Health Sciences Centre (HSC) in Winnipeg is the major healthcare facility serving Manitoba, Northwestern Ontario, and Nunavut. An evaluation of HSC’s adult surgical patient flow revealed that one major barrier to smooth flow was their Operating Room (OR) scheduling system. This thesis presents a new two-stage elective OR scheduling system for HSC, which generates weekly OR schedules that reduce artificial variability in order to facilitate smooth patient flow. The first stage reduces day-to-day variability while the second stage reduces variability occurring within a day. The scheduling processes in both stages are mathematically modelled as multi-objective optimization problems. An attempt was made to solve both models using lexicographic goal programming. However, this proved to be an unacceptable method for the second stage, so a new multi-objective genetic algorithm, Nondominated Sorting Genetic Algorithm II – Operating Room (NSGAII-OR), was developed. Results indicate that if the system is implemented at HSC, their surgical patient flow will likely improve. / October 2008

Subspace clustering identifies the attribute support for each cluster as well as identifying the location and number of clusters. In the most general case, attributes associated with each cluster could be unique. A multi-objective evolutionary method is proposed to identify the unique attribute support of each cluster while detecting its data instances. The proposed algorithm, Symbiotic Evolutionary Subspace Clustering (S-ESC) borrows from symbiosis in the sense that each clustering solution is defined in terms of a host, which is formed by a number of co-evolved cluster centroids (or symbionts). Symbionts define clusters and therefore attribute subspaces, whereas hosts define sets of clusters to constitute a non-degenerate clustering solution. The symbiotic representation of S-ESC is the key to making it scalable to high-dimensional datasets, while a subsampling process makes it scalable to large-scale datasets. Performance of the S-ESC algorithm was found to be robust across a common parameterization utilized throughout.

Health Sciences Centre (HSC) in Winnipeg is the major healthcare facility serving Manitoba, Northwestern Ontario, and Nunavut. An evaluation of HSC’s adult surgical patient flow revealed that one major barrier to smooth flow was their Operating Room (OR) scheduling system. This thesis presents a new two-stage elective OR scheduling system for HSC, which generates weekly OR schedules that reduce artificial variability in order to facilitate smooth patient flow. The first stage reduces day-to-day variability while the second stage reduces variability occurring within a day. The scheduling processes in both stages are mathematically modelled as multi-objective optimization problems. An attempt was made to solve both models using lexicographic goal programming. However, this proved to be an unacceptable method for the second stage, so a new multi-objective genetic algorithm, Nondominated Sorting Genetic Algorithm II – Operating Room (NSGAII-OR), was developed. Results indicate that if the system is implemented at HSC, their surgical patient flow will likely improve.

Health Sciences Centre (HSC) in Winnipeg is the major healthcare facility serving Manitoba, Northwestern Ontario, and Nunavut. An evaluation of HSC’s adult surgical patient flow revealed that one major barrier to smooth flow was their Operating Room (OR) scheduling system. This thesis presents a new two-stage elective OR scheduling system for HSC, which generates weekly OR schedules that reduce artificial variability in order to facilitate smooth patient flow. The first stage reduces day-to-day variability while the second stage reduces variability occurring within a day. The scheduling processes in both stages are mathematically modelled as multi-objective optimization problems. An attempt was made to solve both models using lexicographic goal programming. However, this proved to be an unacceptable method for the second stage, so a new multi-objective genetic algorithm, Nondominated Sorting Genetic Algorithm II – Operating Room (NSGAII-OR), was developed. Results indicate that if the system is implemented at HSC, their surgical patient flow will likely improve.

The world of today is increasingly dependant on a functional, globalized economy. The defence and security establishments’ reliance on supplies and logistics is not new. First responders rely on many tools and systems that are critical to their endeavours. Somewhat disjoint at first glance, these domains share a common need for complex physical or logistical infrastructures such as power plants, ports, supply chains, to name a few examples.All of these are potentially vulnerable to attacks, disruptions, breakdowns, or other activities that disable the infrastructure and consequently cause important physical or economic damage. An obligation exists to protect these critical infrastructures and a decision support system that is able to detect, identify, and mitigate the risk of unwanted events would be invaluable in preventing the disastrous consequences of compromised infrastructure.This thesis explores the design and application of such a system. It starts with a pre-existing, actively researched risk management framework and proposes a methodology to apply it in new contexts, as well as contributions to provide the framework with the ability to solve new problems. Relevant case studies in critical infrastructure protection are presented, as well as applications of the developed methodology with the proposed modifications when suitable. Simulations, results, and insightful discussions are provided for each of the case studies. Finally, research trends, future work, and a conclusion are given, completing this thesis.

In the thesis of “Mohammed Aijaz Mohiuddin”, Engineering Nature-Inspired Heuristics for the Open Shortest Path First Weight Setting Problem, nature inspired heuristics were developed. Besides the existing two objectives, namely maximum utilization and the number of congested links, a third objective namely the number of unused links was used to formulate the fuzzy based objective function for the OSPFWS problem. The idea was to make use unused network links if any. Furthermore, a hybrid fuzzy based evolutionary Particle Swarm Optimization (FEPSO) algorithm was designed that harnessed evolutionary intelligence along with swarm intelligence. The proposed FEPSO algorithm was tested on different size test cases and its performance was mutually compared with other algorithms namely Simulated Annealing, Simulated Evolution, Particle Swarm Optimization, Weighted Aggregation Particle Swarm Optimization, Pareto-dominance Particle Swarm Optimization and Non-dominating Sorting Genetic Algorithm. Obtained results suggested the better performance of FEPSO among other algorithms over majority of test cases. / Thesis (PHD)--University of Pretoria, 2018. / Computer Science / PhD / Unrestricted

In this dissertation, we consider extensions of dynamic programming for combinatorial optimization. We introduce two exact multi-objective optimization algorithms: the multi-stage optimization algorithm that optimizes the problem relative to the ordered sequence of objectives (lexicographic optimization) and the bi-criteria optimization algorithm that simultaneously optimizes the problem relative to two objectives (Pareto optimization). We also introduce a counting algorithm to count optimal solution before and after every optimization stage of multi-stage optimization. We propose a fairly universal approach based on so-called circuits without repetitions in which each element is generated exactly one time. Such circuits represent the sets of elements under consideration (the sets of feasible solutions) and are used by counting, multi-stage, and bi-criteria optimization algorithms. For a given optimization problem, we should describe an appropriate circuit and cost functions. Then, we can use the designed algorithms for which we already have proofs of their correctness and ways to evaluate the required number of operations and the time. We construct conventional (which work directly with elements) circuits without repetitions for matrix chain multiplication, global sequence alignment, optimal paths in directed graphs, binary search trees, convex polygon triangulation, line breaking (text justification), one-dimensional clustering, optimal bitonic tour, and segmented least squares. For these problems, we evaluate the number of operations and the time required by the optimization and counting algorithms, and consider the results of computational experiments. If we cannot find a conventional circuit without repetitions for a problem, we can either create custom algorithms for optimization and counting from scratch or can transform a circuit with repetitions into a so-called syntactical circuit, which is a circuit without repetitions that works not with elements but with formulas representing these elements. We apply both approaches to the optimization of matchings in trees and apply the second approach to the 0/1 knapsack problem. We also briefly introduce our work in operation research with applications to health care. This work extends our interest in the optimization field from developing new methods included in this dissertation towards the practical application.

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The limited available budget along with old aging infrastructure in nation magnifies the role of strategic decision making for maintenance of infrastructure. The challenging objective is to maintain the infrastructure asset systems in a state of good repair and to improve the efficiency and performance of the infrastructure systems while protecting and enhancing the natural environment. Decision makers are in need of a decision support system to consider these multiple objectives and criteria to effectively allocate funding and achieve the highest possible return on investment on their infrastructure. The research proposes and validates a framework for such decisions. The proposed model aims at finding optimal techniques for maintenance of multiple roadway asset items while taking into account time, cost, level of service and environmental impacts. Therefore, the goal is to answer what are the optimal combinations of maintenance techniques for roadway assets while more than one objective is being optimized. In other words, the main objective is to develop a decision support system for selecting and prioritizing necessary actions for MRandR (Maintenance, Repair and Rehabilitation) of multiple asset items in order for a roadway to function within an acceptable level of service, budget, and time while considering environmental impacts. To achieve these desirable outcomes, this model creates a two-stage framework for a sustainable infrastructure asset management. First a multi-objective problem based on the multi colony ant colony optimization is analyzed. The objectives of the problem are: (i) Minimizing maintenance costs, (ii) Minimizing maintenance time, (iii) Minimizing environmental impacts and (iv) Maximizing level of service improvement. In the second stage, the results of the multi objective optimization will be prioritized using a Multi Criteria Decision Making (MCDM) process. The proposed approach will simultaneously optimize four conflicting objectives along with using a multi criteria decision-making technique for ranking the resulted non-dominated solutions of multi objective optimization. The results of implementation of the proposed model on a section of I-64 highway are presented for a sub-set of asset items. Moreover, the proposed model is validated using a scalable test problem as well as comparison with existing examples. Results reveal the capability of the model in generation of optimal solutions for the selection of maintenance strategies. The model optimizes decision making process and benefits decision makers by providing them with solutions for infrastructure asset management while meeting national goals towards sustainability and performance-based approach. In addition, provides a tool to run sensitivity analysis to evaluate annual budget effects and environmental impacts of different resource allocation scenarios. Application of the proposed approach is implemented on roadway asset items but it is not limited to roadways and is applicable to other infrastructure assets. / Ph. D.

The Levenberg-Marquardt algorithm is a classical method for solving nonlinear systems of equations that can come from various applications in engineering and economics. Recently, Levenberg-Marquardt methods turned out to be a valuable principle for obtaining fast convergence to a solution of the nonlinear system if the classical nonsingularity assumption is replaced by a weaker error bound condition. In this way also problems with nonisolated solutions can be treated successfully. Such problems increasingly arise in engineering applications and in mathematical programming. In this thesis we use Levenberg-Marquardt algorithms to deal with nonlinear equations, multi-objective optimization and complementarity problems. We develop new algorithms for solving these problems and investigate their convergence properties. For sufficiently smooth nonlinear equations we provide convergence results for inexact Levenberg-Marquardt type algorithms. In particular, a sharp bound on the maximal level of inexactness that is sufficient for a quadratic (or a superlinear) rate of convergence is derived. Moreover, the theory developed is used to show quadratic convergence of a robust projected Levenberg-Marquardt algorithm. The use of Levenberg-Marquardt type algorithms for unconstrained multi-objective optimization problems is investigated in detail. In particular, two globally and locally quadratically convergent algorithms for these problems are developed. Moreover, assumptions under which the error bound condition for a Pareto-critical system is fulfilled are derived. We also treat nonsmooth equations arising from reformulating complementarity problems by means of NCP functions. For these reformulations, we show that existing smoothness conditions are not satisfied at degenerate solutions. Moreover, we derive new results for positively homogeneous functions. The latter results are used to show that appropriate weaker smoothness conditions (enabling a local Q-quadratic rate of convergence) hold for certain reformulations. / Der Levenberg-Marquardt-Algorithmus ist ein klassisches Verfahren zur Lösung von nichtlinearen Gleichungssystemen, welches in verschiedenen Anwendungen der Ingenieur-und Wirtschaftswissenschaften vorkommen kann. Kürzlich, erwies sich das Verfahren als ein wertvolles Instrument für die Gewährleistung einer schnelleren Konvergenz für eine Lösung des nichtlinearen Systems, wenn die klassische nichtsinguläre Annahme durch eine schwächere Fehlerschranke der eingebundenen Bedingung ersetzt wird. Auf diese Weise, lassen sich ebenfalls Probleme mit nicht isolierten Lösungen erfolgreich behandeln. Solche Probleme ergeben sich zunehmend in den praktischen, ingenieurwissenschaftlichen Anwendungen und in der mathematischen Programmierung. In dieser Arbeit verwenden wir Levenberg-Marquardt- Algorithmus für nichtlinearere Gleichungen, multikriterielle Optimierung - und nichtlineare Komplementaritätsprobleme. Wir entwickeln neue Algorithmen zur Lösung dieser Probleme und untersuchen ihre Konvergenzeigenschaften. Für ausreichend differenzierbare nichtlineare Gleichungen, analysieren und bieten wir Konvergenzergebnisse für ungenaue Levenberg-Marquardt-Algorithmen Typen. Insbesondere, bieten wir eine strenge Schranke für die maximale Höhe der Ungenauigkeit, die ausreichend ist für eine quadratische (oder eine superlineare) Rate der Konvergenz. Darüber hinaus, die entwickelte Theorie wird verwendet, um quadratische Konvergenz eines robusten projizierten Levenberg-Marquardt-Algorithmus zu zeigen. Die Verwendung von Levenberg-Marquardt-Algorithmen Typen für unbeschränkte multikriterielle Optimierungsprobleme im Detail zu untersucht. Insbesondere sind zwei globale und lokale quadratische konvergente Algorithmen für multikriterielle Optimierungsprobleme entwickelt worden. Die Annahmen wurden hergeleitet, unter welche die Fehlerschranke der eingebundenen Bedingung für ein Pareto-kritisches System erfüllt ist. Wir behandeln auch nicht differenzierbare nichtlineare Gleichungen aus Umformulierung der nichtlinearen Komplementaritätsprobleme durch NCP-Funktionen. Wir zeigen für diese Umformulierungen, dass die bestehenden differenzierbaren Bedingungen nicht zufrieden mit degenerierten Lösungen sind. Außerdem, leiten wir neue Ergebnisse für positiv homogene NCP-Funktionen. Letztere Ergebnisse werden verwendet um zu zeigen, dass geeignete schwächeren differenzierbare Bedingungen (so dass eine lokale Q-quadratische Konvergenzgeschwindigkeit ermöglichen) für bestimmte Umformulierungen gelten.