In today's competitive business environment, a firm's ability to make the correct, critical decisions can be translated into a great competitive advantage. Most of these critical real-world decisions involve the optimization not only of multiple objectives simultaneously, but also conflicting objectives, where improving one objective may degrade the performance of one or more of the other objectives. Traditional approaches for solving multiobjective optimization problems typically try to scalarize the multiple objectives into a single objective. This transforms the original multiple optimization problem formulation into a single objective optimization problem with a single solution. However, the drawbacks to these traditional approaches have motivated researchers and practitioners to seek alternative techniques that yield a set of Pareto optimal solutions rather than only a single solution. The problem becomes much more complicated in stochastic environments when the objectives take on uncertain (or "noisy") values due to random influences within the system being optimized, which is the case in real-world environments. Moreover, in stochastic environments, a solution approach should be sufficiently robust and/or capable of handling the uncertainty of the objective values. This makes the development of effective solution techniques that generate Pareto optimal solutions within these problem environments even more challenging than in their deterministic counterparts. Furthermore, many real-world problems involve complicated, "black-box" objective functions making a large number of solution evaluations computationally- and/or financially-prohibitive. This is often the case when complex computer simulation models are used to repeatedly evaluate possible solutions in search of the best solution (or set of solutions). Therefore, multiobjective optimization approaches capable of rapidly finding a diverse set of Pareto optimal solutions would be greatly beneficial. This research proposes two new multiobjective evolutionary algorithms (MOEAs), called fast Pareto genetic algorithm (FPGA) and stochastic Pareto genetic algorithm (SPGA), for optimization problems with multiple deterministic objectives and stochastic objectives, respectively. New search operators are introduced and employed to enhance the algorithms' performance in terms of converging fast to the true Pareto optimal frontier while maintaining a diverse set of nondominated solutions along the Pareto optimal front. New concepts of solution dominance are defined for better discrimination among competing solutions in stochastic environments. SPGA uses a solution ranking strategy based on these new concepts. Computational results for a suite of published test problems indicate that both FPGA and SPGA are promising approaches. The results show that both FPGA and SPGA outperform the improved nondominated sorting genetic algorithm (NSGA-II), widely-considered benchmark in the MOEA research community, in terms of fast convergence to the true Pareto optimal frontier and diversity among the solutions along the front. The results also show that FPGA and SPGA require far fewer solution evaluations than NSGA-II, which is crucial in computationally-expensive simulation modeling applications.

This study explores the applicability of including groundwater recharge and water table variation as additional objective functions in a multi-objective optimization approach to design optimal groundwater monitoring networks. The study was conducted using the Ontario Provincial Groundwater Monitoring Network wells in the Hamilton, Halton, and Credit Valley regions in southern Ontario. The Dual Entropy-Multiobjective Optimization (DEMO) model which has been demonstrated to be sufficiently robust for designing optimum hydrometric networks was used in these analyses. The importance of determining the applicability in using additional design objectives in DEMO, including groundwater recharge and groundwater table seasonal variation, is rooted in the limitations of groundwater data and the time required setting up the models. While recharge allows for the capturing of spatial variability of climate, geomorphology, and geology of the area, the groundwater table series reflect the temporal/seasonal variability. The two set of information are complementary and should provide additional information to the DEMO for optimal network design. Two sources of groundwater recharge data were examined and compared; the recharge provided by the local conservation authorities, calculated using both the Precipitation-Runoff Modeling System (PRMS) and Hydrological Simulation Program--Fortran (HSP--F), and the recharge calculated in situ using only PRMS. The entropy functions are used to identify optimal trade-offs between the maximum possible information content and the minimum shared information between each of the existing and potential monitoring wells. The additional objective functions are used here to quantify the hydrological characteristics of the vadose zone in the aquifer as well as the potential impacts of agricultural, municipal, and industrial uses of groundwater in the area, and thus provide more information for the optimization algorithm to use. Results show that including additional design objectives significantly increases the number of optimal network solutions and provides additional information for potential monitoring well locations. These results suggest that it is worthwhile to include recharge as a design objective if the data is available, and to include groundwater table variation for the design of monitoring wells for shallow groundwater system. / Thesis / Master of Applied Science (MASc)

<p> In this thesis parametric analysis for conic quadratic optimization problems is studied. In parametric analysis, which is often referred to as parametric optimization or parametric programming, a perturbation parameter is introduced into the optimization problem, which means that the coefficients in the objective function of the problem and in the right-hand-side of the constraints are perturbed. First, we describe linear, convex quadratic and second order cone optimization problems and their parametric versions. Second, the theory for finding solutions of the parametric problems is developed. We also present algorithms for solving such problems. Third, we demonstrate how to use parametric optimization techniques to solve multiobjective optimization problems and compute Pareto efficient surfaces. </p> <p> We implement our novel algorithm for hi-parametric quadratic optimization. It utilizes existing solvers to solve auxiliary problems. We present numerical results produced by our parametric optimization package on a number of practical financial and non-financial computational problems. In the latter we consider problems of drug design and beam intensity optimization for radiation therapy. </p> <p> In the financial applications part, two risk management optimization models are developed or extended. These two models are a portfolio replication framework and a credit risk optimization framework. We describe applications of multiobjective optimization to existing financial models and novel models that we have developed. We solve a number of examples of financial multiobjective optimization problems using our parametric optimization algorithms. </p> / Thesis / Doctor of Philosophy (PhD)

In this study,we develop an elitist multiobjective evolutionary algorithm for approximating the Pareto-optimal frontiers of multiobjective optimization problems. The algorithm converges the true Pareto-optimal frontier while keeping the solutions in the population well-spread over the frontier. Diversity of the solutions is maintained by the territory de&amp / #64257 / ning property of the algorithm rather than using an explicit diversity preservation mechanism. This leads to substantial computational e&amp / #64259 / ciency. We test the algorithm on commonly used test problems and compare its performance against well-known benchmark algorithms. In addition to approximating the entire Pareto-optimal frontier,we develop a preference incorporation mechanism to guide the search towards the decision maker&amp / #8217 / s regions of interest. Based on this mechanism, we implement two variants of the algorithm. The &amp / #64257 / rst gathers all preference information before the optimization stage to &amp / #64257 / nd approximations of the desired regions. The second one is an interactive algorithm that focuses on the desired region by interacting with the decision maker during the solution process. Based on tests on 2- and 3-objective problems, we observe that both algorithms converge to the preferred regions.

In this study, we propose a two-phase solution approach for approximating the efficient frontier of a bicriteria hub location problem. We develop an evolutionary algorithm to locate the hubs on the network as the first phase. In the second phase, we develop a bounding procedure based on dominance relations and using the determined bounds, we solve the allocation subproblem for each located hub set. The two-phase approach is tested on the Australian Post data set and it is observed that our approach approximates the entire efficient frontier well. In addition, we suggest an interactive procedure to find the solutions that are in the decision maker&rsquo / s preferred region of the solution space. In this procedure, we progressively incorporate the preferences of the decision maker and direct the search towards the preferred regions. Based on some computational experiments, it is observed that the interactive procedure converges to the preferred regions.

This thesis is devoted toMultiobjective Optimization Design (MOOD) procedures for controller tuning applications, by means of EvolutionaryMultiobjective Optimization (EMO).With such purpose, developments on tools, procedures and guidelines to facilitate this process have been realized. This thesis is divided in four parts. The first part, namely Fundamentals, is devoted on the one hand, to cover the theorical background required for this Thesis; on the other hand, it provides a state of the art review on current applications of MOOD for controller tuning. The second part, Preliminary contributions on controller tuning, states early contributions using the MOOD procedure for controller tuning, identifying gaps on methodologies and tools used in this procedure. The contribution within this part is to identify the gaps between the three fundamental steps of theMOOD procedure: problemdefinition, search and decisionmaking. These gaps are the basis for the developments presented in parts III and IV. The third part, Contributions on MOOD tools, is devoted to improve the tools used in Part II. Although applications on the scope of this thesis are related to controller tuning, such improvements can also be used in other engineering fields. The first contribution regards the decision making process, where tools and guidelines for design concepts comparison in m-dimensional Pareto fronts are stated. The second contribution focuses on amending the gap between search process and decisionmaking. With this in mind, a mechanism for preference inclusion within the evolutionary process is developed. With this it is possible to calculate pertinent approximations of the Pareto front; furthermore, it allows to deal efficiently with many-objective and constrained optimization instances. Finally, in the fourth part, Final contributions on controller tuning, a stochastic sampling procedure for proportional-integral-derivative (PID) controllers is proposed, to guarantee that (1) any sampled controller will stabilize the closed loop and (2) any stabilizing controller could be sampled. Afterwards, two control engineering benchmarks are solved using this sampling strategy, the MOOD guidelines highlighted trough this Thesis for multivariable controller tuning and the tools developed in Part III. / Reynoso Meza, G. (2014). Controller Tuning by Means of Evolutionary Multiobjective Optimization: a Holistic Multiobjective Optimization Design Procedure [Tesis doctoral]. Editorial Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/38248 / Alfresco

El objetivo es desarrollar una herramienta de apoyo a la toma de decisiones para la planificación estratégica de cadenas de suministro (CS). La tarea consiste en determinar el número, ubicación y capacidad de todos los nodos de la CS, su política de expansión, el transporte y la producción entre todos los nodos de la red. El problema se formula como un modelo de programación lineal entera mixta (MILP) que se resuelve utilizando diferentes herramientas. En primer lugar se desarrolló una estrategia de descomposición para acelerar el proceso de resolución En segundo, se utilizó el algoritmo de aproximación para resolver el problema MILP estocástico. Por último, el modelo multi-objetivo incorpora las soluciones de compromiso entre los aspectos económicos y ambientales. Todas las formulaciones se aplicaron al caso real de la industria de caña de azúcar en Argentina. El objetivo de las herramientas es ayudar a los responsables de planificación estratégica de las infraestructuras para la producción de productos químicos. / The aim of this thesis is to provide a decision-support tool for the strategic planning of supply chains (SCs). The task consists of determining the number, location and capacities of all SC facilities, their expansion policy, the transportation links that need to be established, and the production rates and flows of all materials involved in the network. The problem is formulated as a mixed-integer linear programming (MILP) model, which is solved using several mathematical programming tools. First, a decomposition strategy was developed to expedite the solving procedure. Second, the approximation algorithm was utilized to solve the stochastic version of the MILP. Finally, the multi-objective model was developed to incorporate the trade-off between economical and ecological issues. All formulations were applied to a real case based on the Argentinean sugarcane industry. The tools presented are intended to help policy-makers in the strategic planning of infrastructures for chemicals production.

We propose a generic algorithm based on branch-and-bound to generate all efficient solutions of multiobjective combinatorial optimization (MOCO) problems. We present an algorithm specific to multiobjective 0-1 Knapsack Problem based on the generic algorithm. We test the performance of our algorithm on randomly generated sample problems against IBM ILOG CPLEX and we obtain better performance using a problem specific algorithm. We develop a heuristic algorithm by incorporating memory limitations at the expense of solution quality to overcome memory issues of the exact algorithm.

In this thesis we have proposed a variable-length multiobjective genetic algorithm to solve heterogeneous wireless transmitter placement with multiple constraints. Among many factors that may affect the result of placement, we focus on four major requirements, coverage, cost, data rate demand, and overlap. In the proposed algorithm we release the need for the upper bound number of transmitters that is a major constraint in the existing methods and achieve better wireless transmitter placement while considering the transmitter position and design requirement simultaneously. In experiments, we use the free space propagation model, the large scale propagation model which considers the shadowing effect, and the extended Hata-Okumura model to predict the path loss in a real two dimensional indoor environment, and an outdoor environment and even a real three dimensional outdoor environment. Experimental results show that the proposed algorithm can find many feasible solutions for all test cases under four objectives.

This research aims to improve our understanding of multiobjective optimization, by comparing the performance of five multiobjective optimization algorithms, and by proposing a new formulation to consider input uncertainty in multiobjective optimization problems. Four deterministic multiobjective optimization algorithms and one probabilistic algorithm were compared: the Weighted Sum, the Adaptive Weighted Sum, the Normal Constraint, the Normal Boundary Intersection methods, and the Nondominated Sorting Genetic Algorithm-II (NSGA-II). The algorithms were compared using six test problems, which included a wide range of optimization problem types (bounded vs. unbounded, constrained vs. unconstrained). Performance metrics used for quantitative comparison were the total run (CPU) time, number of function evaluations, variance in solution distribution, and numbers of dominated and non-optimal solutions. Graphical representations of the resulting Pareto fronts were also presented. No single method outperformed the others for all performance metrics, and the two different classes of algorithms were effective for different types of problems. NSGA-II did not effectively solve problems involving unbounded design variables or equality constraints. On the other hand, the deterministic algorithms could not solve a problem with a non-continuous objective function. In the second phase of this research, design under uncertainty was considered in multiobjective optimization. The effects of input uncertainty on a Pareto front were quantitatively investigated by developing a multiobjective robust optimization framework. Two possible effects on a Pareto front were identified: a shift away from the Utopia point, and a shrinking of the Pareto curve. A set of Pareto fronts were obtained in which the optimum solutions have different levels of insensitivity or robustness. Four test problems were used to examine the Pareto front change. Increasing the insensitivity requirement of the objective function with regard to input variations moved the Pareto front away from the Utopia point or reduced the length of the Pareto front. These changes were quantified, and the effects of changing robustness requirements were discussed. The approach would provide designers with not only the choice of optimal solutions on a Pareto front in traditional multiobjective optimization, but also an additional choice of a suitable Pareto front according to the acceptable level of performance variation. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2009-08-10 21:59:13.795