It has been argued that much of evolution takes place in the absence of fitness gradients. Such periods of evolution can be analysed by examining the mutational network formed by sequences of equal fitness, that is, the neutral network. It has been demonstrated that, in large populations under a high mutation rate, the population distribution over the neutral network and average mutational robustness are given by the principal eigenvector and eigen- value, respectively, of the network's adjacency matrix. However, little progress has been made towards understanding the manner in which the topology of the neutral network influences the resulting population distribution and robustness. In this work, we build on recent results from spectral graph theory and utilize numerical methods to enhance our understanding of how populations distribute themselves over neutral networks. We demonstrate that, in the presence of certain topological features, the population will undergo an exploration catastrophe and become confined to a small portion of the network. We further derive approximations, in terms of mutational biases, for the population distribution and average robustness in networks with a homogeneous structure. The applicability of these results is explored, first, by a detailed review of the literature in both evolutionary computing and biology concerning the structure of neutral networks. This is extended by studying the actual and predicted population distribution over the neutral networks of H1N1 and H3N2 influenza haemagglutinin during seasons between 2005 and 2016. It is shown that, in some instances, these populations experience an exploration catastrophe. These results provide insight into the behaviour of populations on neutral networks, demonstrating that neutrality does not necessarily lead to an exploration of genotype/phenotype space or an associated increase in population diversity. Moreover, they provide a plausible explanation for conflicting results concerning the relationship between robustness and evolvability.

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This thesis provides a `proof-of-concept' prototype and a design architecture for a Object Oriented (00) database towards the development of a Decision Support System (DSS) for the national freight transport planning problem. Both governments and industry require a Strategic Planning Extranet Decision Support System (SPEDSS) for their effective management of the national Freight Transport Networks (FTN). This thesis addresses the three key problems for the development of a SPEDSS to facilitate national strategic freight planning: 1) scope and scale of data available and required; 2) scope and scale of existing models; and 3) construction of the software. The research approach taken embodies systems thinking and includes the use of: Object Oriented Analysis and Design (OOA/D) for problem encapsulation and database design; artificial neural network (and proposed rule extraction) for knowledge acquisition of the United States FTN data set; and an iterative Object Oriented (00) software design for the development of a `proof-of-concept' prototype. The research findings demonstrate that an 00 approach along with the use of 00 methodologies and technologies coupled with artificial neural networks (ANNs) offers a robust and flexible methodology for the analysis of the FTN problem domain and the design architecture of an Extranet based SPEDSS. The objectives of this research were to: 1) identify and analyse current problems and proposed solutions facing industry and governments in strategic transportation planning; 2) determine the functional requirements of an FTN SPEDSS; 3) perform a feasibility analysis for building a FTN SPEDSS `proof-of-concept' prototype and (00) database design; 4) develop a methodology for a national `internet-enabled' SPEDSS model and database; 5) construct a `proof-of-concept' prototype for a SPEDSS encapsulating identified user requirements; 6) develop a methodology to resolve the issue of the scale of data and data knowledge acquisition which would act as the `intelligence' within a SPDSS; 7) implement the data methodology using Artificial Neural Networks (ANNs) towards the validation of it; and 8) make recommendations for national freight transportation strategic planning and further research required to fulfil the needs of governments and industry. This thesis includes: an 00 database design for encapsulation of the FTN; an `internet-enabled' Dynamic Modelling Methodology (DMM) for the virtual modelling of the FTNs; a Unified Modelling Language (UML) `proof-of-concept' prototype; and conclusions and recommendations for further collaborative research are identified.

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Time series anomaly detection receives increasing research interest given the growing number of data-rich application domains. Recent additions to anomaly detection methods in research literature include deep learning algorithms. The nature and performance of these algorithms in sequence analysis enable them to learn hierarchical discriminating features and time-series temporal nature. However, their performance is affected by the speed at which the time series arrives, the use of a fixed threshold, and the assumption of Gaussian distribution on the prediction error to identify anomalous values. An exact parametric distribution is often not directly relevant in many applications and it’s often difficult to select an appropriate threshold that will differentiate anomalies with noise. Thus, implementations need the Prediction Interval (PI) that quantifies the level of uncertainty associated with the Deep Neural Network (DNN) point forecasts, which helps in making a better-informed decision and mitigates against false anomaly alerts. To achieve this, a new anomaly detection method is proposed that computes the uncertainty in estimates using quantile regression and used the quantile interval to identify anomalies. Similarly, to handle the speed at which the data arrives, an online anomaly detection method is proposed where a model is trained incrementally to adapt to the concept drift that improves prediction. This is implemented using a window-based strategy, in which a time series is broken into sliding windows of sub-sequences as input to the model. To adapt to concept drift, the model is updated when changes occur in the new arrival instances. This is achieved by using anomaly likelihood which is computed using the Q-function to define the abnormal degree of the current data point based on the previous data points. Specifically, when concept drift occurs, the proposed method will mark the current data point as anomalous. However, when the abnormal behavior continues for a longer period of time, the abnormal degree of the current data point will be low compared to the previous data points using the likelihood. As such, the current data point is added to the previous data to retrain the model which will allow the model to learn the new characteristics of the data and hence adapt to the concept changes thereby redefining the abnormal behavior. The proposed method also incorporates feature extraction to capture structural patterns in the time series. This is especially significant for multivariate time-series data, for which there is a need to capture the complex temporal dependencies that may exist between the variables. In summary, this thesis contributes to the theory, design, and development of algorithms and models for the detection of anomalies in both static and evolving time series data. Several experiments were conducted, and the results obtained indicate the significance of this research on offline and online anomaly detection in both static and evolving time-series data. In chapter 3, the newly proposed method (Deep Quantile Regression Anomaly Detection Method) is evaluated and compared with six other prediction-based anomaly detection methods that assume a normal distribution of prediction or reconstruction error for the identification of anomalies. Results in the first part of the experiment indicate that DQR-AD obtained relatively better precision than all other methods which demonstrates the capability of the method in detecting a higher number of anomalous points with low false positive rates. Also, the results show that DQR-AD is approximately 2 – 3 times better than the DeepAnT which performs better than all the remaining methods on all domains in the NAB dataset. In the second part of the experiment, sMAP dataset is used with 4-dimensional features to demonstrate the method on multivariate time-series data. Experimental result shows DQR-AD have 10% better performance than AE on three datasets (SMAP1, SMAP3, and SMAP5) and equal performance on the remaining two datasets. In chapter 5, two levels of experiments were conducted basis of false-positive rate and concept drift adaptation. In the first level of the experiment, the result shows that online DQR-AD is 18% better than both DQR-AD and VAE-LSTM on five NAB datasets. Similarly, results in the second level of the experiment show that the online DQR-AD method has better performance than five counterpart methods with a relatively 10% margin on six out of the seven NAB datasets. This result demonstrates how concept drift adaptation strategies adopted in the proposed online DQR-AD improve the performance of anomaly detection in time series. / Petroleum Technology Development Fund (PTDF)

MSc (Statistics) / Department of Statistics / Short-term load forecasting in South Africa using machine learning and statistical models is discussed in this study. The research is focused on carrying out a comparative analysis in forecasting hourly electricity demand. This study was carried out using South Africa’s aggregated hourly load data from Eskom. The comparison is carried out in this study using support vector regression (SVR), stochastic gradient boosting (SGB), artificial neural networks (NN) with generalized additive model (GAM) as a benchmark model in forecasting hourly electricity demand. In both modelling frameworks, variable selection is done using least absolute shrinkage and selection operator (Lasso). The SGB model yielded the least root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) on testing data. SGB model also yielded the least RMSE, MAE and MAPE on training data. Forecast combination of the models’ forecasts is done using convex combination and quantile regres- sion averaging (QRA). The QRA was found to be the best forecast combination model ibased on the RMSE, MAE and MAPE. / NRF