A Scalability Study and New Algorithms for Large-Scale Many-Objective Optimization

Many real-world optimization problems contain multiple (often conflicting) goals to be optimized concurrently, commonly referred to as multi-objective problems (MOPs). Over the past few decades, a plethora of multi-objective algorithms have been proposed, often tested on MOPs possessing two or three objectives. Unfortunately, when tasked with solving MOPs with four or more objectives, referred to as many-objective problems (MaOPs), a large majority of optimizers experience significant performance degradation. The downfall of these optimizers is that simultaneously maintaining a well-spread set of solutions along with appropriate selection pressure to converge becomes difficult as the number of objectives increase. This difficulty is further compounded for large-scale MaOPs, i.e., MaOPs possessing large amounts of decision variables. In this thesis, we explore the challenges of many-objective optimization and propose three new promising algorithms designed to efficiently solve MaOPs. Experimental results demonstrate the proposed optimizers to perform very well, often outperforming state-of-the-art many-objective algorithms.

Inverse Illumination Design with Genetic Programming

Interior illumination is a complex problem involving numerous interacting factors. This research applies genetic programming towards problems in illumination design. The Radiance system is used for performing accurate illumination simulations. Radiance accounts for a number of important environmental factors, which we exploit during fitness evaluation. Illumination requirements include local illumination intensity from natural and artificial sources, colour, and uniformity. Evolved solutions incorporate design elements such as artificial lights, room materials, windows, and glass properties. A number of case studies are examined, including many-objective problems involving up to 7 illumination requirements, the design of a decorative wall of lights, and the creation of a stained-glass window for a large public space. Our results show the technical and creative possibilities of applying genetic programming to illumination design.

Zero-sum problems in finite cyclic groups

The purpose of this thesis is to investigate some open problems in the area of combinatorial number theory referred to as zero-sum theory. A zero-sequence in a finite cyclic group G is said to have the basic property if it is equivalent under group automorphism to one which has sum precisely IGI when this sum is viewed as an integer. This thesis investigates two major problems, the first of which is referred to as the basic pair problem. This problem seeks to determine conditions for which every zero-sequence of a given length in a finite abelian group has the basic property. We resolve an open problem regarding basic pairs in cyclic groups by demonstrating that every sequence of length four in Zp has the basic property, and we conjecture on the complete solution of this problem. The second problem is a 1988 conjecture of Kleitman and Lemke, part of which claims that every sequence of length n in Zn has a subsequence with the basic property. If one considers the special case where n is an odd integer we believe this conjecture to hold true. We verify this is the case for all prime integers less than 40, and all odd integers less than 26. In addition, we resolve the Kleitman-Lemke conjecture for general n in the negative. That is, we demonstrate a sequence in any finite abelian group isomorphic to Z2p (for p ~ 11 a prime) containing no subsequence with the basic property. These results, as well as the results found along the way, contribute to many other problems in zero-sum theory.

Bone speed of sound in overweight and normal-weight girls and adolescents

Over the last two decades, the prevalence of obesity in the general population has been steadily increasing. Obesity is a major issue in scientific research because it is associated with many health problems, one of which is bone quality. In adult females, adiposity is associated with increased bone mineral density, suggesting that there is a protective effect of fat on bone. However, the association between adiposity and bone strength during childhood is not clear. Thus, the purpose of this study was to compare bone strength, as reflected by speed of sound (SOS), of overweight and obese girls and adolescents with normal-weight age-matched controls. Data from 75 females included normal-weight girls (G-NW; body fat:::; 25%; n = 21), overweight and obese girls (GOW; body fat ~ 28%; n = 19), normal-weight adolescents (A-NW, body fat:::; 25%; n = 13) and overweight and obese adolescents (A-OW; body fat ~ 28%; n = 22). Nutrition was assessed with a 24-hour recall questionnaire and habitual physical activity was measured for one week using accelerometry. Using quantitative ultrasound (QUS; Sunlight Omnisense™), bone SOS was measured at the distal radius and mid-tibia. No differences were found between groups in daily total energy, calcium or vitamin D intake. However, all groups were below the recommended daily calcium intake of 1300 mg (Osteoporosis Canada, 2008). Adolescents were significantly less active than girls (14.7 ± 0.6 vs. 6.3 ± 0.6% active for G and A, respectively). OW accumulated significantly less minutes of moderate-to-very vigorous physical activity per day (MVPA) than NW in both age groups (114 ± 6 vs. 57 ± 5 min/day for NW and OW, i respectively). Girls had significantly lower radial SOS (3794 ± 87 vs. 3964 ± 64 mls for G-NW and A-NW, respectively), and tibial SOS (3678 ± 86 vs. 3878 ± 52 mls for G-NW and A-NW, respectively) than adolescents. Radial SOS was similar in the two adiposity groups within each age group. However, tibial SOS was lower in the two overweight groups (3601 ± 75 mls vs. 3739 ± 134 mls for G-OW and A-OW, respectively) compared with the age-matched normal-weight controls. Body fat percentage negatively correlated with tibial SOS in the study sample as a whole (r = -0.30). However, when split into groups, percent bo~y fat correlated with tibial SOS only in the A-OW group (r = -0.53). MVPA correlated with tibial SOS (r = 0.40), once age was partialed out. In conclusion, in contrast withthe higher bone strength characteristic of obese adult women, overweight and obese girls and adolescents are characterized by low tibial bone strength, as assessed with QUS. The differences between adiposity groups in tibial SOS may be at least partially due to the reduced weight-bearing physical activity levels in the overweight girls and adolescents. However, other factors, such as hormonal influences associated with high body fat may also playa role in reducing bone strength in overweight girls. Further research is required to reveal the mechanisms causing low bone strength in overweight and obese children and adolescents.

Public service reform and the role of the Auditor General /

The objective of this thesis is to study the involvement of the Auditor General in the proposal, implementation and review of major public service reform initiatives during a period spanning nearly forty years, from the early 1960s to 2001 . This period began with the Glassco Commission and concludes at the end of the term in office of Auditor General Denis Desautels in 2001. It has been demonstrated throughout this work that the role of the OAG has varied, from proponent to critic, from instigator to reviewer. In the past forty years the OAG's mandate has changed to meet the requirements of critical analysis of government operations and this has been aptly demonstrated in the office's relationship to the issue of public service reform. It has been argued that many of the problems facing the public service are cultural in nature. Reform initiatives have taken on a number of various forms with each addressing a different set of priorities. However, there has been a great deal of consistency in the cultural values that these initiatives articulate. Throughout this thesis attention has been paid to values. Values define a culture and cultural change is required within the Canadian federal public service. How and when this cultural change will occur is but one question to be answered. During the period under consideration in this thesis the government undertook several significant public service reform initiatives. Those examined in this thesis include: The Royal Commission on Government Organization, The Special Committee on the Review of Personnel Management and the Merit Principle, The Royal Commission on Financial Management and Accountability, Increased Ministerial Authority and Accountability, Public Service 2000, Program Review and finally La Releve. The involvement, or interest, of the Auditor General's Office on the subject of public service reform is generally articulated through the means of its annual reports to Parliament although there have been supplementary undertakings on this issue. Such material relevant to this study include: Towards Better Governance: Public Service Reform in New Zealand (1984-94) and its Relevance to Canada and Reform in the Australian Public Service. Annual reports to Parliament include: "Values, Service and Performance," (1990), "Canada's Public Service Reform and Lessons Learned from Selected Jurisdictions," (1993), "Maintaining a Competent and Efficient Public Service," (1997), and "Expenditure and Work Force Reduction in Selected Departments,"

Generating Aesthetically Pleasing Images in a Virtual Environment using Particle Swarm Optimization

This research focuses on generating aesthetically pleasing images in virtual environments using the particle swarm optimization (PSO) algorithm. The PSO is a stochastic population based search algorithm that is inspired by the flocking behavior of birds. In this research, we implement swarms of cameras flying through a virtual world in search of an image that is aesthetically pleasing. Virtual world exploration using particle swarm optimization is considered to be a new research area and is of interest to both the scientific and artistic communities. Aesthetic rules such as rule of thirds, subject matter, colour similarity and horizon line are all analyzed together as a multi-objective problem to analyze and solve with rendered images. A new multi-objective PSO algorithm, the sum of ranks PSO, is introduced. It is empirically compared to other single-objective and multi-objective swarm algorithms. An advantage of the sum of ranks PSO is that it is useful for solving high-dimensional problems within the context of this research. Throughout many experiments, we show that our approach is capable of automatically producing images satisfying a variety of supplied aesthetic criteria.

Multi-Objective Genetic Algorithms for the Single Allocation Hub Location Problem

Hub Location Problems play vital economic roles in transportation and telecommunication networks where goods or people must be efficiently transferred from an origin to a destination point whilst direct origin-destination links are impractical. This work investigates the single allocation hub location problem, and proposes a genetic algorithm (GA) approach for it. The effectiveness of using a single-objective criterion measure for the problem is first explored. Next, a multi-objective GA employing various fitness evaluation strategies such as Pareto ranking, sum of ranks, and weighted sum strategies is presented. The effectiveness of the multi-objective GA is shown by comparison with an Integer Programming strategy, the only other multi-objective approach found in the literature for this problem. Lastly, two new crossover operators are proposed and an empirical study is done using small to large problem instances of the Civil Aeronautics Board (CAB) and Australian Post (AP) data sets.

The effects of consistency and inconsistency between attentional focus and task objective in learning a golf putting task

Converging evidence has demonstrated learning advantages when an individual is instructed to focus their attention externally. However, many of the motor tasks utilized in past research had clear external objectives (i.e., putting accuracy), creating a compatible relationship between an external focus of attention (i.e., outcome) and an external task objective (i.e., putting accuracy). The present study examined whether or not the consistency of instructions and task objective would differentially impact the acquisition of a golf putting task. Participants performed a putting task in a control condition or in one of four experimental conditions resulting from the factorial interaction of task instructions (internal or external) and task objective (internal or external). The retention and transfer data revealed that participants who received an external task objective demonstrated superior outcome scores. Participants who received technique information paired with outcome information demonstrated superior technique scores.

A Study of Ordered Gene Problems Featuring DNA Error Correction and DNA Fragment Assembly with a Variety of Heuristics, Genetic Algorithm Variations, and Dynamic Representations

Ordered gene problems are a very common classification of optimization problems. Because of their popularity countless algorithms have been developed in an attempt to find high quality solutions to the problems. It is also common to see many different types of problems reduced to ordered gene style problems as there are many popular heuristics and metaheuristics for them due to their popularity. Multiple ordered gene problems are studied, namely, the travelling salesman problem, bin packing problem, and graph colouring problem. In addition, two bioinformatics problems not traditionally seen as ordered gene problems are studied: DNA error correction and DNA fragment assembly. These problems are studied with multiple variations and combinations of heuristics and metaheuristics with two distinct types or representations. The majority of the algorithms are built around the Recentering- Restarting Genetic Algorithm. The algorithm variations were successful on all problems studied, and particularly for the two bioinformatics problems. For DNA Error Correction multiple cases were found with 100% of the codes being corrected. The algorithm variations were also able to beat all other state-of-the-art DNA Fragment Assemblers on 13 out of 16 benchmark problem instances.

Characterizing Dynamic Optimization Benchmarks for the Comparison of Multi-Modal Tracking Algorithms

Population-based metaheuristics, such as particle swarm optimization (PSO), have been employed to solve many real-world optimization problems. Although it is of- ten sufficient to find a single solution to these problems, there does exist those cases where identifying multiple, diverse solutions can be beneficial or even required. Some of these problems are further complicated by a change in their objective function over time. This type of optimization is referred to as dynamic, multi-modal optimization. Algorithms which exploit multiple optima in a search space are identified as niching algorithms. Although numerous dynamic, niching algorithms have been developed, their performance is often measured solely on their ability to find a single, global optimum. Furthermore, the comparisons often use synthetic benchmarks whose landscape characteristics are generally limited and unknown. This thesis provides a landscape analysis of the dynamic benchmark functions commonly developed for multi-modal optimization. The benchmark analysis results reveal that the mechanisms responsible for dynamism in the current dynamic bench- marks do not significantly affect landscape features, thus suggesting a lack of representation for problems whose landscape features vary over time. This analysis is used in a comparison of current niching algorithms to identify the effects that specific landscape features have on niching performance. Two performance metrics are proposed to measure both the scalability and accuracy of the niching algorithms. The algorithm comparison results demonstrate the algorithms best suited for a variety of dynamic environments. This comparison also examines each of the algorithms in terms of their niching behaviours and analyzing the range and trade-off between scalability and accuracy when tuning the algorithms respective parameters. These results contribute to the understanding of current niching techniques as well as the problem features that ultimately dictate their success.