2000 Mathematics Subject Classification: 17B37; 05E15

The purpose of this work is to provide simulation-based support for making optimal (or near-optimal) decisions in situations where decision makers are faced with imperfect information. We develop several novel techniques and algorithms for simulation-based optimization and decision support and apply them to two categories of problems: (i) Unmanned Aerial Vehicle (UAV) path planning in search operations, and; (ii) optimization of business process models. Common features of these two problems for which analytical approaches are not available, are the presence of imperfect information and their inherent complexity. In the UAV path planning problem, the objective is to define the path of a UAV searching for a target on a known road network. It is assumed that the target is moving toward a goal and we have some uncertain information about the start point of the target, its velocity, and the final goal of the target. The target does not take evasive action to avoid being detected. The UAV is equipped with a sensor, which may detect the target once it is in the sensor’s scope. Nevertheless, the detection process is uncertain and the sensor is subject to both false-positive and false-negative errors. We propose three different solutions, two of which are simulation-based. The most promising solution is an on-line simulation-based method that estimates the location of the target by using a Sequential Monte Carlo (SMC) method. During the entire mission, different UAV paths are simulated and the one is chosen that most reduces the uncertainty about the location of the target. In the optimization of the business process models, several different but related problems are addressed: (i) we define a measure of performance for a business process model based on the value added by agents (employees) to the process; (ii) we use this model for optimization of the business process models. Different types of processes are distinguished and methods for finding the optimal or near-optimal solutions are provided; (iii) we propose a model for estimating the performance of collaborative agents. This model is used to solve a class of Assignment Problems (AP), where tasks are assigned to collaborative agents; (iv) we propose a model for team activity and the performance of a team of agents. We introduce different collaboration strategies between agents and a negotiation algorithm for resolving conflicts between agents. We compare the effect of different strategies on the output of the team. Most of the studied cases are complex problems for which no analytical solution is available. Simulation methods are successfully applied to these problems. They are shown to be more general than analytical models for handling uncertainty since they usually have fewer assumptions and impose no restrictions on the probability distributions involved. Our investigation confirms that simulation is a powerful tool for providing decision-making support. Moreover, our proposed algorithms and methods in the accompanying articles contribute to providing support for making optimal and in some cases near-optimal decisions: (i) our tests of the UAV simulation-based search methods on a simulator show that the on-line simulation method has generally a high performance and detects the target in a reasonable time. The performance of this method was compared with the detection time when the UAV had the exact information about the initial location of the target, its velocity, and its path (minimum detection time). This comparison indicated that the online simulation method in many cases achieved a near-optimal performance in the studied scenario; (ii) our business process optimization framework combines simulation with the Hungarian method and finds the optimal solution for all cases where the assignment of tasks does not change the workflow of the process. For the most general cases, where the assignment of tasks may change the workflow, we propose an algorithm that finds near-optimal solutions. In this algorithm, simulation, which deals with the uncertainty in the process, is combined with the Hungarian method and hill-climbing heuristics. In the study of assigning tasks to collaborative agents we suggest a Genetic Algorithm (GA) that finds near-optimal solutions with a high degree of accuracy, stability, scalability and robustness. While investigating the effect of different agent strategies on the output of a team, we find that the output of a team is near-optimal, when agents choose a collaboration strategy that follows the principle of least effort (Zipf’s law) and use our suggested algorithm for negotiation and resolving conflicts. / QC 20111202

The potential benefits that automation could bring to a wide variety of real-world tasks are numerous and well recognised. There has been significant research undertaken into automation in general, but for real-time automation of complex systems (involving complex geometries and dynamics) the problem is far from a solved one. One of the key tasks in a surface mining operation is that of using shovels or excavators to load material onto haul trucks for transportation. Since it is such a crucial task to a number of production cycles, it is a clear area where the productivity and safety benefits of automation could have a large impact. A number of projects are being undertaken concurrently to move towards first partial, and then full, automation of this mining subsystem. This thesis focusses on the collision avoidance problem, specifically on forming a collision hull that distinguishes between intersecting and non-intersecting configurations of two objects. Techniques from computer graphics are leveraged to develop a data structure that stores and organises relevant information about real-world systems for motion-planning tasks, ensuring that the necessary data is available and in a form suited to the task at hand. The Minkowski Sum operation, which can be used fairly directly to form the collision hull of two convex objects under translation, is extended to develop an operation to form the exact collision hull of two arbitrary objects to determine the applicability of such a scheme to complex systems in real-time. A level of detail solution is then proposed, where the Minkowski Hull of bounding hierarchies allows unnecessary parts of the hull to be calculated only in a coarse manner, thus offsetting a lot of the computational cost for any given test. This approach is investigated for both translational motion and joint-space motion. Collision detection is not collision avoidance, and so the algorithms developed in the thesis are tested in a number of applications, to demonstrate their suitability to the collision avoidance task. The applications (discrete collision prediction, visibility graph path planning, and the formulation of a Model Predictive Controller) are restricted versions of the true problems with some simplifying assumptions, but they show the algorithms to be capable both in their execution speed and the information that they provide.

Thesis (M.S.)--Ohio University, November, 2001. / Title from PDF t.p.

Thesis (M.S.)--Ohio University, June, 2004. / Title from PDF t.p. Includes bibliographical references (leaves 96-97).

Thesis (Ph. D.)--University of Washington, 1992. / Vita. Includes bibliographical references (leaves [150]-155).

Thesis (M.Eng.) -- Memorial University of Newfoundland. 1975. / Typescript. Bibliography : leaves 102-103. Also available online.

Thesis (M.C.S.) - Carleton University, 1992. / Also available in electronic format on the Internet.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2006. / Title from title screen (site viewed April 26, 2007). PDF text: vii, 164 p. : ill. UMI publication number: AAT 3229555. Includes bibliographical references. Also available in microfilm and microfiche formats.

Thesis (MEng)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: This thesis presents a robust, sampling-based path planning algorithm for commercial airliners that simultaneously performs collision avoidance both with intruder aircraft and terrain. The existing resolution systems implemented on commercial airliners are fast and reliable; however, they do possess certain limitations. This thesis aims to propose an algorithm that is capable of rectifying some of these limitations. The development and research required to derive this conflict resolution system is supplied in the document, including a detailed literature study explaining the selection of the final algorithm. The proposed algorithm applies an incremental sampling-based technique to determine a safe path quickly and reliably. The algorithm makes use of a local planning method to ensure that the paths proposed by the system are indeed flyable. Additional search optimisation techniques are implemented to reduce the computational complexity of the algorithm. As the number of samples increases, the algorithm strives towards an optimal solution; thereby deriving a safe, near-optimal path that avoids the predicted conflict region. The development and justification of the different methods used to adapt the basic algorithm for the application as a confiict resolution system are described in depth. The final system is simulated using a simplified aircraft model. The simulation results show that the proposed algorithm is able to successfully resolve various conflict scenarios, including the generic two aircraft scenario, terrain only scenario, a two aircraft with terrain scenario and a multiple aircraft and terrain scenario. The developed algorithm is tested in cluttered dynamic environments to ensure that it is capable of dealing with airport scenarios. A statistical analysis of the simulation results shows that the algorithm finds an initial resolution path quickly and reliably, while utilising all additional computation time to strive towards a near-optimal solution. / AFRIKAANSE OPSOMMING: Hierdie tesis bied 'n robuuste, monster-gebaseerde roetebeplanningsalgoritme vir kommersiële vliegtuie aan, wat botsingvermyding met indringervliegtuie en met die terrein gelyktydig uitvoer. Die bestaande konflikvermyding- stelsels wat op kommersiële vliegtuie geïmplementeer word, is vinnig en betroubaar; dit het egter ook sekere tekortkominge. Hierdie tesis is daarop gemik om 'n algoritme voor te stel wat in staat is om sommige van hierdie tekortkominge reg te stel. Die ontwikkeling en navorsing wat nodig was om hierdie konflik-vermyding-algoritme af te lei, word in die dokument voorgelê, insluitende 'n gedetailleerde literatuurstudie wat die keuse van die finale algoritme verduidelik. Die voorgestelde algoritme pas 'n inkrementele, monster-gebaseerde tegniek toe om vinnig en betroubaar 'n veilige roete te bepaal. Die algoritme maak gebruik van 'n lokale beplanningsmetode om te verseker dat die roetes wat die stelsel voorstel inderdaad uitvoerbaar is. Aanvullende soektog-optimeringstegnieke word geïmplementeer om die berekeningskompleksiteit van die algoritme te verlaag. Soos die aantal monsters toeneem, streef die algoritme na 'n optimale oplossing; sodoende herlei dit na 'n veilige, byna-optimale roete wat die voorspelde konflikgebied vermy. Die ontwikkeling en regverdiging van die verskillende metodes wat gebruik is om die basiese algoritme aan te pas vir die toepassing daarvan as 'n konflik-vermyding-stelsels word in diepte beskryf. Die finale stelsel word gesimuleer deur 'n vereenvoudigde vliegtuigmodel te gebruik. Die simulasie resultate dui daarop dat die voorgestelde algoritme verskeie konflikscenario's suksesvol kan oplos, insluitend die generiese tweevliegtuigscenario, die slegs-terreinscenario, die tweevliegtuig-met-terreinscenario en die veelvuldige vliegtuig-enterreinscenario. Die ontwikkelde algoritme is in 'n beisge (cluttered), dinamiese omgewing getoets om te verseker dat dit 'n besige lughawescenario kan hanteer. 'n Statistiese ontleding van die simulasie resultate bewys dat die algoritme vinnig en betroubaar 'n aanvanklike oplossingspad kan vind, addisioneel word die oorblywende berekeningstyd ook gebruik om na 'n byna optimaleoplossing te streef.