A broader research project was conducted about intergenerational relationships. The focus of this study was about adolescents’ experiences of care in relationships with people older than 60 years, who live in an environment where resources are constrained. Care usually occurs in relationships and can take either the form of practical care or emotional care, or both which can occur simultaneously. Practical care involves behaviours, while emotional care involves feelings. Both are aimed at attending to other people’s needs. Previous studies on intergenerational relationships and care largely focused on either informal and practical care-giving, which are mainly provided by adult children to older people; or on the informal and practical care-giving provided by grandparents to grandchildren. Research on relational experiences between Setswana-speaking older people and young adults in South Africa has indicated ambivalence in their relationships. While another South African study on the relational experiences between Setswana-speaking older people and their grandchildren, who are in their middle childhood, reported supportive and caring relationships. Limited research exists about care in the relationships between adolescents and older people. Care as a relational phenomenon in intergenerational relationships is explained by the Self-Interactional Group Theory (SIGT), and is used in this study as the theoretical framework. SIGT explains the interactional manifestation of intergenerational relations, and conceptualises that intergenerational relationships are continuously created and co-created, which influences the meaning that is attached to care. This theory further explains the intra-individual, inter-individual and group level interactions that take place between the adolescents and older people. According to SIGT, intergenerational interactions are embedded in the socio-cultural, socio-economical, socio-political and the physical environments in which they take place. This study was conducted in Vaalharts, situated in the Northern Cape Province of South Africa. This community is economically vulnerable and resources are constrained. A qualitative research method was used to describe adolescents’ experiences of care. Fourteen adolescents between the ages of 12 and 16 years participated in the research. Non-probability, purposive sampling was used to select the participants. The participants took part in the Mmogo-method ®, which is a visual participatory data gathering method, to elicit the experiences of care. Eight of the participants were part of the care-group, while the other six were part of the respect-group. All 14 participants received a journal with questions about care and respect to enlighten the data further. For this study, only the data about care was used. The Mmogo-method ® required the participants to build a visual presentation using clay, beads and sticks, about their experiences of care in relation to people older than 60 years. On completion, the rest of the participants were then asked to augment the individual’s explanation with their own views. The explanations were recorded and transcribed verbatim, while the visual representations were photographed and served as visual data. The data were analysed by the use of thematic and visual analysis. Trustworthiness was ensured by the use of credibility, dependability, transferability and conformability strategies. Additionally, the ethical guidelines provided by the Health Professions Council of South Africa for Psychologists were followed (Health Professions Act 56 of 1974). It was found that the adolescents were able to identify older people’s practical care and emotional care needs, and take action to provide them with appropriate care. The adolescents showed care in the form of practical activities, emotional support, showing respect, and obtaining an education. Findings further indicated that adolescents received care only in the form of practical care. These findings may be an indication that, from the adolescents’ perspective, there is an imbalance between the giving and receiving of practical and emotional care. Intervention programs can then focus on ways to help ensure that both practical and emotional care occurs in a more balanced manner. / MSc (Research Psychology), North-West University, Potchefstroom Campus, 2015

A broader research project was conducted about intergenerational relationships. The focus of this study was about adolescents’ experiences of care in relationships with people older than 60 years, who live in an environment where resources are constrained. Care usually occurs in relationships and can take either the form of practical care or emotional care, or both which can occur simultaneously. Practical care involves behaviours, while emotional care involves feelings. Both are aimed at attending to other people’s needs. Previous studies on intergenerational relationships and care largely focused on either informal and practical care-giving, which are mainly provided by adult children to older people; or on the informal and practical care-giving provided by grandparents to grandchildren. Research on relational experiences between Setswana-speaking older people and young adults in South Africa has indicated ambivalence in their relationships. While another South African study on the relational experiences between Setswana-speaking older people and their grandchildren, who are in their middle childhood, reported supportive and caring relationships. Limited research exists about care in the relationships between adolescents and older people. Care as a relational phenomenon in intergenerational relationships is explained by the Self-Interactional Group Theory (SIGT), and is used in this study as the theoretical framework. SIGT explains the interactional manifestation of intergenerational relations, and conceptualises that intergenerational relationships are continuously created and co-created, which influences the meaning that is attached to care. This theory further explains the intra-individual, inter-individual and group level interactions that take place between the adolescents and older people. According to SIGT, intergenerational interactions are embedded in the socio-cultural, socio-economical, socio-political and the physical environments in which they take place. This study was conducted in Vaalharts, situated in the Northern Cape Province of South Africa. This community is economically vulnerable and resources are constrained. A qualitative research method was used to describe adolescents’ experiences of care. Fourteen adolescents between the ages of 12 and 16 years participated in the research. Non-probability, purposive sampling was used to select the participants. The participants took part in the Mmogo-method ®, which is a visual participatory data gathering method, to elicit the experiences of care. Eight of the participants were part of the care-group, while the other six were part of the respect-group. All 14 participants received a journal with questions about care and respect to enlighten the data further. For this study, only the data about care was used. The Mmogo-method ® required the participants to build a visual presentation using clay, beads and sticks, about their experiences of care in relation to people older than 60 years. On completion, the rest of the participants were then asked to augment the individual’s explanation with their own views. The explanations were recorded and transcribed verbatim, while the visual representations were photographed and served as visual data. The data were analysed by the use of thematic and visual analysis. Trustworthiness was ensured by the use of credibility, dependability, transferability and conformability strategies. Additionally, the ethical guidelines provided by the Health Professions Council of South Africa for Psychologists were followed (Health Professions Act 56 of 1974). It was found that the adolescents were able to identify older people’s practical care and emotional care needs, and take action to provide them with appropriate care. The adolescents showed care in the form of practical activities, emotional support, showing respect, and obtaining an education. Findings further indicated that adolescents received care only in the form of practical care. These findings may be an indication that, from the adolescents’ perspective, there is an imbalance between the giving and receiving of practical and emotional care. Intervention programs can then focus on ways to help ensure that both practical and emotional care occurs in a more balanced manner. / MSc (Research Psychology), North-West University, Potchefstroom Campus, 2015

Computational fluid dynamics has progressed to the point where it is now possible to simulate flows with large eddy turbulence, free surfaces and other complex features. However, the success of these models often depends on the accuracy of the advection scheme supporting them. Two such schemes are the constrained interpolation profile method (CIP) and the interpolated differential operator method (IDO). They share the same space discretisation but differ in their respectively semi-Lagrangian and Eulerian formulations. They both belong to a family of high-order, compact methods referred to as the multi-moment methods. In the absence of sufficient information in the literature, this thesis begins by taxonomising various multi-moment space discretisations and appraising their linear advective properties. In one dimension it is found that the CIP/IDO with order (2N -1) has an identical spectrum and memory cost to the Nth order discontinuous Galerkin method. Tests confirm that convergence rates are consistent with nominal orders of accuracy, suggesting that CIP/IDO is a better choice for smooth propagation problems. In two dimensions, six Cartesian multi-moment schemes of third order are compared using both spectral analysis and time-domain testing. Three of these schemes economise on the number of moments that need to be stored, with one CIP/IDO variant showing improved isotropy, another failing to maintain its nominal order of accuracy, and one of the conservative variants having eigenvalues with positive real parts: it is stable only in a semi-Lagrangian formulation. These findings should help researchers who are interested in using multi-moment schemes in their solvers but are unsure as to which are suitable. The thesis then addresses the question as to whether a multi-moment method could be implemented on a Cartesian cut cell grid. Such grids are attractive for supporting arbitrary, possibly moving boundaries with minimal grid regeneration. A pair of novel conservative fourth order schemes is proposed. The first scheme, occupying the Cartesian interior, has unprecedented low memory cost and is proven to be conditionally stable. The second, occupying the cut cells, involves a profile reconstruction that is guaranteed to be well-behaved for any shape of cell. However, analysis of the second scheme in a simple grid arrangement reveals positive real parts, so it is not stable in an Eulerian formulation. Stability in a hybrid formulation remains open to question.

Higher-order basis functions are widely used to model currents and fields in numerical simulations of electromagnetics problems because of the greater accuracy and computational efficiency they can provide. Different problem formulations, such as method of moments (MoM) and the finite element method (FEM) require different constraints on basis functions for optimal performance, such as normal or tangential continuity between cells. In this thesis, a method of automatically generating bases that satisfy the desired basis constraints is applied to a MoM formulation for scattering problems using surface integral equations. Numerical results demonstrate the accuracy of this approach, and show good system matrix conditioning when compared to other higher-order bases.

This thesis is devoted to two $\mathcal{NP}$-complete combinatorial optimization problems arising in computational biology, the well-studied \emph{multiple sequence alignment} problem and the new formulated \emph{interval constraint coloring} problem. It shows that advanced mathematical programming techniques are capable of solving large scale real-world instances from biology to optimality. Furthermore, it reveals alternative methods that provide approximate solutions. In the first part of the thesis, we present a \emph{Lagrangian relaxation} approach for the multiple sequence alignment (MSA) problem. The multiple alignment is one common mathematical abstraction of the comparison of multiple biological sequences, like DNA, RNA, or protein sequences. If the weight of a multiple alignment is measured by the sum of the projected pairwise weights of all pairs of sequences in the alignment, then finding a multiple alignment of maximum weight is $\mathcal{NP}$-complete if the number of sequences is not fixed. The majority of the available tools for aligning multiple sequences implement heuristic algorithms; no current exact method is able to solve moderately large instances or instances involving sequences exhibiting a lower degree of similarity. We present a branch-and-bound (B\&B) algorithm for the MSA problem.\ignore{the multiple sequence alignment problem.} We approximate the optimal integer solution in the nodes of the B\&B tree by a Lagrangian relaxation of an ILP formulation for MSA relative to an exponential large class of inequalities, that ensure that all pairwise alignments can be incorporated to a multiple alignment. By lifting these constraints prior to dualization the Lagrangian subproblem becomes an \emph{extended pairwise alignment} (EPA) problem: Compute the longest path in an acyclic graph, that is penalized a charge for entering ``obstacles''. We describe an efficient algorithm that solves the EPA problem repetitively to determine near-optimal \emph{Lagrangian multipliers} via subgradient optimization. The reformulation of the dualized constraints with respect to additionally introduced variables improves the convergence rate dramatically. We account for the exponential number of dualized constraints by starting with an empty \emph{constraint pool} in the first iteration to which we add cuts in each iteration, that are most violated by the convex combination of a small number of preceding Lagrangian solutions (including the current solution). In this \emph{relax-and-cut} scheme, only inequalities from the constraint pool are dualized. The interval constraint coloring problem appears in the interpretation of experimental data in biochemistry. Monitoring hydrogen-deuterium exchange rates via mass spectroscopy is a method used to obtain information about protein tertiary structure. The output of these experiments provides aggregate data about the exchange rate of residues in overlapping fragments of the protein backbone. These fragments must be re-assembled in order to obtain a global picture of the protein structure. The interval constraint coloring problem is the mathematical abstraction of this re-assembly process. The objective of the interval constraint coloring problem is to assign a color (exchange rate) to a set of integers (protein residues) such that a set of constraints is satisfied. Each constraint is made up of a closed interval (protein fragment) and requirements on the number of elements in the interval that belong to each color class (exchange rates observed in the experiments). We introduce a polyhedral description of the interval constraint coloring problem, which serves as a basis to attack the problem by integer linear programming (ILP) methods and tools, which perform well in practice. Since the goal is to provide biochemists with all possible candidate solutions, we combine related solutions to equivalence classes in an improved ILP formulation in order to reduce the running time of our enumeration algorithm. Moreover, we establish the polynomial-time solvability of the two-color case by the integrality of the linear programming relaxation polytope $\mathcal{P}$, and also present a combinatorial polynomial-time algorithm for this case. We apply this algorithm as a subroutine to approximate solutions to instances with arbitrary but fixed number of colors and achieve an order of magnitude improvement in running time over the (exact) ILP approach. We show that the problem is $\mathcal{NP}$-complete for arbitrary number of colors, and we provide algorithms that, given an instance with $\mathcal{P}\neq\emptyset$, find a coloring that satisfies all the coloring requirements within $\pm 1$ of the prescribed value. In light of our $\mathcal{NP}$-completeness result, this is essentially the best one can hope for. Our approach is based on polyhedral theory and randomized rounding techniques. In practice, data emanating from the experiments are noisy, which normally causes the instance to be infeasible, and, in some cases, even forces $\mathcal{P}$ to be empty. To deal with this problem, the objective of the ILP is to minimize the total sum of absolute deviations from the coloring requirements over all intervals. The combinatorial approach for the two-color case optimizes the same objective function. Furthermore, we use this combinatorial method to compute, in a Lagrangian way, a bound on the minimum total error, which is exploited in a branch-and-bound manner to determine all optimal colorings. Alternatively, we study a variant of the problem in which we want to maximize the number of requirements that are satisfied. We prove that this variant is $\mathcal{APX}$-hard even in the two-color case and thus does not admit a polynomial time approximation scheme (PTAS) unless $\mathcal{P}=\mathcal{NP}$. Therefore, we slightly (by a factor of $(1+\epsilon)$) relax the condition on when a requirement is satisfied and propose a \emph{quasi-polynomial time approximation scheme} (QPTAS) which finds a coloring that ``satisfies'' the requirements of as many intervals as possible.

Freight transportation is an integral element of various supply chains and has a complex and dynamical interrelationship with human economic activities. Modern logistical strategies paved way to the current supply chain organisation and logistics network design resulting in a more global economy and huge economies of scale. Recent trends of volatility of oil price have major implications in the movement of commodities across the supply chains. Likewise, climate change issues have presented urgent challenges in reducing carbon emissions for the transport and logistics sector. Pressure on the sector comes from both governments and consumers alike, demanding future sustainability as well as corporate environmental and social responsibility. The original contribution of this research is to investigate the system-wide dynamics of freight transportation and production in the context of supply chains. A theoretical framework called the ‘Geographic Adaptive Potential’ or GAP is built to understand how constraints in energy and emissions affect the production and distribution of commodities. The changes in the supply chain were investigated in four different components, namely a) the potential to shift to less energy and emissions intensive modes for long-haul freight, b) logistical strategies in the last leg of the chain or urban freight and c) local production and distribution, and d) the accessibility of potential customers to the markets. The design of the GAP components is in correspondence with the links of the supply chain. The analyses yielded an evaluation of the adaptive capacity of the freight transport and production system. For long-haul freight, a GIS-based model was created called the ‘New Zealand Intermodal Freight Network’ or NZIFN. It is an optimisation tool integrating the road, rail and shipping network of New Zealand and calculates that minimum time, operating costs, energy and emissions routes between 2 given locations. The case studies of Auckland to Wellington and Auckland to Christchurch distributions of non-perishable products established that even a marginal increase of rail and coastal shipping share produced around 10% reduction in both freight energy and greenhouse gas emissions. In the study of the last leg of the supply chain, the truck trip generation rates of different food stores were investigated. The strongest factors influencing the trip rates to a store are its size and product variation, the latter being a new parameter introduced in the dissertation. It is defined as the total number of brands for 6 chosen commodities commonly found in the stores. The trip rates together with the truck type and distance travelled were used to compute the freight energy usage of the stores. Results revealed that supermarkets consume the most energy for their delivery operations but relative to its physical size, they are more energy efficient than smaller stores. This is due to the utilisation of advanced logistical strategies such as freight consolidation and the effective use of distribution centres. The localised production chapter was explored in the context of Farmers’ markets and their difference with the conventional supermarket distribution system. Using a freight transport energy audit, the energy intensities of both systems were compared. The findings showed that Farmers’ markets were more energy-intensive than supermarkets owing to the low volumes of goods delivered to the market and the lack of freight consolidation effort in the system. The study on the active mode access of potential customers to both Farmers’ markets and supermarkets captured the interplay between freight and personal transport and is the final component of GAP. The results of the ArcGIS based model called ‘Active Mode Access’ or AMA demonstrated that both Farmers’ markets and supermarkets have the same level of accessibility for walking or biking customers. However, the calculations also showed that almost 87% of New Zealanders have no AMA to stores and are at risk for fuel price increase. Finally, the key result of this dissertation is the assessment that there is actually limited adaptive capacity of the freight transport and production system. This is due to network infrastructure and geographical constraints as well as commodity type and mode compatibility and other operational concerns. Due to these limitations, the GAP model assessed that reduction in energy and allowable emissions will ultimately reduce the amount of commodities moved in the system.

A flexible workforce or a versatile machine is employed to perform various types of operations. Often these resources are associated with setups. Whenever a worker or machine switches from processing one type of operation to another a setup time may be required although several operations of a same type can be processed in succession after a single setup. The presence of setups gives rise to the problem of choosing batch sizes that are neither too large nor too small. In the last one and a half decade, many researchers have addressed the problem of scheduling with batching. A majority of articles assumes that there is only one type of scarce resource, which is typically machine. Often there can be two scarce resources such as a worker and a machine or a machine and a tool. We propose a resource constrained scheduling model with a single operator and two or more machines. Whenever the operator changes machine, a setup time is required that may be sequence dependent or sequence independent. We consider the two cases of an open shop and a flow shop. In the open shop case, the order in which a job visits the machines is unrestricted. In the flow shop case, every job must visit the machines in the same order. We consider various scheduling objectives. For variable number of machines, many cases are intractable. We discuss some dominance properties that narrow down the search for an optimal schedule. We present a dynamic programming approach which solves a large number of cases. The running time of the dynamic program is polynomial for a fixed number of machines. For the case of two machines, we show that the dominance properties have a nice interpretation. We develop some algorithms and justify their use by establishing running times, comparing the running times with those of the existing algorithms, and testing the performance of the algorithms.

This dissertation explores approaches to the satisfiability problem, focusing on local search methods. The research endeavours to better understand how and why some local search methods are effective. At the root of this understanding are a set of metrics that characterize the behaviour of local search methods. Based on this understanding, two new local search methods are proposed and tested, the first, SDF, demonstrating the value of the insights drawn from the metrics, and the second, ESG, achieving state-of-the-art performance and generalizing the approach to arbitrary 0-1 integer linear programming problems. This generality is demonstrated by applying ESG to combinatorial auction winner determination. Further augmentations to local search are proposed and examined, exploring hybrids that incorporate aspects of backtrack search methods.

The aim of this research is to demonstrate some more efficient approaches to solve the n-1 security constrained optimal power flow (SCOPF) problems by using structure-exploiting primal-dual interior point methods (IPM). Firstly, we consider a DC-SCOPF model, which is a linearized version of AC-SCOPF. One new reformulation of the DC-SCOPF model is suggested, in which most matrices that need to be factorized are constant. Consequently, most numerical factorizations and a large number of back-solve operations only need to be performed once throughout the entire IPM process. In the framework of the structure-exploiting IPM implementation, one of the major computational efforts consists of forming the Schur complement matrix, which is very computationally expensive if no further measure is applied. One remedy is to apply a preconditioned iterative method to solve the corresponding linear systems which appear in assembling the Schur complement matrix. We suggest two main schemes to pick a good and robust preconditioner for SCOPF problems based on combining different “active” contingency scenarios. The numerical results show that our new approaches are much faster than the default structure-exploiting method in OOPS, and also that it requires less memory. The second part of this thesis goes to the standard AC-SCOPF problem, which is a nonlinear and nonconvex optimization problem. We present a new contingency generation algorithm: it starts with solving the basic OPF problem, which is a much smaller problem of the same structure, and then generates contingency scenarios dynamically when needed. Some theoretical analysis of this algorithm is shown for the linear case, while the numerical results are exciting, as this new algorithm works for both AC and DC cases. It can find all the active scenarios and significantly reduce the number of scenarios one needs to contain in the model. As a result, it speeds up the solving process and may require less IPM iterations. Also, some heuristic algorithms are designed and presented to predict the active contingencies for the standard AC-SCOPF, based on the use of AC-OPF or DC-SCOPF. We test our heuristic algorithms on the modified IEEE 24-bus system, and also present their corresponding numerical results in the thesis.

It is expected that the grid of the future differs from the current system by the increased integration of distributed generation, distributed storage, demand response, power electronics, and communications and sensing technologies. The consequence is that the physical structure of the system becomes significantly more distributed. The existing centralized control structure is not suitable any more to operate such a highly distributed system. This thesis is dedicated to providing a promising solution to a class of energy management problems in power systems with a high penetration of distributed resources. This class includes optimal dispatch problems such as optimal power flow, security constrained optimal dispatch, optimal power flow control and coordinated plug-in electric vehicles charging. Our fully distributed algorithm not only handles the computational complexity of the problem, but also provides a more practical solution for these problems in the emerging smart grid environment. This distributed framework is based on iteratively solving in a distributed fashion the first order optimality conditions associated with the optimization formulations. A multi-agent viewpoint of the power system is adopted, in which at each iteration, every network agent updates a few local variables through simple computations, and exchanges information with neighboring agents. Our proposed distributed solution is based on the consensus+innovations framework, in which the consensus term enforces agreement among agents while the innovations updates ensure that local constraints are satisfied.