Computing the collapse load and identifying the associated mechanism of block assemblage structures is an important task in historical restoration works. The research in this thesis is to contribute to the modelling and analysis of rigid block structures in dry frictional contact. The models can be applied to various structures such as masonry arches) vaults) domes, walls or piles in heritage buildings. Estimates of the collapse load are made by solving the underlying mathematical programming problems. 2-D and 3-D models are formulated and different contact assumptions (concavity and convexity) are investigated. Both associated and nonassociated flow rules are accounted for. The associative problem can be robustly solved by the bound theorems of classical plasticity theory. However, the result is often not valid. The nonassociated rule which shows up as a complementarity relationship in the governing system is the major challenge of the project. The 3-D model is more difficult to deal with as compared to the 2-D case. Proposed methods are presented to treat the nonlinear 3-D problem (Lorentz cone) by formulating it as a second-order cone problem or by piecewise linearizing the cone as a polyhedral. Various computational methods are proposed to obtain the best upper bound collapse load for the nonassociative model. One method formulates some extended complementarity problems that are able to restrict the domain of the collapse load variable to search for better solutions. The best method uses nonlinear programming) specifically mathematical programming with equilibrium constraints problems) to attempt to directly minimize the collapse load. Some enumerative schemes are also attempted to map out all the nonassociative solutions but proved to be computationally expensive. Various 2-D and 3-D examples are demonstrated for several different types of structures.

No description available.

Mathematical programming (MP) can be used for developing classification models for the two–group classification problem. An MP model can be used to generate a discriminant function that separates the observations in a training sample of known group membership into the specified groups optimally in terms of a group separation criterion. The simplest models for MP discriminant analysis are linear programming models in which the group separation measure is generally based on the deviations of misclassified observations from the discriminant function. MP discriminant analysis models have been tested extensively over the last 30 years in developing classifiers for the two–group classification problem. However, in the comparative studies that have included MP models for classifier development, the MP discriminant analysis models either lack appropriate normalisation constraints or they do not use the proper data transformation. In addition, these studies have generally been based on relatively small datasets. This thesis investigates the development of MP discriminant analysis models that incorporate appropriate normalisation constraints and data transformations. These MP models are tested on binary classification problems, with an emphasis on credit scoring problems, particularly application scoring, i.e. a two–group classification problem concerned with distinguishing between good and bad applicants for credit based on information from application forms and other relevant data. The performance of these MP models is compared with the performance of statistical techniques and machine learning methods and it is shown that MP discriminant analysis models can be useful tools for developing classifiers. Another topic covered in this thesis is feature selection. In order to make classification models easier to understand, it is desirable to develop parsimonious classification models with a limited number of features. Features should ideally be selected based on their impact on classification accuracy. Although MP discriminant analysis models can be extended for feature selection based on classification accuracy, there are computational difficulties in applying these models to large datasets. A new MP heuristic for selecting features is suggested based on a feature selection MP discriminant analysis model in which maximisation of classification accuracy is the objective. The results of the heuristic are promising in comparison with other feature selection methods. Classifiers should ideally be developed from datasets with approximately the same number of observations in each class, but in practice classifiers must often be developed from imbalanced datasets. New MP formulations are proposed to overcome the difficulties associated with generating discriminant functions from imbalanced datasets. These formulations are tested using datasets from financial institutions and the performance of the MP-generated classifiers is compared with classifiers generated by other methods. Finally, the ordinal classification problem is considered. MP methods for the ordinal classification problem are outlined and a new MP formulation is tested on a small dataset.

No description available.

Network design problems involving survivability usually include trade-off of the potential for lost revenues and customer goodwill against the extra costs required to increase the network survivability. It also involves selection of nodes and edges from lists of potential sets to accomplish certain desirable properties. In many applications it is imperative to have built-in reliability or survivability of the network. Delays of traffic are undesirable since it affects quality of service (QoS) to clients of the network. In this dissertation we consider the construction of an optimization system for network design with survivability properties that may help in the planning of mesh topologies while maintaining a certain degree of survivability of the network. This is done by providing for at least two diverse paths between certain "special" nodes to provide protection against any single edge or node failure. This part is modelled by using mixed integer programming techniques. A software product called CPLEX then solves these models and various facilities are built into the decision support system to allow the decision maker to experiment with some topological and flow requirement changes. / Thesis (M.Sc. (Computer Science))--North-West University, Potchefstroom Campus, 2007

The economic efficiency of water development in Utah, including transfer systems, has seldom been examined, nor has the costs of public policies which result in deviations from efficient allocations. In order that public officials be better informed about water allocations , the present effort examines the efficient allocation of water in time frames up to 2020 under several alternative assumptions and calculates the cost of alternative policies. Us ing mathematical programming techniques, a computer mode l is developed to determine the supply (marginal cost) and demand (value of marginal product) relationships for agricultural water, given depletions for municipal and industrial (M & I) and wetland requirements. The model maximizes net profit per acre t o an average agriculturalist in each of ten study areas in Utah. Proposed interbasin transfers and their costs are included in supply. The optimal solution gene rated is an efficient allocation, since maximization of net profits occurs only when value of marginal product equals marginal cost. The requirements for M & I water are projected into the future using trending and probable industrial development. An efficient allocation (optimal solution) is generated by the model f or 1965, 1980, 1990, 2000, 2010, and 20 20. Th e timing of investments in water distribution systems can be determined from these solutions. Using alternative assumptions about policies (minimum inflows to Great Salt Lake and water salvage) several alternative temporal distributions are determined. Additionally, the effect of restrictions on groundwater pumping (present levels of storage must be maintained) are examined. The costs to users in higher supply curves (marginal costs) are approximated by areas between supply curves. In addition, losses to agricultural users from diminished efficient new production can be approximated. The critical factors in large proposed water transfers in Utah appear to be the growth of M & I requirements along the Wasatch Front, particularly in the Jordan River Basin. Sufficient water is available in the Colorado River Basins to provide maximum transfers, full oil shale and power generation development, and efficient agricultural production. Restrictions on groundwater pumping and water salvage in the Jordan River Basin and maintenance of high inflows to Great Salt Lake make transfers necessary sooner. The costs of such restrictions approaches 25 percent of the total investment by agriculture in transfer systems. If no r e strictions are made, but investment in these systems occurs now, a loss of foregone returns to alternative investment equal to about 70 percent of the total agricultural investment is incurred by society.

Thesis (M.Sc. (Computer Science))--North-West University, Potchefstroom Campus, 2007.

Various drying models have been developed in the extent which they are available for the analysis of drying processes in a variety of practical drying systems. However, most were focused only on a single unit operation; mainly the dryer. Nevertheless other unit operations such as cooling and tempering units are also employed in industrial drying systems. Therefore, there is an important need for an integrated analysis of rice drying systems which takes into account all the interactions between the units that appear in a drying process. The aim is to select a process out of the large number of alternatives and operating conditions which meet the specified performance. In this work, the synthesis problem of drying processes will be thoroughly investigated using various drying models. Both simplified (empirical) and rigorous (theoretical) models were used. The aim is to find the optimum configuration and operating conditions which satisfy two optimization criteria. One is to maximize the quality (head rice yield) and the other is to minimize the energy consumption. To solve the synthesis problem, mathematical programming will be used as a tool. Three major steps involving the application of mathematical programming in synthesis problems were developed and presented; superstructure representation, problem formulation and optimization strategy. For the synthesis problem using empirical models, the problem was formulated as an MINLP model. However, due to the fact that different mathematical models are often possible for the same synthesis problem and the recent advances in modeling techniques, generalized disjunctive programming (GDP), known as an alternative model to MINLP, was used. The objectives are to investigate the benefit of using GDP as an alternative model to MINLP and also to exploit a disjunction part of a GDP model for integrating alternative choices of empirical drying models to eliminate the problem of having drying models which are valid only in a small range of operating conditions. The results showed that different drying strategies were obtained from using different drying models in the case of maximum head of rice yield (quality) while the same strategies have been found from using different drying models in the case of minimum energy consumption. This finding is due to the reason that quality as an objective function is highly nonlinear; therefore it contains many local solutions while the energy objective function is a simple linear function. In the aspect of using GDP model, we found that GDP models provide good structure of variable relationships which can improve the search strategy and solution efficiency for the problem dealing with highly nonlinear functions such as in the case of maximum head price yield. Moreover, because of this good characteristic of MINLP based GDP model, the synthesis problem of rice drying processes dealing with various kinds of empirical models can be solved in reasonable time in GAMS. Nonetheless, in the case that the optimization problem is dealing with the simple mathematical function, the GDP model did not outperform the ad hoc MINLP model for the case of minimizing energy consumption. Also, GDP modeling framework facilitated the problem formulation of the synthesis problem which had two drying models valid in a different range of drying operations in rice drying processes. The synthesis problem using theoretical models arising from the simultaneous heat and mass transfer balances gave rise to a mixed-integer nonlinear programming (MIDO) model. Such problem is highly nonlinear, multimodal and discontinuous in nature and is very difficult to solve. A hybrid method which combines genetic algorithms (GAs) and control vector parameterization (CVP) approach was proposed to solve this problem. In the case of maximum head rice yield, the results of the synthesis problem showed that high quality rice grain can be preserved regardless of the choice of drying configuration as long as the drying process is operated under a condition which produces the least amount of moisture gradient within the rice grain. Many local optimum solutions which gave rise to different drying configurations and operating policies were found from using different initial guesses. In the case of minimum energy consumption, the results showed that a cooling-tempering configuration which operates at ambient temperature gave the minimum energy consumption. Different initial guesses converged to the same drying configuration (cooling-tempering) but different operating policies and total number of passes. Moreover, since the optimal operating time in a cooling unit is at the upper operating bound allowed in this unit, the effect of the bound of operating time for a cooling unit on the total number of passes required was studied. The results showed that less number of passes would be obtained if longer periods of cooling are allowed. The hybrid proposed method was able to solve MIDO problems; albeit at a relatively large computational expense. For the comparison aspect between the theoretical and empirical models for synthesis of rice drying processes, empirical models are easier to use for the synthesis problem but they are valid only within the range which they were developed. Also, there is a need for developing a model for each particular unit employed in rice drying processes. For the synthesis problem with theoretical models, this problem gives rise to the most difficult class of optimization problems; however, a theoretical model provides a better understanding of the drying kinetics happening in rice grain. Moreover, theoretical models alleviate the need to develop models for each particular unit employed in rice drying systems. The common feature found from using theoretical and empirical models is that head rice yield objective function always gives rise to different choices of drying configurations while the energy objective function always give rise to a unique drying configuration (cooling-tempering). Different drying strategies have been found from using different drying models. These alternative configurations provide a broader vision on the operation of drying systems. To decide which one is the best, other factors must be taken into account such as investment cost, term of uses and available technology.

Various drying models have been developed in the extent which they are available for the analysis of drying processes in a variety of practical drying systems. However, most were focused only on a single unit operation; mainly the dryer. Nevertheless other unit operations such as cooling and tempering units are also employed in industrial drying systems. Therefore, there is an important need for an integrated analysis of rice drying systems which takes into account all the interactions between the units that appear in a drying process. The aim is to select a process out of the large number of alternatives and operating conditions which meet the specified performance. In this work, the synthesis problem of drying processes will be thoroughly investigated using various drying models. Both simplified (empirical) and rigorous (theoretical) models were used. The aim is to find the optimum configuration and operating conditions which satisfy two optimization criteria. One is to maximize the quality (head rice yield) and the other is to minimize the energy consumption. To solve the synthesis problem, mathematical programming will be used as a tool. Three major steps involving the application of mathematical programming in synthesis problems were developed and presented; superstructure representation, problem formulation and optimization strategy. For the synthesis problem using empirical models, the problem was formulated as an MINLP model. However, due to the fact that different mathematical models are often possible for the same synthesis problem and the recent advances in modeling techniques, generalized disjunctive programming (GDP), known as an alternative model to MINLP, was used. The objectives are to investigate the benefit of using GDP as an alternative model to MINLP and also to exploit a disjunction part of a GDP model for integrating alternative choices of empirical drying models to eliminate the problem of having drying models which are valid only in a small range of operating conditions. The results showed that different drying strategies were obtained from using different drying models in the case of maximum head of rice yield (quality) while the same strategies have been found from using different drying models in the case of minimum energy consumption. This finding is due to the reason that quality as an objective function is highly nonlinear; therefore it contains many local solutions while the energy objective function is a simple linear function. In the aspect of using GDP model, we found that GDP models provide good structure of variable relationships which can improve the search strategy and solution efficiency for the problem dealing with highly nonlinear functions such as in the case of maximum head price yield. Moreover, because of this good characteristic of MINLP based GDP model, the synthesis problem of rice drying processes dealing with various kinds of empirical models can be solved in reasonable time in GAMS. Nonetheless, in the case that the optimization problem is dealing with the simple mathematical function, the GDP model did not outperform the ad hoc MINLP model for the case of minimizing energy consumption. Also, GDP modeling framework facilitated the problem formulation of the synthesis problem which had two drying models valid in a different range of drying operations in rice drying processes. The synthesis problem using theoretical models arising from the simultaneous heat and mass transfer balances gave rise to a mixed-integer nonlinear programming (MIDO) model. Such problem is highly nonlinear, multimodal and discontinuous in nature and is very difficult to solve. A hybrid method which combines genetic algorithms (GAs) and control vector parameterization (CVP) approach was proposed to solve this problem. In the case of maximum head rice yield, the results of the synthesis problem showed that high quality rice grain can be preserved regardless of the choice of drying configuration as long as the drying process is operated under a condition which produces the least amount of moisture gradient within the rice grain. Many local optimum solutions which gave rise to different drying configurations and operating policies were found from using different initial guesses. In the case of minimum energy consumption, the results showed that a cooling-tempering configuration which operates at ambient temperature gave the minimum energy consumption. Different initial guesses converged to the same drying configuration (cooling-tempering) but different operating policies and total number of passes. Moreover, since the optimal operating time in a cooling unit is at the upper operating bound allowed in this unit, the effect of the bound of operating time for a cooling unit on the total number of passes required was studied. The results showed that less number of passes would be obtained if longer periods of cooling are allowed. The hybrid proposed method was able to solve MIDO problems; albeit at a relatively large computational expense. For the comparison aspect between the theoretical and empirical models for synthesis of rice drying processes, empirical models are easier to use for the synthesis problem but they are valid only within the range which they were developed. Also, there is a need for developing a model for each particular unit employed in rice drying processes. For the synthesis problem with theoretical models, this problem gives rise to the most difficult class of optimization problems; however, a theoretical model provides a better understanding of the drying kinetics happening in rice grain. Moreover, theoretical models alleviate the need to develop models for each particular unit employed in rice drying systems. The common feature found from using theoretical and empirical models is that head rice yield objective function always gives rise to different choices of drying configurations while the energy objective function always give rise to a unique drying configuration (cooling-tempering). Different drying strategies have been found from using different drying models. These alternative configurations provide a broader vision on the operation of drying systems. To decide which one is the best, other factors must be taken into account such as investment cost, term of uses and available technology.

Network design problems usually include the selection of nodes and arcs from lists of potential sets to accomplish certain desirable properties. Foremost is often the capability to accommodate the flow demands at a reasonable cost. In many applications it is also imperative to have built-in reliability or survivability of the network. Delays of traffic are undesirable since it affects Quality of Service (QoS) to clients of the network. It is seldom possible to start a design for a new network and have the luxury of designing topology as well as the optimal flow(routing). In this dissertation we consider the construction of a network optimization system. This system may be used in the planning of network mesh topologies and link capacities to avoid costly designs and congestion or to give advice on congestion relief in existing networks. This is done by selecting parts of a network that may be prone to congestion and model this part by using mixed integer programming techniques. These models are then solved by using a software product called CPLEX and various facilities are built into the decision support system to allow the decision maker to experiment with some topological and flow requirement changes. / Thesis (M.Sc. (Computer Science))--North-West University, Potchefstroom Campus, 2005.