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Dissertation/Thesis Abstract

Sequential Evolutionary Operations of Trigonometric Simplex Designs for High-Dimensional Unconstrained Optimization Applications
by Musafer, Hassan, Ph.D., University of Bridgeport, 2020, 94; 28155872
Abstract (Summary)

This dissertation proposes a novel mathematical model for the Amoeba or the Nelder-Mead simplex optimization (NM) algorithm. The proposed Hassan NM (HNM) algorithm allows components of the reflected vertex to adapt to different operations, by breaking down the complex structure of the simplex into multiple triangular simplexes that work sequentially to optimize the individual components of mathematical functions. When the next formed simplex is characterized by different operations, it gives the simplex similar reflections to that of the NM algorithm, but with rotation through an angle determined by the collection of nonisometric features. As a consequence, the generating sequence of triangular simplexes is guaranteed that not only they have different shapes, but also they have different directions, to search the complex landscape of mathematical problems and to perform better performance than the traditional hyperplanes simplex. To test reliability, efficiency, and robustness, the proposed algorithm is examined on three areas of large-scale optimization categories: systems of nonlinear equations, nonlinear least squares, and unconstrained minimization. The experimental results confirmed that the new algorithm delivered better performance than the traditional NM algorithm, represented by a famous Matlab function, known as fminsearch.

In addition, the new trigonometric simplex design provides a platform for further development of reliable and robust sparse autoencoder software (SAE) for intrusion detection system (IDS) applications. The proposed error function for the SAE is designed to make a trade-off between the latent state representation for more mature features and network regularization by applying the sparsity constraint in the output layer of the proposed SAE network. In addition, the hyperparameters of the SAE are tuned based on the HNM algorithm and were proved to give a better capability of extracting features in comparison with the existing developed algorithms. In fact, the proposed SAE can be used for not only network intrusion detection systems, but also other applications pertaining to deep learning, feature extraction, and pattern analysis. Results from experimental tests showed that the different layers of the enhanced SAE could efficiently adapt to various levels of learning hierarchy. Finally, additional tests demonstrated that the proposed IDS architecture could provide a more compact and effective immunity system for different types of network attacks with a significant detection accuracy of 99.63% and an F-measure of 0.996, on average, when penalizing sparsity constraint directly on the synaptic weights within the network.

Indexing (document details)
Advisor: Mahmood, Ausif
Commitee: Patra, Prabir , Dichter, Julius , Faezipour, Miad , Tokgoz, Emre
School: University of Bridgeport
Department: Computer Science and Engineering
School Location: United States -- Connecticut
Source: DAI-A 82/5(E), Dissertation Abstracts International
Subjects: Computer Engineering, Design, Applied Mathematics
Keywords: Advanced sparse autoencoder, Hyperparameter optimization, Intrusion detection system, Systems of nonlinear equations, Trigonometric simplex designs, Unconstrained minimization, fminsearch
Publication Number: 28155872
ISBN: 9798691238512
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