studies / M. Ed. (Didactics)

Text in English, abstract in English and Afrikaans / The teaching and learning of Euclidean geometry in black South African schools is characterised by teachers' poor knowledge of Euclidean geometry and the use of traditional teaching methods that encourage rote learning. In the light of this, the study investigated the extent to which learners perform in Process-Based Instruction. Process-Based Instruction is characterised by the gradual transfer of instruction from the teacher to the learner. In Process-Based Instruction learners are expected to communicate thought, form concepts and master theorems by drawing, 'showed with and used hands', talking and writing. Learners' performance is assessed by rubrics and is analysed using graphs. The findings of the empirical investigation revealed that learners of both grades 8 and 9 cannot communicate thought by any media (talking, writing 'showed with and used hands' and drawing). A few learners formed a few concepts and mastered theorems. On the basis of the findings and the shortcomings of the study recommendations are made. / Die onderrig van Euclediaanse Meetkunde in swart Suid-Afrikaanse skole word gekenmerk aan onderwysers se swak kennis van die vak, asook die gebruik van onderrigmetodes wat op die leerder se geheue staatmaak. Hierdie studie ondersoek die sukses van leerders se prestasie in proses-gebasseerde ondenig. Proses-gebaseerde onderig word gekenmerk aan die geleidelike oordra van kennis, van die onderwyser na die leerder. Daar word van leerders verwag om gedagtes oor te dra, konsepte (begrippe) te verstaan en stellings onder die knie te kry deur middel van sketse, die gebruik van gebare, verbale verduideliking en skriftelike werk. Leerders se prestasie word geevalueer deur die gebruik van klassifisering in kolomme (rubrics) en word ge-analiseer deur gralieke. Die bevinding van die empieriese ondersoek het getoon dat leerders van sowel graad 8 as graad 9 nie gedagtes kan oordra deur enige van die gemelde metodes nie. 'n Paar leerders het wel enkele begrippe verstaan en kon stellings bemeester. Na aanleiding van die bevindings van die studie en die tekortkominge wat daardeur opgespoor is, word sekere voorstelle gemaak. / Didactics / M. Ed. (Didactics)

International Telemetering Conference Proceedings / October 27-30, 1997 / Riviera Hotel and Convention Center, Las Vegas, Nevada / This paper proves theoretically that GDOP decreases as the number of satellites is increased.This paper proposes two recursive algorithms for calculating the GDOP and positioning solution.These algorithms not only can recursively calculate the GDOP and positioning solution, but also is very flexible in obtaining the best four-satellite positioning solution ,the best five-satellite positioning solution and the all visible satellite positioning solution according to given requirements. In the need of the two algorithms,this paper extends the definition of the GDOP to the case in which the number of visible satellites is less than 4.

The p-median problem is an NP-complete combinatorial optimization problem often used in the fields of facility location and clustering. Given a graph with n nodes and an integer p < n, the p-median problem seeks a set of p medians such that the sum of the distances of the n nodes from their nearest median is minimized. This dissertation develops a genetic algorithm that generates solutions to the p-median problem that improves on previously published genetic algorithms by implementing operators that exploit domain specific information. More specifically, this GA explores the following: (1) The advantages of using "good" solutions generated using extant heuristics in the initial generation of chromosomes. (2) The effectiveness of a crossover operation that exchanges centers in the same neighborhood rather than exchanging arbitrarily chosen subsets of centers. (3) The efficacy of using a biased mutation operator that favors replacing existing medians from less fit chromosomes with non-median nodes from the same neighborhood as the median being replaced. Using published problem sets with known solutions, this dissertation examines solutions identified by the new genetic algorithm in order to determine the accuracy, efficiency and performance characteristics of the new algorithm. In addition, it tests the contribution of each of the algorithm's operators by systematically controlling for all the other factors. The results of the analysis showed that integrating operators that exploited domain specific information did have an overall positive impact on the genetic algorithm. In addition, the results showed that using a structured initial population had little impact on the algorithm's ability to find an optimal solution but it did create a better initial solution and allowed the algorithm to produce a relatively good solution early in the search. Also, the analysis showed that a directed approach to crossover operations was effective and produced superior solutions. Finally, the analysis showed that a directed approach toward mutation did not have a large impact on the overall functionality of the algorithm and may be inferior to an arbitrary approach to mutation.

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