The aim and objective of this research is to formulate and solve a multi-objective optimization problem for the optimal placement of multiple rows and multiple columns of fixed flat-plate solar collectors in a field. This is to maximize energy collected from the solar collectors and minimize the investment in terms of the field and collector cost. The resulting multi-objective optimization problem will be solved using genetic algorithm techniques. It is necessary to consider multiple columns of collectors as this can result in obtaining higher amounts of energy from these collectors when costs and maintenance or replacement of damaged parts are concerned. The formulation of such a problem is dependent on several factors, which include shading of collectors, inclination of collectors, distance between the collectors, latitude of location and the global solar radiation (direct beam and diffuse components). This leads to a multi-objective optimization problem. These kind of problems arise often in nature and can be difficult to solve. However the use of evolutionary algorithm techniques has proven effective in solving these kind of problems. Optimizing the distance between the collector rows, the distance between the collector columns and the collector inclination angle, can increase the amount of energy collected from a field of solar collectors thereby maximizing profit and improving return on investment. In this research, the multi-objective optimization problem is solved using two optimization approaches based on genetic algorithms. The first approach is the weighted sum approach where the multi-objective problem is simplified into a single objective optimization problem while the second approach is finding the Pareto front. / Dissertation (MEng)--University of Pretoria, 2012. / Electrical, Electronic and Computer Engineering / MEng / Unrestricted

Due to an increasing awareness of the importance of sustainable energy use, multi-objective optimization problems for upper-level energy systems are continually being developed and improved. This paper focuses on the modeling and optimization of the Helsinki district heating system and establishing the basis for modeling the Finnish power network. The optimization of the district heating system is conducted for a twenty four hour winter demand period. Partial load behavior of the generators is included by introducing non-linear functions for costs, emissions, and the exergetic efficiency. A fuel cost sensitivity analysis is conducted on the system by considering ten combinations of fuel costs based on high, medium, and low prices for each fuel. The solution sets, called Pareto fronts, are evaluated by post-processing techniques in order to determine the best solution from the optimal set. Because units between some of objective functions are non-commensurable, objective values are normalized and weighted. The results indicate that for today\'s fuel prices the best solution includes a dominating usage of natural gas technologies, while if the price of natural gas is higher than other fuels, natural gas technologies are often not included in the best solution. All of the necessary costs, emissions, and operating information is provided for the the Finnish power network in order to employ a multi-objective optimization on the system. / Master of Science

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The Pareto Principle, also known as the 80–20 rule, is the observation that 20% of input (e.g., workers) produce 80% of the results. Consistent with this principle, previous research has identified a group (20%) of families, the Vital Few, who provide a disproportionate amount of foster care and are more willing to foster children with special needs. The ability to predict the emergence of these families has important implications for recruitment, support and placement stability, as well as longevity of foster families. This study replicated and extended previous research by conducting a follow-up study of 107 families (90% response rate) 17 years after pre-service training. Consistent with previous research we found a small proportion (10%) of families who provide a disproportionate amount of care in terms of length of service and number of children fostered, approved to foster, adopted, and removed at families’ request. At the completion of pre-service training Vital Few families were more likely to have had previous foster parent experience and one or more children in their homes; mothers and fathers in the Vital Few were older, and fathers reported less education. Also, at pre-service training more Vital Few families said they would foster sibling groups (100 vs. 64%), but there were no other differences in terms of willingness to foster children with special needs. This study further validates the utility of the Pareto Principle for understanding foster families and, by extension, has important implications for the well-being and stability of foster children.

There is a small, methodologically diverse body of research indicating that approximately 20% of families provide disproportionate amounts of foster caregiving, place fewer restrictions on characteristics of children they are willing to foster and actually do foster, and provide caregiving environments as good as or better than those provided by other foster families. Cherry and Orme (2013) conceptualized this phenomenon in terms of the Pareto Principle, also known as the 80-20 rule or the Vital Few, and they refer to these 20% of families as the Vital Few and the remaining 80% as the Useful Many. This review will examine and synthesize the available research on Vital Few foster families and explore next steps in the development of this body of research.

The Pareto Principle, also known as the 80-20 rule or the Vital Few, has been successfully used as a framework to identify the small proportion of highly productive foster parents who provide a disproportionate amount of care. This study replicated and extended this research using a nationally representative sample of foster families ( N=. 876) with a focus on willingness to foster, and actually fostering, children with special needs. Using latent class analysis, two classes of foster parents were identified: one accounted for 19% of respondents and the other 81%. We refer to the former as the Vital Few and the latter as the Useful Many. Vital Few respondents fostered 74.2% of foster children - 11 times more than the Useful Many, although only fostering two times longer. They also had almost 1-1/2 times as many foster children in their homes at the time of the study. Notably, the Vital Few were willing to foster more types of children with special needs and a higher percentage had actually fostered children with each of the seven types of special needs studied. The classes were similar demographically except that Vital Few respondents were less likely to work outside the home and Vital Few mothers were slightly less educated as compared to Useful Many mothers. This study further validates the utility of the Pareto Principle for understanding foster parents and, by extension, has important implications for the well-being and stability of foster children with special needs. Considerations for supporting the Vital Few, including education and training needs, are discussed.

Product families are frequently used to provide consumers with a variety of appealing products and to help maintain reasonably low production costs for manufacturers. Three common objectives in the design of product families are used to balance the interests of both consumers and manufacturers. These objectives are to maximize (i) product performance, (ii) product distinctiveness as perceived by the consumer, and (iii) product commonality as seen by the manufacturer. In this thesis, three methods are introduced that use multiobjective optimization and Smart Pareto filtering to satisfy the three objectives of product family design. The methods are progressive in nature and begin with the selection of product family members using Smart filtering and develop through the establishment of scale- based product platforms to the design of combined scale- based and module-based product platforms. Each of the methods is demonstrated using a well-know universal electric motor example problem. The results of each method are then compared to a benchmark electric motor product family that was previously defined in the literature. Additionally, a pressure vessel example problem is used to further demonstrate the first of the three methods.

Natural and predictable changes in consumer needs often require the development of new products. Providing solutions that anticipate, account for, and allow for these changes over time is a significant challenge to manufacturers and design engineers. Products that adapt to these changes through the addition of modules reduce production costs through product commonality and provide a set of products that cater to customization and adaptation. In this thesis, a multiobjective optimization design method using s-Pareto frontiers – sets of non-dominated designs from disparate design models - is developed and used to identify a set of optimal adaptive product designs that satisfy changing consumer needs. The novel intent of the method is to design a product that adapts to changing consumer needs by moving from one location on the s-Pareto frontier to another through the addition of a module and/or reconfiguration. The six-step method is described as follows: (A) Characterize the multiobjective design space. (B) Identify the anticipated regions of interest within the search space based on predicted future needs. (C) Identify the platform design variables that minimize the performance losses due to commonality across the anticipated regions of interest. (D) Assemble the s-Pareto frontier within each region of interest. (E) Determine the values of all design variables for the optimal product design in each region of interest by multiobjective optimization. (F) Identify the module design variables, and identify the platform and module designs by constrained module design. An example of the design of a simple unmanned air vehicle is used to demonstrate application of the method for a single Pareto frontier case. The design of a manual irrigation pump is used to demonstrate application of the method for a s-Pareto frontier case. In addition, these examples show the ability of the method to design a product that adapts to changing consumer needs by traversing the s-Pareto frontier.

Computer simulation is a popular method that is often used as a decision support tool in industry to estimate the performance of systems too complex for analytical solutions. It is a tool that assists decision-makers to improve organizational performance and achieve performance objectives in which simulated conditions can be randomly varied so that critical situations can be investigated without real-world risk. Due to the stochastic nature of many of the input process variables in simulation models, the output from the simulation model experiments are random. Thus, experimental runs of computer simulations yield only estimates of the values of performance objectives, where these estimates are themselves random variables. Most real-world decisions involve the simultaneous optimization of multiple, and often conflicting, objectives. Researchers and practitioners use various approaches to solve these multiobjective problems. Many of the approaches that integrate the simulation models with stochastic multiple objective optimization algorithms have been proposed, many of which use the Pareto-based approaches that generate a finite set of compromise, or tradeoff, solutions. Nevertheless, identification of the most preferred solution can be a daunting task to the decisionmaker and is an order of magnitude harder in the presence of stochastic objectives. However, to the best of this researcher’s knowledge, there has been no focused efforts and existing work that attempts to reduce the number of tradeoff solutions while considering the stochastic nature of a set of objective functions. In this research, two approaches that consider multiple stochastic objectives when reducing the set of the tradeoff solutions are designed and proposed. The first proposed approach is an a posteriori approach, which uses a given set of Pareto optima as input. The second iv approach is an interactive-based approach that articulates decision-maker preferences during the optimization process. A detailed description of both approaches is given, and computational studies are conducted to evaluate the efficacy of the two approaches. The computational results show the promise of the proposed approaches, in that each approach effectively reduces the set of compromise solutions to a reasonably manageable size for the decision-maker. This is a significant step beyond current applications of decision-making process in the presence of multiple stochastic objectives and should serve as an effective approach to support decisionmaking under uncertainty

The complete design process for a new nuclear power plant concept is costly, long, complicated, and the work is generally split between several specialized groups. These design groups separately do their best to design the portion of the reactor that falls in their expertise according to the design criteria before passing the design to the subsequent design group. Ultimately, the work of each design group is combined, with significant iteration between groups striving to facilitate the integration of each of the heavily interdependent systems. Such complex interaction between experts leads to three significant problems: (1) the issues associated with knowledge management, (2) the lack of design optimization, and (3) the failure to discover the hidden interdependencies between different design parameters that may exist. Some prior work has been accomplished in both developing common frame of reference (CFR) support systems to aid in the design process and applying optimization to nuclear system design.The purpose of this work is to use multi-objective optimization to address the second and third problems above on a small subset of reactor design scenarios. Multi-objective optimization generates several design optima in the form of a Pareto front, which portrays the optimal trade-off between design objectives. As a major part of this work, a system design optimization tool is created, namely the Optimization and Preference Tool for the Improvement of Nuclear Systems (OPTIONS). The OPTIONS tool is initially applied to several individual nuclear systems: the power conversion system (PCS) of the Integral, Inherently Safe Light Water Reactor (I²S-LWR), the Kalina cycle being proposed as the PCS for a LWR, the PERCS (or Passive Endothermic Reaction Cooling System), and the core loop of the Zion plant. Initial sensitivity analysis work and the application of the Non-dominated Sorting Particle Swarm Optimization (NSPSO) method provides a Pareto front of design optima for the PCS of the I²S-LWR, while bringing to light some hidden pressure interdependencies for generating steam using a flash drum. A desire to try many new PCS configurations leads to the development of an original multi-objective optimization method, namely the Mixed-Integer Non-dominated Sorting Genetic Algorithm (MI-NSGA). With this method, the OPTIONS tool provides a novel and improved Pareto front with additional optimal PCS configurations. Then, the simpler NSGA method is used to optimize the Kalina cycle, the PERCS, and the Zion core loop, providing each problem with improved designs and important objective trade-off information. Finally, the OPTIONS tool uses the MI-NSGA method to optimize the integration of three systems (Zion core loop, PERCS, and Rankine cycle PCS) while increasing efficiency, decreasing costs, and improving performance. In addition, the tool is outfitted to receive user preference input to improve the convergence of the optimization to a Pareto front.