This research has been defined in response to the Winnipeg children's hospital (WCH) challenges such as long waiting times, delays and cancellations in surgical flow. Preliminary studies on the surgical flow revealed that definition and implementation of successful process improvement projects (PIPs) along with application of an efficient master surgical schedule (MSS) are efficient solutions to the critical problems in WCH. In the first phase of this work, a process improvement program including three major PIPs, is defined and implemented in WCH in order to improve the efficiency of the processes providing surgical service for patients. In the second phase, two new multi-objective mathematical models are presented to develop efficient MSSs for operating room department (OR) in WCH.

Multi-objective optimization metaheuristics (MOMs) are powerful methods for solving complex optimization problems but can require a large number of function evaluations to find optimal solutions. Thus, an efficient multi-objective optimization method should generate accurate and diverse solutions in a timely manner. Improving MOMs convergence speed is an important and challenging research problem which is the scope of this thesis. This thesis conducted the most comprehensive comparative study ever in MOMs. Based on the results, multi-objective (MO) versions of particle swarm optimization (PSO) and differential evolution (DE) algorithms achieved the highest performances; therefore, these two MOMs have been selected as bases for further acceleration in this thesis. To accelerate the selected MOMs, this work focuses on the incorporation of leadership concept to MO variants of DE and PSO algorithms. Two complex case studies of MO design of renewable energy systems are proposed to demonstrate the efficiency of the proposed MOMs. This thesis proposes three new MOMs, namely, leader and speed constraint multi-objective PSO (LSMPSO), opposition-based third evolution step of generalized DE (OGDE3), and multi-objective DE with leadership enhancement (MODEL) which are compared with seven state-of-the-art MOMS using various benchmark problems. LSMPSO was found to be the fastest MOM for the problem undertaken. Further, LSMPSO achieved the highest solutions accuracy for optimal design of a photovoltaic farm in Toronto area. OGDE3 is the first successful application of OBL to a MOM with single population (no-coevolution) using leadership and self-adaptive concepts; the convergence speed of OGDE3 outperformed the other MOMs for the problems solved. MODEL embodies leadership concept into mutation operator of GDE3 algorithm. MODEL achieved the highest accuracy for the 30 studied benchmark problems. Furthermore, MODEL achieved the highest solution accuracy for a MO optimization problem of hydrogen infrastructures design across the province Ontario between 2008 and 2025 considering electricity infrastructure constraints.

In this study, we consider the hub location problem of PTT, first realized by Cetiner (2003), and propose the evaluation of multiple decision criteria while locating hubs. Since the mathematical model for the problem is too large to be solved, we utilize heuristic methods in the solution procedure. While doing this, we first test two algorithms, NSGA-II and SPEA2, on different hub location problems and use the algorithm with better performance while solving the PTT problem.

This thesis introduces a multi-objective variation of the personnel assignment problem, by including additional hierarchical and team constraints, which put restrictions on possible matchings of the bipartite graph. Besides maximization of summation of weights that are assigned to the edges of the graph, these additional constraints are also treated as objectives which are subject to minimization. In this work, different genetic algorithm approaches to multi-objective optimization are considered to solve the problem. Weighted Sum &ndash / a classical approach, VEGA - a non-elitist multi-objective evolutionary algorithm, and SPEA &ndash / a popular elitist multi-objective evolutionary algorithm, are considered as means of solution to the problem, and their performances are compared with respect to a number of multi-objective optimization criteria.

One of the main advantages of the Gantry-Tau machine is a large accessible workspace\footprint ratio compared to many other parallel machines. The Gantry-Tau improves this ratio further by allowing a change of assembly mode without internal link collisions or collisions between the links and the moving TCP platform. In this Thesis some of the features of the Gantry-Tau structure are described and results are presented from the analysis of the kinematic, elastostatic and elastodynamic properties of the PKM. However, the optimal kinematic, elastostatic and elastodynamic design parameters of the machine are still difficult to calculate and this thesis introduces a multi-objective optimisation scheme based on the geometric approach for the workspace area, unreachable area, joint angle limitations and link collisions as well as the functional dependencies of the elements of the static matrix and the Laplace transform to define the first resonance frequency and Cartesian and torsional stiffness. The method to calculate the first resonance frequency assumes that each link and universal joint can be described by a mass-springdamper model and calculates the transfer function from a Cartesian (TCP) force or torque to Cartesian position or orientation. The geometric methods involve the simple geometric shapes (spheres, circles, segments, etc) and vectors. The functional dependencies are based on the properties between the kinematic parameters. These approaches are significantly faster than analytical methods based on the inverse kinematics or the general Finite Elements Method (FEM). The reconfigurable Gantry-Tau kinematic design obtained by multi-objective optimisation gives the following features: • Workspace/footprint ratio more than 3.19. • First resonance frequency greater than 48 Hz. • Lowest Cartesian stiffness in the workspace 5N/μm. • The unreachable space in the middle of the workspace is not detected. • No link collisions. The results show that by careful design of the PKM, a collision free workspace without the unreachable area in the middle can be achieved. High stiffness and high first resonance frequency are important parameters for the the Gantry-Tau when used in industrial applications, such as cutting, milling and drilling of steel or aluminium and pick-and-place operations. These applications require high static and dynamic accuracy in combination with high speed and acceleration. The optimisation parameters are the support frame lengths, actuator positions,endeffector kinematics and the robot’s arm lengths. Because of the fast computational speed of the geometric approaches and computational time saving of the methods based on the functional dependency, they are ideal for inclusion in a design optimisation framework, normally a nonlinear optimisation routine. In this Thesis the evolutionary algorithm based on the complex search method is used to optimise the 3-DOF Gantry-Tau. The existing lab prototype of this machine was assembled and completed at the University of Agder

The interval programming model (IvP) is a mathematical programmingmodel for representing and solving multi-objective optimizationproblems. The central characteristic of the model is the use ofpiecewise linearly defined objective functions and a solution methodthat searches through the combination space of pieces rather thanthrough the actual decision space. The piecewise functions typicallyrepresent an approximation of some underlying function, but thisconcession is balanced on the positive side by relative freedom fromfunction form assumptions as well as the assurance of global optimality.In this paper the model and solution algorithms are described, and theapplicability of IvP to certain applications arediscussed.

Renewable energy (RE) resources are relatively unpredictable and dependent on climatic conditions. The negative effects of existing randomness in RE resources can be reduced by the integration of RE resources into what is called Hybrid Renewable Energy Systems (HRES). The design of HRES remains as a complicated problem since there is uncertainty in energy prices, demand, and RE sources. In addition, it is a multi-objective design since several conflicting objectives must be considered. In this thesis, an optimal sizing approach has been proposed to aid decision makers in sizing and performance analysis of this kind of energy supply systems. First, a straightforward methodology based on ε-constraint method is proposed for optimal sizing of HRESs containing RE power generators and two storage devices. The ε-constraint method has been applied to minimize simultaneously the total net present cost of the system, unmet load, and fuel emission. A simulation-based particle swarm optimization approach has been used to tackle the multi-objective optimization problem. In the next step, a Pareto-based search technique, named dynamic multi-objective particle swarm optimization, has been performed to improve the quality of the Pareto front (PF) approximated by the ε-constraint method. The proposed method is examined for a case study including wind turbines, photovoltaic panels, diesel generators, batteries, fuel cells, electrolyzers, and hydrogen tanks. Well-known metrics from the literature are used to evaluate the generated PF. Afterward, a multi-objective approach is presented to consider the economic, reliability and environmental issues at various renewable energy ratio values when optimizing the design of building energy supply systems. An existing commercial apartment building operating in a cold Canadian climate has been described to apply the proposed model. In this test application, the model investigates the potential use of RE resources for the building. Furthermore, the application of plug-in electric vehicles instead of gasoline car for transportation is studied. Comparing model results against two well-known reported multi-objective algorithms has also been examined. Finally, the existing uncertainties in RE and load are explicitly incorporated into the model to give more accurate and realistic results. An innovative and easy to implement stochastic multi-objective approach is introduced for optimal sizing of an HRES. / February 2016

ENGLISH ABSTRACT: It is very seldom that a decision-making problem concerns only a single value or objective. The process of simultaneously optimising two or more con icting objectives is known as multi-objective optimisation (MOO). A number of metaheuristics have been successfully adapted for MOO. The aim of this study was to investigate the feasibility of applying an agent-based modelling approach to MOO. The (s; S) inventory problem was chosen as the application eld for this approach and Anylogic used as model platform. Agents in the model were responsible for inventory and sales management, and had to negotiate with each other in order to nd optimal reorder strategies. The introduction of concepts such as agent satisfaction indexes, aggression factors, and recollection ability guided the negotiation process between the agents. The results revealed that the agents had the ability to nd good strategies. The Pareto front generated from their proposed strategies was a good approximation to the known front. The approach was also successfully applied to a recognised MOO test problem proving that it has the potential to solve a variety of MOO problems. Future research could focus on further developing this approach for more practical applications such as complex supply chain systems, nancial models, risk analysis and economics. / AFRIKAANSE OPSOMMING: Daar is weinig besluitnemingsprobleme waar slegs 'n enkele waarde of doelwit ter sprake is. Die proses waar twee of meer doelwitte, wat in konflik staan met mekaar, gelyktydig optimiseer word, staan bekend as multi-doelwit optimisering (MOO). 'n Aantal metaheuristieke is al suksesvol aangepas vir MOO. Die doelwit van hierdie studie was om ondersoek in te stel na die lewensvatbaarheid van die toepassing van 'n agent gebasseerde modelerings benadering tot MOO. As toepassingsveld vir hierdie benadering was die (s; S) voorraad probleem gekies en Anylogic was gebruik as model platform. In die model was agente verantwoordelik vir voorraad- en verkope bestuur. Hulle moes onderling met mekaar onderhandel om die optimale bestelling strategiee te verkry. Konsepte soos agentbevrediging, aggressie faktore en herinneringsvermoens is ingestel om die onderhandeling tussen die agente te bewerkstellig. Die resultate het gewys dat die agente oor die vermoe beskik om met goeie strategiee vorendag te kom. Die Pareto fronte wat gegenereer is deur hul voorgestelde strategiee was 'n goeie benadering tot die bekende front. Die benadering was ook suksesvol toegepas op 'n erkende MOO toets-probleem wat bewys het dat dit oor die potensiaal beskik om 'n verskeidenheid van MOO probleme op te los. Toekomstige navorsing kan daarop fokus om hierdie benadering verder te ontwikkel vir meer praktiese toepassings soos komplekse voorsieningskettingstelsels, finnansiele modelle, risiko-analises en ekonomie.

Le contenu de cette thèse est divisé en deux parties. La première partie de cette thèse porte sur l'étude d'approches heuristiques pour approximer des fronts de Pareto. Nous proposons un nouvel algorithme de recherche locale pour résoudre des problèmes d'optimisation combinatoire. Cette technique est intégrée dans un modèle opérationnel générique où l'algorithme évolue vers de nouvelles solutions formées en combinant des solutions trouvées dans les étapes précédentes. Cette méthode améliore les algorithmes de recherche locale existants pour résoudre le problème d'assignation quadratique bi- et tri-objectifs.La seconde partie se focalise sur les algorithmes d'ordonnancement dans un contexte non-préemptif. Plus précisément, nous étudions le problème de la minimisation du stretch maximum sur une seule machine pour une exécution online. Nous présentons des résultats positifs et négatifs, puis nous donnons une solution optimale semi-online. Nous étudions ensuite le problème de minimisation du stretch sur une seule machinedans le modèle récent de la réjection. Nous montrons qu'il existe un rapport d'approximation en O(1) pour minimiser le stretch moyen. Nous montrons également qu'il existe un résultat identique pour la minimisation du flot moyen sur une machine. Enfin, nous étudions le problème de la minimisation du somme des flots pondérés dans un contexte online. / The content of this thesis is divided into two parts. The first part of the thesis deals with the study of heuristic based approaches for the approximation Pareto fronts. We propose a new Double Archive Pareto local search algorithm for solving multi-objective combinatorial optimization problems. We embed our technique into a genetic framework where our algorithm restarts with the set of new solutions formed by recombination and mutation of solutions found in the previous run. This method improves upon the existing Pareto local search algorithm for bi-objective and tri-objective quadratic assignment problem.In the second part of the thesis, we focus on non-preemptive scheduling algorithms. Here, we study the online problem of minimizing maximum stretch on a single machine. We present both positive and negative theoretical results. Then, we provide an optimally competitive semi-online algorithm. Furthermore, we study the problem of minimizing stretch on a single machine in a recently proposed rejection model. We show that there exists an O(1)-approximation ratio for minimizing average stretch. We also show that there exists an O(1)-approximation ratio for minimizing average flow time on a single machine. Lastly, we study the weighted average flow time minimization problem in online settings. We present a mathematical programming based framework that unifies multiple resource augmentation. Using the concept of duality, we show that there exists an O(1)-competitive algorithm for solving the weighted average flow time problem on unrelated machines. Furthermore, we proposed that this idea can be extended to minimizing l_k norms of weighted flow problem on unrelated machines.

abstract: Surgery is one of the most important functions in a hospital with respect to operational cost, patient flow, and resource utilization. Planning and scheduling the Operating Room (OR) is important for hospitals to improve efficiency and achieve high quality of service. At the same time, it is a complex task due to the conflicting objectives and the uncertain nature of surgeries. In this dissertation, three different methodologies are developed to address OR planning and scheduling problem. First, a simulation-based framework is constructed to analyze the factors that affect the utilization of a catheterization lab and provide decision support for improving the efficiency of operations in a hospital with different priorities of patients. Both operational costs and patient satisfaction metrics are considered. Detailed parametric analysis is performed to provide generic recommendations. Overall it is found the 75th percentile of process duration is always on the efficient frontier and is a good compromise of both objectives. Next, the general OR planning and scheduling problem is formulated with a mixed integer program. The objectives include reducing staff overtime, OR idle time and patient waiting time, as well as satisfying surgeon preferences and regulating patient flow from OR to the Post Anesthesia Care Unit (PACU). Exact solutions are obtained using real data. Heuristics and a random keys genetic algorithm (RKGA) are used in the scheduling phase and compared with the optimal solutions. Interacting effects between planning and scheduling are also investigated. Lastly, a multi-objective simulation optimization approach is developed, which relaxes the deterministic assumption in the second study by integrating an optimization module of a RKGA implementation of the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to search for Pareto optimal solutions, and a simulation module to evaluate the performance of a given schedule. It is experimentally shown to be an effective technique for finding Pareto optimal solutions. / Dissertation/Thesis / Ph.D. Industrial Engineering 2010