About regularity properties in variational analysis and applications in optimization
- Authors: Nguyen, Hieu Thao
- Date: 2015
- Type: Text , Thesis , PhD
- Full Text:
- Description: Regularity properties lie at the core of variational analysis because of their importance for stability analysis of optimization and variational problems, constraint qualications, qualication conditions in coderivative and subdierential calculus and convergence analysis of numerical algorithms. The thesis is devoted to investigation of several research questions related to regularity properties in variational analysis and their applications in convergence analysis and optimization. Following the works by Kruger, we examine several useful regularity properties of collections of sets in both linear and Holder-type settings and establish their characterizations and relationships to regularity properties of set-valued mappings. Following the recent publications by Lewis, Luke, Malick (2009), Drusvyatskiy, Ioe, Lewis (2014) and some others, we study application of the uniform regularity and related properties of collections of sets to alternating projections for solving nonconvex feasibility problems and compare existing results on this topic. Motivated by Ioe (2000) and his subsequent publications, we use the classical iteration scheme going back to Banach, Schauder, Lyusternik and Graves to establish criteria for regularity properties of set-valued mappings and compare this approach with the one based on the Ekeland variational principle. Finally, following the recent works by Khanh et al. on stability analysis for optimization related problems, we investigate calmness of set-valued solution mappings of variational problems.
- Description: Doctor of Philosophy
- Description: Regularity properties lie at the core of variational analysis because of their importance for stability analysis of optimization and variational problems, constraint qualications, qualication conditions in coderivative and subdierential calculus and convergence analysis of numerical algorithms. The thesis is devoted to investigation of several research questions related to regularity properties in variational analysis and their applications in convergence analysis and optimization. Following the works by Kruger, we examine several useful regularity properties of collections of sets in both linear and H
- Authors: Nguyen, Hieu Thao
- Date: 2015
- Type: Text , Thesis , PhD
- Full Text:
- Description: Regularity properties lie at the core of variational analysis because of their importance for stability analysis of optimization and variational problems, constraint qualications, qualication conditions in coderivative and subdierential calculus and convergence analysis of numerical algorithms. The thesis is devoted to investigation of several research questions related to regularity properties in variational analysis and their applications in convergence analysis and optimization. Following the works by Kruger, we examine several useful regularity properties of collections of sets in both linear and Holder-type settings and establish their characterizations and relationships to regularity properties of set-valued mappings. Following the recent publications by Lewis, Luke, Malick (2009), Drusvyatskiy, Ioe, Lewis (2014) and some others, we study application of the uniform regularity and related properties of collections of sets to alternating projections for solving nonconvex feasibility problems and compare existing results on this topic. Motivated by Ioe (2000) and his subsequent publications, we use the classical iteration scheme going back to Banach, Schauder, Lyusternik and Graves to establish criteria for regularity properties of set-valued mappings and compare this approach with the one based on the Ekeland variational principle. Finally, following the recent works by Khanh et al. on stability analysis for optimization related problems, we investigate calmness of set-valued solution mappings of variational problems.
- Description: Doctor of Philosophy
- Description: Regularity properties lie at the core of variational analysis because of their importance for stability analysis of optimization and variational problems, constraint qualications, qualication conditions in coderivative and subdierential calculus and convergence analysis of numerical algorithms. The thesis is devoted to investigation of several research questions related to regularity properties in variational analysis and their applications in convergence analysis and optimization. Following the works by Kruger, we examine several useful regularity properties of collections of sets in both linear and H
Literature on image segmentation based on split - and - Merge techniques
- Faruquzzaman, A. B. M., Paiker, Nafize, Arafat, Jahidul, Ali, Mortuza, Sorwar, Golam
- Authors: Faruquzzaman, A. B. M. , Paiker, Nafize , Arafat, Jahidul , Ali, Mortuza , Sorwar, Golam
- Date: 2008
- Type: Text , Conference proceedings , Conference paper
- Relation: ICITA 2008, Cairns, Qld., 23-26 June, ICITA, published in Proceedings of 5th International Conference on Information Technology and Application pp. 120-125.
- Full Text: false
- Reviewed:
- Description: Image segmentation is a feverish issue due to drastically increasing the use of computer and the Internet. Various algorithms have been invented on this aspect. Among them, split-and-merge (SM) algorithm is highly lucrative now-a-days due to its simplicity and effectiveness in the sector of image processing. Numerous researchers have performed their research work on this algorithm to triumph over its drawbacks for its sustainable and competent implementation. This paper has consolidated the useful consideration and proposal of various researchers to formulate a strong base of knowledge for the future researcher. It has also tinted few unsettled drawbacks of SM algorithm which will open the casement of brainstorming as well as persuade them for future research on SM algorithm, thereby allow SM algorithm to attain a globally optimal algorithm for image segmentation.
- Description: 5th International Conference on Information Technology and Applications, ICITA 2008
The choice of a similarity measure with respect to its sensitivity to outliers
- Rubinov, Alex, Sukhorukova, Nadezda, Ugon, Julien
- Authors: Rubinov, Alex , Sukhorukova, Nadezda , Ugon, Julien
- Date: 2010
- Type: Text , Journal article
- Relation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms Vol. 17, no. 5 (2010), p. 709-721
- Full Text:
- Reviewed:
- Description: This paper examines differences in the choice of similarity measures with respect to their sensitivity to outliers in clustering problems, formulated as mathematical programming problems. Namely, we are focusing on the study of norms (norm-based similarity measures) and convex functions of norms (function-norm-based similarity measures). The study consists of two parts: the study of theoretical models and numerical experiments. The main result of this study is a criterion for the outliers sensitivity with respect to the corresponding similarity measure. In particular, the obtained results show that the norm-based similarity measures are not sensitive to outliers whilst a very widely used square of the Euclidean norm similarity measure (least squares) is sensitive to outliers. Copyright © 2010 Watam Press.
- Authors: Rubinov, Alex , Sukhorukova, Nadezda , Ugon, Julien
- Date: 2010
- Type: Text , Journal article
- Relation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms Vol. 17, no. 5 (2010), p. 709-721
- Full Text:
- Reviewed:
- Description: This paper examines differences in the choice of similarity measures with respect to their sensitivity to outliers in clustering problems, formulated as mathematical programming problems. Namely, we are focusing on the study of norms (norm-based similarity measures) and convex functions of norms (function-norm-based similarity measures). The study consists of two parts: the study of theoretical models and numerical experiments. The main result of this study is a criterion for the outliers sensitivity with respect to the corresponding similarity measure. In particular, the obtained results show that the norm-based similarity measures are not sensitive to outliers whilst a very widely used square of the Euclidean norm similarity measure (least squares) is sensitive to outliers. Copyright © 2010 Watam Press.
Optimization of parameters of the Kelvin element in vibration analysis
- Kuznetsov, Alexey, Mammadov, Musa, Hajilarov, Eldar
- Authors: Kuznetsov, Alexey , Mammadov, Musa , Hajilarov, Eldar
- Date: 2009
- Type: Text , Conference paper
- Relation: Paper presented at 2009 IEEE International Conference on Industrial Technology, ICIT 2009, Churchill, VIC January 2009
- Full Text:
- Description: In this paper we consider the problem of finding optimal parameters of the Kelvin element in vibration analysis. This problem is based on finding analytical solution of the initial ODE for development of the optimization model. Such technique allows us to compute optimal parameters of Kelvin element.
- Authors: Kuznetsov, Alexey , Mammadov, Musa , Hajilarov, Eldar
- Date: 2009
- Type: Text , Conference paper
- Relation: Paper presented at 2009 IEEE International Conference on Industrial Technology, ICIT 2009, Churchill, VIC January 2009
- Full Text:
- Description: In this paper we consider the problem of finding optimal parameters of the Kelvin element in vibration analysis. This problem is based on finding analytical solution of the initial ODE for development of the optimization model. Such technique allows us to compute optimal parameters of Kelvin element.
Performance assessment of a solar dryer system using small parabolic dish and alumina/oil nanofluid : simulation and experimental study
- Arkian, Amir, Najafi, Gholamhassan, Gorjian, Shiva, Loni, Reyhaneh, Bellos, Evangelos, Yusaf, Talal
- Authors: Arkian, Amir , Najafi, Gholamhassan , Gorjian, Shiva , Loni, Reyhaneh , Bellos, Evangelos , Yusaf, Talal
- Date: 2019
- Type: Text , Journal article
- Relation: Energies Vol. 12, no. 24 (Dec 2019), p. 22
- Full Text:
- Reviewed:
- Description: In this study, a small dish concentrator with a cylindrical cavity receiver was experimentally investigated as the heat source of a dryer. The system was examined for operation with pure thermal oil and Al2O3/oil nanofluid as the working fluids in the solar system. Moreover, the design, the development, and the evaluation of the dried mint plant are presented in this work. Also, the solar dryer system was simulated by the SolidWorks and ANSYS CFX software. On the other side, the color histogram of the wet and dried mint samples based on the RGB method was considered. The results revealed that the different temperatures of the solar working fluids at the inlet and outlet of the cavity receiver showed similar trend data compared to the variation of the solar radiation during the experimental test. Moreover, it is found that the cavity heat gain and thermal efficiency of the solar system was improved by using the nanofluid as the solar working fluid. Furthermore, the required time for mint drying had decreased by increasing the drying temperature and increasing air speed. The highest drying time was measured equal to 320 min for the condition of the air speed equal to 0.5 m/s and the drying temperature of 30 degrees C. A good agreement was observed between the calculated numerical results and measured experimental data. Finally, based on the color histogram of the wet and dried mint samples, it was concluded that intensity amount of the red color of the mint increased with the drying process compared to intensity amount of the red color of the wet mint sample.
- Authors: Arkian, Amir , Najafi, Gholamhassan , Gorjian, Shiva , Loni, Reyhaneh , Bellos, Evangelos , Yusaf, Talal
- Date: 2019
- Type: Text , Journal article
- Relation: Energies Vol. 12, no. 24 (Dec 2019), p. 22
- Full Text:
- Reviewed:
- Description: In this study, a small dish concentrator with a cylindrical cavity receiver was experimentally investigated as the heat source of a dryer. The system was examined for operation with pure thermal oil and Al2O3/oil nanofluid as the working fluids in the solar system. Moreover, the design, the development, and the evaluation of the dried mint plant are presented in this work. Also, the solar dryer system was simulated by the SolidWorks and ANSYS CFX software. On the other side, the color histogram of the wet and dried mint samples based on the RGB method was considered. The results revealed that the different temperatures of the solar working fluids at the inlet and outlet of the cavity receiver showed similar trend data compared to the variation of the solar radiation during the experimental test. Moreover, it is found that the cavity heat gain and thermal efficiency of the solar system was improved by using the nanofluid as the solar working fluid. Furthermore, the required time for mint drying had decreased by increasing the drying temperature and increasing air speed. The highest drying time was measured equal to 320 min for the condition of the air speed equal to 0.5 m/s and the drying temperature of 30 degrees C. A good agreement was observed between the calculated numerical results and measured experimental data. Finally, based on the color histogram of the wet and dried mint samples, it was concluded that intensity amount of the red color of the mint increased with the drying process compared to intensity amount of the red color of the wet mint sample.
Global optimality conditions and optimization methods for polynomial programming problems and their applications
- Authors: Tian, Jing
- Date: 2014
- Type: Text , Thesis , PhD
- Full Text:
- Description: The polynomial programming problem which has a polynomial objective function, either with no constraints or with polynomial constraints occurs frequently in engineering design, investment science, control theory, network distribution, signal processing and locationallocation contexts. Moreover, the polynomial programming problem is known to be Nondeterministic Polynomial-time hard (NP-hard). The polynomial programming problem has attracted a lot of attention, including quadratic, cubic, homogenous or normal quartic programming problems as special cases. Existing methods for solving polynomial programming problems include algebraic methods and various convex relaxation methods. Especially, among these methods, semidefinite programming (SDP) and sum of squares (SOS) relaxations are very popular. Theoretically, SDP and SOS relaxation methods are very powerful and successful in solving the general polynomial programming problem with a compact feasible region. However, the solvability in practice depends on the size or the degree of the polynomial programming problem and the required accuracy. Hence, solving large scale SDP problems still remains a computational challenge. It is well-known that traditional local optimization methods are designed based on necessary local optimality conditions, i.e., Karush-Kuhn-Tucker (KKT) conditions. Motivated by this, some researchers proposed a necessary global optimality condition for a quadratic programming problem and designed a new local optimization method according to the necessary global optimality condition. In this thesis, we try to apply this idea to cubic and quatic programming problems, and further to general unconstrained and constrained polynomial programming problems. For these polynomial programming problems, we will investigate necessary global optimality conditions and design new local optimization methods according to these conditions. These necessary global optimality conditions are generally stronger than KKT conditions. Hence, the obtained new local minimizers by using the new local optimization methods may improve some KKT points. Our ultimate aim is to design global optimization methods for these polynomial programming problems. We notice that the filled function method is one of the well-known and practical auxiliary function methods used to achieve a global minimizer. In this thesis, we design global optimization methods by combining the new proposed local optimization methods and some auxiliary functions. The numerical examples illustrate the efficiency and stability of the optimization methods. Finally, we discuss some applications for solving some sensor network localization problems and systems of polynomial equations. It is worth mentioning that we apply the idea and the results for polynomial programming problems to nonlinear programming problems (NLP). We provide an optimality condition and design new local optimization methods according to the optimality condition and design global optimization methods for the problem (NLP) by combining the new local optimization methods and an auxiliary function. In order to test the performance of the global optimization methods, we compare them with two other heuristic methods. The results demonstrate our methods outperform the two other algorithms.
- Description: Doctor of Philosophy
- Authors: Tian, Jing
- Date: 2014
- Type: Text , Thesis , PhD
- Full Text:
- Description: The polynomial programming problem which has a polynomial objective function, either with no constraints or with polynomial constraints occurs frequently in engineering design, investment science, control theory, network distribution, signal processing and locationallocation contexts. Moreover, the polynomial programming problem is known to be Nondeterministic Polynomial-time hard (NP-hard). The polynomial programming problem has attracted a lot of attention, including quadratic, cubic, homogenous or normal quartic programming problems as special cases. Existing methods for solving polynomial programming problems include algebraic methods and various convex relaxation methods. Especially, among these methods, semidefinite programming (SDP) and sum of squares (SOS) relaxations are very popular. Theoretically, SDP and SOS relaxation methods are very powerful and successful in solving the general polynomial programming problem with a compact feasible region. However, the solvability in practice depends on the size or the degree of the polynomial programming problem and the required accuracy. Hence, solving large scale SDP problems still remains a computational challenge. It is well-known that traditional local optimization methods are designed based on necessary local optimality conditions, i.e., Karush-Kuhn-Tucker (KKT) conditions. Motivated by this, some researchers proposed a necessary global optimality condition for a quadratic programming problem and designed a new local optimization method according to the necessary global optimality condition. In this thesis, we try to apply this idea to cubic and quatic programming problems, and further to general unconstrained and constrained polynomial programming problems. For these polynomial programming problems, we will investigate necessary global optimality conditions and design new local optimization methods according to these conditions. These necessary global optimality conditions are generally stronger than KKT conditions. Hence, the obtained new local minimizers by using the new local optimization methods may improve some KKT points. Our ultimate aim is to design global optimization methods for these polynomial programming problems. We notice that the filled function method is one of the well-known and practical auxiliary function methods used to achieve a global minimizer. In this thesis, we design global optimization methods by combining the new proposed local optimization methods and some auxiliary functions. The numerical examples illustrate the efficiency and stability of the optimization methods. Finally, we discuss some applications for solving some sensor network localization problems and systems of polynomial equations. It is worth mentioning that we apply the idea and the results for polynomial programming problems to nonlinear programming problems (NLP). We provide an optimality condition and design new local optimization methods according to the optimality condition and design global optimization methods for the problem (NLP) by combining the new local optimization methods and an auxiliary function. In order to test the performance of the global optimization methods, we compare them with two other heuristic methods. The results demonstrate our methods outperform the two other algorithms.
- Description: Doctor of Philosophy
Hybridizing five neural-metaheuristic paradigms to predict the pillar stress in bord and pillar method
- Zhou, Jian, Chen, Yuxin, Chen, Hui, Khandelwal, Manoj, Monjezi, Masoud, Peng, Kang
- Authors: Zhou, Jian , Chen, Yuxin , Chen, Hui , Khandelwal, Manoj , Monjezi, Masoud , Peng, Kang
- Date: 2023
- Type: Text , Journal article
- Relation: Frontiers in Public Health Vol. 11, no. (2023), p.
- Full Text:
- Reviewed:
- Description: Pillar stability is an important condition for safe work in room-and-pillar mines. The instability of pillars will lead to large-scale collapse hazards, and the accurate estimation of induced stresses at different positions in the pillar is helpful for pillar design and guaranteeing pillar stability. There are many modeling methods to design pillars and evaluate their stability, including empirical and numerical method. However, empirical methods are difficult to be applied to places other than the original environmental characteristics, and numerical methods often simplify the boundary conditions and material properties, which cannot guarantee the stability of the design. Currently, machine learning (ML) algorithms have been successfully applied to pillar stability assessment with higher accuracy. Thus, the study adopted a back-propagation neural network (BPNN) and five elements including the sparrow search algorithm (SSA), gray wolf optimizer (GWO), butterfly optimization algorithm (BOA), tunicate swarm algorithm (TSA), and multi-verse optimizer (MVO). Combining metaheuristic algorithms, five hybrid models were developed to predict the induced stress within the pillar. The weight and threshold of the BPNN model are optimized by metaheuristic algorithms, in which the mean absolute error (MAE) is utilized as the fitness function. A database containing 149 data samples was established, where the input variables were the angle of goafline (A), depth of the working coal seam (H), specific gravity (G), distance of the point from the center of the pillar (C), and distance of the point from goafline (D), and the output variable was the induced stress. Furthermore, the predictive performance of the proposed model is evaluated by five metrics, namely coefficient of determination (R2), root mean squared error (RMSE), variance accounted for (VAF), mean absolute error (MAE), and mean absolute percentage error (MAPE). The results showed that the five hybrid models developed have good prediction performance, especially the GWO-BPNN model performed the best (Training set: R2 = 0.9991, RMSE = 0.1535, VAF = 99.91, MAE = 0.0884, MAPE = 0.6107; Test set: R2 = 0.9983, RMSE = 0.1783, VAF = 99.83, MAE = 0.1230, MAPE = 0.9253). Copyright © 2023 Zhou, Chen, Chen, Khandelwal, Monjezi and Peng.
- Authors: Zhou, Jian , Chen, Yuxin , Chen, Hui , Khandelwal, Manoj , Monjezi, Masoud , Peng, Kang
- Date: 2023
- Type: Text , Journal article
- Relation: Frontiers in Public Health Vol. 11, no. (2023), p.
- Full Text:
- Reviewed:
- Description: Pillar stability is an important condition for safe work in room-and-pillar mines. The instability of pillars will lead to large-scale collapse hazards, and the accurate estimation of induced stresses at different positions in the pillar is helpful for pillar design and guaranteeing pillar stability. There are many modeling methods to design pillars and evaluate their stability, including empirical and numerical method. However, empirical methods are difficult to be applied to places other than the original environmental characteristics, and numerical methods often simplify the boundary conditions and material properties, which cannot guarantee the stability of the design. Currently, machine learning (ML) algorithms have been successfully applied to pillar stability assessment with higher accuracy. Thus, the study adopted a back-propagation neural network (BPNN) and five elements including the sparrow search algorithm (SSA), gray wolf optimizer (GWO), butterfly optimization algorithm (BOA), tunicate swarm algorithm (TSA), and multi-verse optimizer (MVO). Combining metaheuristic algorithms, five hybrid models were developed to predict the induced stress within the pillar. The weight and threshold of the BPNN model are optimized by metaheuristic algorithms, in which the mean absolute error (MAE) is utilized as the fitness function. A database containing 149 data samples was established, where the input variables were the angle of goafline (A), depth of the working coal seam (H), specific gravity (G), distance of the point from the center of the pillar (C), and distance of the point from goafline (D), and the output variable was the induced stress. Furthermore, the predictive performance of the proposed model is evaluated by five metrics, namely coefficient of determination (R2), root mean squared error (RMSE), variance accounted for (VAF), mean absolute error (MAE), and mean absolute percentage error (MAPE). The results showed that the five hybrid models developed have good prediction performance, especially the GWO-BPNN model performed the best (Training set: R2 = 0.9991, RMSE = 0.1535, VAF = 99.91, MAE = 0.0884, MAPE = 0.6107; Test set: R2 = 0.9983, RMSE = 0.1783, VAF = 99.83, MAE = 0.1230, MAPE = 0.9253). Copyright © 2023 Zhou, Chen, Chen, Khandelwal, Monjezi and Peng.
Optimality conditions in nonconvex optimization via weak subdifferentials
- Kasimbeyli, Refail, Mammadov, Musa
- Authors: Kasimbeyli, Refail , Mammadov, Musa
- Date: 2011
- Type: Text , Journal article
- Relation: Nonlinear Analysis, Theory, Methods and Applications Vol. 74, no. 7 (2011), p. 2534-2547
- Full Text:
- Reviewed:
- Description: In this paper we study optimality conditions for optimization problems described by a special class of directionally differentiable functions. The well-known necessary and sufficient optimality condition of nonsmooth convex optimization, given in the form of variational inequality, is generalized to the nonconvex case by using the notion of weak subdifferentials. The equivalent formulation of this condition in terms of weak subdifferentials and augmented normal cones is also presented. © 2011 Elsevier Ltd. All rights reserved.
From convex to nonconvex: A loss function analysis for binary classification
- Zhao, Lei, Mammadov, Musa, Yearwood, John
- Authors: Zhao, Lei , Mammadov, Musa , Yearwood, John
- Date: 2010
- Type: Text , Conference paper
- Relation: Paper presented at10th IEEE International Conference on Data Mining Workshops, ICDMW 2010 p. 1281-1288
- Full Text:
- Reviewed:
- Description: Problems of data classification can be studied in the framework of regularization theory as ill-posed problems. In this framework, loss functions play an important role in the application of regularization theory to classification. In this paper, we review some important convex loss functions, including hinge loss, square loss, modified square loss, exponential loss, logistic regression loss, as well as some non-convex loss functions, such as sigmoid loss, ø-loss, ramp loss, normalized sigmoid loss, and the loss function of 2 layer neural network. Based on the analysis of these loss functions, we propose a new differentiable non-convex loss function, called smoothed 0-1 loss function, which is a natural approximation of the 0-1 loss function. To compare the performance of different loss functions, we propose two binary classification algorithms for binary classification, one for convex loss functions, the other for non-convex loss functions. A set of experiments are launched on several binary data sets from the UCI repository. The results show that the proposed smoothed 0-1 loss function is robust, especially for those noisy data sets with many outliers. © 2010 IEEE.
- Authors: Zhao, Lei , Mammadov, Musa , Yearwood, John
- Date: 2010
- Type: Text , Conference paper
- Relation: Paper presented at10th IEEE International Conference on Data Mining Workshops, ICDMW 2010 p. 1281-1288
- Full Text:
- Reviewed:
- Description: Problems of data classification can be studied in the framework of regularization theory as ill-posed problems. In this framework, loss functions play an important role in the application of regularization theory to classification. In this paper, we review some important convex loss functions, including hinge loss, square loss, modified square loss, exponential loss, logistic regression loss, as well as some non-convex loss functions, such as sigmoid loss, ø-loss, ramp loss, normalized sigmoid loss, and the loss function of 2 layer neural network. Based on the analysis of these loss functions, we propose a new differentiable non-convex loss function, called smoothed 0-1 loss function, which is a natural approximation of the 0-1 loss function. To compare the performance of different loss functions, we propose two binary classification algorithms for binary classification, one for convex loss functions, the other for non-convex loss functions. A set of experiments are launched on several binary data sets from the UCI repository. The results show that the proposed smoothed 0-1 loss function is robust, especially for those noisy data sets with many outliers. © 2010 IEEE.
The effect of regularization on drug-reaction relationships
- Mammadov, Musa, Zhao, L., Zhang, Jianjun
- Authors: Mammadov, Musa , Zhao, L. , Zhang, Jianjun
- Date: 2012
- Type: Text , Journal article
- Relation: Optimization Vol. 61, no. 4 (2012), p. 405-422
- Full Text:
- Reviewed:
- Description: The least-squares method is a standard approach used in data fitting that has important applications in many areas in science and engineering including many finance problems. In the case when the problem under consideration involves large-scale sparse matrices regularization methods are used to obtain more stable solutions by relaxing the data fitting. In this article, a new regularization algorithm is introduced based on the Karush-Kuhn-Tucker conditions and the Fisher-Burmeister function. The Newton method is used for solving corresponding systems of equations. The advantages of the proposed method has been demonstrated in the establishment of drug-reaction relationships based on the Australian Adverse Drug Reaction Advisory Committee database. © 2012 Copyright Taylor and Francis Group, LLC.
- Authors: Mammadov, Musa , Zhao, L. , Zhang, Jianjun
- Date: 2012
- Type: Text , Journal article
- Relation: Optimization Vol. 61, no. 4 (2012), p. 405-422
- Full Text:
- Reviewed:
- Description: The least-squares method is a standard approach used in data fitting that has important applications in many areas in science and engineering including many finance problems. In the case when the problem under consideration involves large-scale sparse matrices regularization methods are used to obtain more stable solutions by relaxing the data fitting. In this article, a new regularization algorithm is introduced based on the Karush-Kuhn-Tucker conditions and the Fisher-Burmeister function. The Newton method is used for solving corresponding systems of equations. The advantages of the proposed method has been demonstrated in the establishment of drug-reaction relationships based on the Australian Adverse Drug Reaction Advisory Committee database. © 2012 Copyright Taylor and Francis Group, LLC.
Integrated production system optimization using global optimization techniques
- Mason, T. L., Emelle, C., Van Berkel, J., Bagirov, Adil, Kampas, F., Pinter, J. D.
- Authors: Mason, T. L. , Emelle, C. , Van Berkel, J. , Bagirov, Adil , Kampas, F. , Pinter, J. D.
- Date: 2007
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 3, no. 2 (May 2007), p. 257-277
- Full Text:
- Reviewed:
- Description: Many optimization problems related to integrated oil and gas production systems are nonconvex and multimodal. Additionally, apart from the innate nonsmoothness of many optimization problems, nonsmooth functions such as minimum and maximum functions may be used to model flow/pressure controllers and cascade mass in the gas gathering and blending networks. In this paper we study the application of different versions of the derivative free Discrete Gradient Method (DGM) as well as the Lipschitz Global Optimizer (LGO) suite to production optimization in integrated oil and gas production systems and their comparison with various local and global solvers used with the General Algebraic Modeling System (GAMS). Four nonconvex and nonsmooth test cases were constructed from a small but realistic integrated gas production system optimization problem. The derivation of the system of equations for the various test cases is also presented. Results demonstrate that DGM is especially effective for solving nonsmooth optimization problems and its two versions are capable global optimization algorithms. We also demonstrate that LGO solves successfully the presented test (as well as other related real-world) problems.
- Description: C1
- Description: 2003004725
- Authors: Mason, T. L. , Emelle, C. , Van Berkel, J. , Bagirov, Adil , Kampas, F. , Pinter, J. D.
- Date: 2007
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 3, no. 2 (May 2007), p. 257-277
- Full Text:
- Reviewed:
- Description: Many optimization problems related to integrated oil and gas production systems are nonconvex and multimodal. Additionally, apart from the innate nonsmoothness of many optimization problems, nonsmooth functions such as minimum and maximum functions may be used to model flow/pressure controllers and cascade mass in the gas gathering and blending networks. In this paper we study the application of different versions of the derivative free Discrete Gradient Method (DGM) as well as the Lipschitz Global Optimizer (LGO) suite to production optimization in integrated oil and gas production systems and their comparison with various local and global solvers used with the General Algebraic Modeling System (GAMS). Four nonconvex and nonsmooth test cases were constructed from a small but realistic integrated gas production system optimization problem. The derivation of the system of equations for the various test cases is also presented. Results demonstrate that DGM is especially effective for solving nonsmooth optimization problems and its two versions are capable global optimization algorithms. We also demonstrate that LGO solves successfully the presented test (as well as other related real-world) problems.
- Description: C1
- Description: 2003004725
Learning Bayesian networks based on optimization approaches
- Authors: Taheri, Sona
- Date: 2012
- Type: Text , Thesis , PhD
- Full Text:
- Description: Learning accurate classifiers from preclassified data is a very active research topic in machine learning and artifcial intelligence. There are numerous classifier paradigms, among which Bayesian Networks are very effective and well known in domains with uncertainty. Bayesian Networks are widely used representation frameworks for reasoning with probabilistic information. These models use graphs to capture dependence and independence relationships between feature variables, allowing a concise representation of the knowledge as well as efficient graph based query processing algorithms. This representation is defined by two components: structure learning and parameter learning. The structure of this model represents a directed acyclic graph. The nodes in the graph correspond to the feature variables in the domain, and the arcs (edges) show the causal relationships between feature variables. A directed edge relates the variables so that the variable corresponding to the terminal node (child) will be conditioned on the variable corresponding to the initial node (parent). The parameter learning represents probabilities and conditional probabilities based on prior information or past experience. The set of probabilities are represented in the conditional probability table. Once the network structure is constructed, the probabilistic inferences are readily calculated, and can be performed to predict the outcome of some variables based on the observations of others. However, the problem of structure learning is a complex problem since the number of candidate structures grows exponentially when the number of feature variables increases. This thesis is devoted to the development of learning structures and parameters in Bayesian Networks. Different models based on optimization techniques are introduced to construct an optimal structure of a Bayesian Network. These models also consider the improvement of the Naive Bayes' structure by developing new algorithms to alleviate the independence assumptions. We present various models to learn parameters of Bayesian Networks; in particular we propose optimization models for the Naive Bayes and the Tree Augmented Naive Bayes by considering different objective functions. To solve corresponding optimization problems in Bayesian Networks, we develop new optimization algorithms. Local optimization methods are introduced based on the combination of the gradient and Newton methods. It is proved that the proposed methods are globally convergent and have superlinear convergence rates. As a global search we use the global optimization method, AGOP, implemented in the open software library GANSO. We apply the proposed local methods in the combination with AGOP. Therefore, the main contributions of this thesis include (a) new algorithms for learning an optimal structure of a Bayesian Network; (b) new models for learning the parameters of Bayesian Networks with the given structures; and finally (c) new optimization algorithms for optimizing the proposed models in (a) and (b). To validate the proposed methods, we conduct experiments across a number of real world problems. Print version is available at: http://library.federation.edu.au/record=b1804607~S4
- Description: Doctor of Philosophy
Global optimality conditions and optimization methods for quadratic assignment problems
- Wu, Zhiyou, Yang, Yongjian, Bai, Fusheng, Tian, Jing
- Authors: Wu, Zhiyou , Yang, Yongjian , Bai, Fusheng , Tian, Jing
- Date: 2012
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 218, no. 11 (2012), p. 6214-6231
- Full Text:
- Reviewed:
- Description: In this paper some global optimality conditions for general quadratic {0, 1} programming problems with linear equality constraints are discussed and then some global optimality conditions for quadratic assignment problems (QAP) are presented. A local optimization method for (QAP) is derived according to the necessary global optimality conditions. A global optimization method for (QAP) is presented by combining the sufficient global optimality conditions, the local optimization method and some auxiliary functions. Some numerical examples are given to illustrate the efficiency of the given optimization methods. © 2011 Elsevier Inc. All rights reserved.
- Authors: Wu, Zhiyou , Yang, Yongjian , Bai, Fusheng , Tian, Jing
- Date: 2012
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 218, no. 11 (2012), p. 6214-6231
- Full Text:
- Reviewed:
- Description: In this paper some global optimality conditions for general quadratic {0, 1} programming problems with linear equality constraints are discussed and then some global optimality conditions for quadratic assignment problems (QAP) are presented. A local optimization method for (QAP) is derived according to the necessary global optimality conditions. A global optimization method for (QAP) is presented by combining the sufficient global optimality conditions, the local optimization method and some auxiliary functions. Some numerical examples are given to illustrate the efficiency of the given optimization methods. © 2011 Elsevier Inc. All rights reserved.
Optimization of multiple classifiers in data mining based on string rewriting systems
- Dazeley, Richard, Kelarev, Andrei, Yearwood, John, Mammadov, Musa
- Authors: Dazeley, Richard , Kelarev, Andrei , Yearwood, John , Mammadov, Musa
- Date: 2009
- Type: Text , Journal article
- Relation: Asian-European Journal of Mathematics Vol. 2, no. 1 (2009), p. 41-56
- Relation: https://purl.org/au-research/grants/arc/DP0211866
- Relation: https://purl.org/au-research/grants/arc/LP0669752
- Full Text:
- Description: Optimization of multiple classifiers is an important problem in data mining. We introduce additional structure on the class sets of the classifiers using string rewriting systems with a convenient matrix representation. The aim of the present paper is to develop an efficient algorithm for the optimization of the number of errors of individual classifiers, which can be corrected by these multiple classifiers.
- Authors: Dazeley, Richard , Kelarev, Andrei , Yearwood, John , Mammadov, Musa
- Date: 2009
- Type: Text , Journal article
- Relation: Asian-European Journal of Mathematics Vol. 2, no. 1 (2009), p. 41-56
- Relation: https://purl.org/au-research/grants/arc/DP0211866
- Relation: https://purl.org/au-research/grants/arc/LP0669752
- Full Text:
- Description: Optimization of multiple classifiers is an important problem in data mining. We introduce additional structure on the class sets of the classifiers using string rewriting systems with a convenient matrix representation. The aim of the present paper is to develop an efficient algorithm for the optimization of the number of errors of individual classifiers, which can be corrected by these multiple classifiers.
On the kinematics and synthesis of a geared five-bar slider-crank mechanism
- Sultan, Ibrahim, Kalim, Azfar
- Authors: Sultan, Ibrahim , Kalim, Azfar
- Date: 2011
- Type: Text , Journal article
- Relation: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science Vol. 225, no. 5 (2011), p. 1253-1261
- Full Text:
- Reviewed:
- Description: The geared five-bar mechanism possesses kinematic abilities that qualify its utility in various industrial applications. Small changes to the mechanism topology or dimensions create new designs with different motion characteristics. This article presents design-orientated kinematical insights and mathematical treatments for the embodiment of the mechanism in which the end gear is eccentrically pivoted to a sliding element. For its synthesis, a kinematic classification is introduced and approximate curves are used to guide the motion of the slider. A gradient-based Levenberg-Marquardt formulation is employed for the optimization procedure. Geometric, mobility, and dimensional constraints are utilized together with numerical position equations for the analysis. Two case studies are presented at the end of this article to highlight the versatility of the mechanism and prove the validity of the presented mathematical model.
- Authors: Sultan, Ibrahim , Kalim, Azfar
- Date: 2011
- Type: Text , Journal article
- Relation: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science Vol. 225, no. 5 (2011), p. 1253-1261
- Full Text:
- Reviewed:
- Description: The geared five-bar mechanism possesses kinematic abilities that qualify its utility in various industrial applications. Small changes to the mechanism topology or dimensions create new designs with different motion characteristics. This article presents design-orientated kinematical insights and mathematical treatments for the embodiment of the mechanism in which the end gear is eccentrically pivoted to a sliding element. For its synthesis, a kinematic classification is introduced and approximate curves are used to guide the motion of the slider. A gradient-based Levenberg-Marquardt formulation is employed for the optimization procedure. Geometric, mobility, and dimensional constraints are utilized together with numerical position equations for the analysis. Two case studies are presented at the end of this article to highlight the versatility of the mechanism and prove the validity of the presented mathematical model.
Evaluation of slug flow-induced flexural loading in pipelines using a surrogate model
- Sultan, Ibrahim, Reda, Ahmed, Forbes, Gareth
- Authors: Sultan, Ibrahim , Reda, Ahmed , Forbes, Gareth
- Date: 2013
- Type: Text , Journal article
- Relation: Journal of Offshore Mechanics and Arctic Engineering Vol. 135, no. 3 (2013), p. 8
- Full Text:
- Reviewed:
- Description: Slug flow induces vibration in pipelines, which may, in some cases, result in fatigue failure. This can result from dynamic stresses, induced by the deflection and bending moment in the pipe span, growing to levels above the endurance limits of the pipeline material. As such, it is of paramount importance to understand and quantify the size of the pipeline response to slug flow under given speed and damping conditions. This paper utilizes the results of an optimization procedure to devise a surrogate closed-form model, which can be employed to calculate the maximum values of the pipeline loadings at given values of speed and damping parameters. The surrogate model is intended to replace the computationally costly numerical procedure needed for the analysis. The maximum values of the lateral deflection and bending moment, along with their locations, have been calculated using the optimization method of stochastic perturbation and successive approximations ( SPSA). The accuracy of the proposed surrogate model will be validated numerically, and the model will be subsequently used in a numerical example to demonstrate its applicability in industrial situations. An accompanying spreadsheet with this worked example is also given.
- Description: C1
Master control unit based power exchange strategy for interconnected microgrids
- Batool, Munira, Islam, Syed, Shahnia, Farhad
- Authors: Batool, Munira , Islam, Syed , Shahnia, Farhad
- Date: 2017
- Type: Text , Conference proceedings , Conference paper
- Relation: 2017 Australasian Universities Power Engineering Conference, AUPEC 2017; Melbourne, Australia; 19th-22nd November 2017 Vol. 2017, p. 1-6
- Full Text:
- Reviewed:
- Description: Large remote area networks normally have self-suffi-cient electricity systems. These systems also rely on non-dispatchable DGs (N-DGs) for overall reduction in cost of electricity production. It is a fact that uncertainties included in the nature of N-DGs as well as load demand can cause cost burden on islanded microgrids (MGs). This paper proposes development of power exchange strategy for an interconnected MGs (IMG) system as part of large remote area network with optimized controls of dispatchable (D-DGs) which are members of master control unit (MCU). MCU analysis includes equal cost increment principle to give idea about the amount of power exchange which could take place with neighbor MGs in case of overloading situation. Sudden changes in N-DGs and load are defined as interruptions and are part of analysis too. Optimization problem is formulated on the basis of MCU adjustment for overloading or under loading situation and suitability of support MG (S-MG) in IMG system for power exchange along with key features of low cost and minimum technical impacts. Mixed integer linear programming (MILP) technique is applied to solve the formulated problem. The impact of proposed strategy is assessed by numerical analysis in MATLAB programming under stochastic environment.
- Authors: Batool, Munira , Islam, Syed , Shahnia, Farhad
- Date: 2017
- Type: Text , Conference proceedings , Conference paper
- Relation: 2017 Australasian Universities Power Engineering Conference, AUPEC 2017; Melbourne, Australia; 19th-22nd November 2017 Vol. 2017, p. 1-6
- Full Text:
- Reviewed:
- Description: Large remote area networks normally have self-suffi-cient electricity systems. These systems also rely on non-dispatchable DGs (N-DGs) for overall reduction in cost of electricity production. It is a fact that uncertainties included in the nature of N-DGs as well as load demand can cause cost burden on islanded microgrids (MGs). This paper proposes development of power exchange strategy for an interconnected MGs (IMG) system as part of large remote area network with optimized controls of dispatchable (D-DGs) which are members of master control unit (MCU). MCU analysis includes equal cost increment principle to give idea about the amount of power exchange which could take place with neighbor MGs in case of overloading situation. Sudden changes in N-DGs and load are defined as interruptions and are part of analysis too. Optimization problem is formulated on the basis of MCU adjustment for overloading or under loading situation and suitability of support MG (S-MG) in IMG system for power exchange along with key features of low cost and minimum technical impacts. Mixed integer linear programming (MILP) technique is applied to solve the formulated problem. The impact of proposed strategy is assessed by numerical analysis in MATLAB programming under stochastic environment.
Effects of a proper feature selection on prediction and optimization of drilling rate using intelligent techniques
- Liao, Xiufeng, Khandelwal, Manoj, Yang, Haiqing, Koopialipoor, Mohammadreza, Murlidhar, Bhatawdekar
- Authors: Liao, Xiufeng , Khandelwal, Manoj , Yang, Haiqing , Koopialipoor, Mohammadreza , Murlidhar, Bhatawdekar
- Date: 2020
- Type: Text , Journal article
- Relation: Engineering with Computers Vol. 36, no. 2 (Apr 2020), p. 499-510
- Full Text:
- Reviewed:
- Description: One of the important factors during drilling times is the rate of penetration (ROP), which is controlled based on different variables. Factors affecting different drillings are of paramount importance. In the current research, an attempt was made to better recognize drilling parameters and optimize them based on an optimization algorithm. For this purpose, 618 data sets, including RPM, flushing media, and compressive strength parameters, were measured and collected. After an initial investigation, the compressive strength feature of samples, which is an important parameter from the rocks, was used as a proper criterion for classification. Then using intelligent systems, three different levels of the rock strength and all data were modeled. The results showed that systems which were classified based on compressive strength showed a better performance for ROP assessment due to the proximity of features. Therefore, these three levels were used for classification. A new artificial bee colony algorithm was used to solve this problem. Optimizations were applied to the selected models under different optimization conditions, and optimal states were determined. As determining drilling machine parameters is important, these parameters were determined based on optimal conditions. The obtained results showed that this intelligent system can well improve drilling conditions and increase the ROP value for three strength levels of the rocks. This modeling system can be used in different drilling operations.
- Authors: Liao, Xiufeng , Khandelwal, Manoj , Yang, Haiqing , Koopialipoor, Mohammadreza , Murlidhar, Bhatawdekar
- Date: 2020
- Type: Text , Journal article
- Relation: Engineering with Computers Vol. 36, no. 2 (Apr 2020), p. 499-510
- Full Text:
- Reviewed:
- Description: One of the important factors during drilling times is the rate of penetration (ROP), which is controlled based on different variables. Factors affecting different drillings are of paramount importance. In the current research, an attempt was made to better recognize drilling parameters and optimize them based on an optimization algorithm. For this purpose, 618 data sets, including RPM, flushing media, and compressive strength parameters, were measured and collected. After an initial investigation, the compressive strength feature of samples, which is an important parameter from the rocks, was used as a proper criterion for classification. Then using intelligent systems, three different levels of the rock strength and all data were modeled. The results showed that systems which were classified based on compressive strength showed a better performance for ROP assessment due to the proximity of features. Therefore, these three levels were used for classification. A new artificial bee colony algorithm was used to solve this problem. Optimizations were applied to the selected models under different optimization conditions, and optimal states were determined. As determining drilling machine parameters is important, these parameters were determined based on optimal conditions. The obtained results showed that this intelligent system can well improve drilling conditions and increase the ROP value for three strength levels of the rocks. This modeling system can be used in different drilling operations.
On the design of a class of rotary compressors using bayesian optimization
- Lu, Kui, Phung, Truong, Sultan, Ibrahim
- Authors: Lu, Kui , Phung, Truong , Sultan, Ibrahim
- Date: 2021
- Type: Text , Journal article
- Relation: Machines Vol. 9, no. 10 (2021), p.
- Full Text:
- Reviewed:
- Description: The optimization process of compressors is usually regarded as a ‘black-box’ problem, in which the mathematical form underlying the relationship between design parameters and the design objective is impractical and costly to be obtained. To solve the ‘black-box’ problem, Bayesian optimization has been proven as an accurate and efficient method. However, the application of such a method in the design of compressors is rarely discussed, particularly no work has been reported in terms of the positive displacement type compressor. Therefore, this paper aims to introduce the Bayesian optimization to the design of positive displacement compressors through the optimization process of the novel limaçon compressor. In this paper, a two-stage optimization process is presented, in which the first stage optimizes the geometric parameters as per design requirements and the second stage focuses on revealing an optimum setting of port geometries that improves machine performance. A numerical illustration is offered to prove the validity of the presented approach. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
- Authors: Lu, Kui , Phung, Truong , Sultan, Ibrahim
- Date: 2021
- Type: Text , Journal article
- Relation: Machines Vol. 9, no. 10 (2021), p.
- Full Text:
- Reviewed:
- Description: The optimization process of compressors is usually regarded as a ‘black-box’ problem, in which the mathematical form underlying the relationship between design parameters and the design objective is impractical and costly to be obtained. To solve the ‘black-box’ problem, Bayesian optimization has been proven as an accurate and efficient method. However, the application of such a method in the design of compressors is rarely discussed, particularly no work has been reported in terms of the positive displacement type compressor. Therefore, this paper aims to introduce the Bayesian optimization to the design of positive displacement compressors through the optimization process of the novel limaçon compressor. In this paper, a two-stage optimization process is presented, in which the first stage optimizes the geometric parameters as per design requirements and the second stage focuses on revealing an optimum setting of port geometries that improves machine performance. A numerical illustration is offered to prove the validity of the presented approach. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Multi-level supervisory emergency control for operation of remote area microgrid clusters
- Batool, Munira, Shahnia, Farhad, Islam, Syed
- Authors: Batool, Munira , Shahnia, Farhad , Islam, Syed
- Date: 2019
- Type: Text , Journal article
- Relation: Journal of Modern Power Systems and Clean Energy Vol. 7, no. 5 (Sep 2019), p. 1210-1228
- Full Text:
- Reviewed:
- Description: Remote and regional areas are usually supplied by isolated and self-sufficient electricity systems, which are called as microgrids (MGs). To reduce the overall cost of electricity production, MGs rely on non-dispatchable renewable sources. Emergencies such as overloading or excessive generation by renewable sources can result in a substantial voltage or frequency deviation in MGs. This paper presents a supervisory controller for such emergencies. The key idea is to remedy the emergencies by optimal internal or external support. A multi-level controller with soft, intermedial and hard actions is proposed. The soft actions include the adjustment of the droop parameters of the sources and the controlling of the charge/discharge of energy storages. The intermedial action is exchanging power with neighboring MGs, which is highly probable in large remote areas. As the last remedying resort, curtailing loads or renewable sources are assumed as hard actions. The proposed controller employs an optimization technique consisting of certain objectives such as reducing power loss in the tie-lines amongst MGs and the dependency of an MG to other MGs, as well as enhancing the contribution of renewable sources in electricity generation. Minimization of the fuel consumption and emissions of conventional generators, along with frequency and voltage deviation, is the other desired objectives. The performance of the proposal is evaluated by several numerical analyses in MATLAB (R).
- Authors: Batool, Munira , Shahnia, Farhad , Islam, Syed
- Date: 2019
- Type: Text , Journal article
- Relation: Journal of Modern Power Systems and Clean Energy Vol. 7, no. 5 (Sep 2019), p. 1210-1228
- Full Text:
- Reviewed:
- Description: Remote and regional areas are usually supplied by isolated and self-sufficient electricity systems, which are called as microgrids (MGs). To reduce the overall cost of electricity production, MGs rely on non-dispatchable renewable sources. Emergencies such as overloading or excessive generation by renewable sources can result in a substantial voltage or frequency deviation in MGs. This paper presents a supervisory controller for such emergencies. The key idea is to remedy the emergencies by optimal internal or external support. A multi-level controller with soft, intermedial and hard actions is proposed. The soft actions include the adjustment of the droop parameters of the sources and the controlling of the charge/discharge of energy storages. The intermedial action is exchanging power with neighboring MGs, which is highly probable in large remote areas. As the last remedying resort, curtailing loads or renewable sources are assumed as hard actions. The proposed controller employs an optimization technique consisting of certain objectives such as reducing power loss in the tie-lines amongst MGs and the dependency of an MG to other MGs, as well as enhancing the contribution of renewable sources in electricity generation. Minimization of the fuel consumption and emissions of conventional generators, along with frequency and voltage deviation, is the other desired objectives. The performance of the proposal is evaluated by several numerical analyses in MATLAB (R).