List of Titles

Hyperbolic smoothing function method for minimax problems

- Bagirov, Adil, Al Nuaimat, Alia, Sultanova, Nargiz

Authors: Bagirov, Adil , Al Nuaimat, Alia , Sultanova, Nargiz
Date: 2013
Type: Text , Journal article
Relation: Optimization Vol. 62, no. 6 (2013), p. 759-782
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Description: In this article, an approach for solving finite minimax problems is proposed. This approach is based on the use of hyperbolic smoothing functions. In order to apply the hyperbolic smoothing we reformulate the objective function in the minimax problem and study the relationship between the original minimax and reformulated problems. We also study main properties of the hyperbolic smoothing function. Based on these results an algorithm for solving the finite minimax problem is proposed and this algorithm is implemented in general algebraic modelling system. We present preliminary results of numerical experiments with well-known nonsmooth optimization test problems. We also compare the proposed algorithm with the algorithm that uses the exponential smoothing function as well as with the algorithm based on nonlinear programming reformulation of the finite minimax problem. © 2013 Copyright Taylor and Francis Group, LLC.
Description: 2003011099

Nonsmooth nonconvex optimization approach to clusterwise linear regression problems

- Bagirov, Adil, Ugon, Julien, Mirzayeva, Hijran

Authors: Bagirov, Adil , Ugon, Julien , Mirzayeva, Hijran
Date: 2013
Type: Text , Journal article
Relation: European Journal of Operational Research Vol. 229, no. 1 (2013), p. 132-142
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Description: Clusterwise regression consists of finding a number of regression functions each approximating a subset of the data. In this paper, a new approach for solving the clusterwise linear regression problems is proposed based on a nonsmooth nonconvex formulation. We present an algorithm for minimizing this nonsmooth nonconvex function. This algorithm incrementally divides the whole data set into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate a good starting point for solving global optimization problems at each iteration of the incremental algorithm. Such an approach allows one to find global or near global solution to the problem when the data sets are sufficiently dense. The algorithm is compared with the multistart Späth algorithm on several publicly available data sets for regression analysis. © 2013 Elsevier B.V. All rights reserved.
Description: 2003011018

Subgradient and bundle methods for nonsmooth optimization

- Makela, Marko, Karmitsa, Napsu, Bagirov, Adil

Authors: Makela, Marko , Karmitsa, Napsu , Bagirov, Adil
Date: 2013
Type: Text , Book chapter
Relation: Numerical methods for differential equations, optimization, and technological problems p.
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Description: The nonsmooth optimization methods can mainly be divided into two groups: subgradient and bundle methods. Usually, when developing new algorithms and testing them, the comparison is made between similar kinds of methods. The goal of this work is to test and compare different bundle and subgradient methods as well as some hybrids of these two and/or some others. The test set included a large amount of different unconstrained nonsmooth minimization problems, e.g., convex and nonconvex problems, piecewise linear and quadratic problems, and problems with different sizes. Rather than foreground some method over the others, our aim is to get some insight on which method is suitable for certain types of problems.

A novel approach to optimal pump scheduling in water distribution systems

- Bagirov, Adil, Barton, Andrew, Mala-Jetmarova, Helena, Al Nuaimat, Alia, Ahmed, S. T., Sultanova, Nargiz, Yearwood, John

Authors: Bagirov, Adil , Barton, Andrew , Mala-Jetmarova, Helena , Al Nuaimat, Alia , Ahmed, S. T. , Sultanova, Nargiz , Yearwood, John
Date: 2012
Type: Text , Conference paper
Relation: 14th Water Distribution Systems Analysis Conference 2012, WDSA 2012 Vol. 1; Adelaide, Australia; 24th-27th September; p. 618-631
Relation: http://purl.org/au-research/grants/arc/LP0990908
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Description: The operation of a water distribution system is a complex task which involves scheduling of pumps, regulating water levels of storages, and providing satisfactory water quality to customers at required flow and pressure. Pump scheduling is one of the most important tasks of the operation of a water distribution system as it represents the major part of its operating costs. In this paper, a novel approach for modeling of pump scheduling to minimize energy consumption by pumps is introduced which uses pump's start/end run times as continuous variables. This is different from other approaches where binary integer variables for each hour are typically used which is considered very impractical from an operational perspective. The problem is formulated as a nonlinear programming problem and a new algorithm is developed for its solution. This algorithm is based on the combination of the grid search with the Hooke-Jeeves pattern search method. The performance of the algorithm is evaluated using literature test problems applying the hydraulic simulation model EPANet.
Description: E1

Application of optimisation-based data mining techniques to medical data sets: A comparative analysis

- Dzalilov, Zari, Bagirov, Adil, Mammadov, Musa

Authors: Dzalilov, Zari , Bagirov, Adil , Mammadov, Musa
Date: 2012
Type: Text , Conference paper
Relation: IMMM 2102: The Second International Conference on Advances in Information Mining and Management p. 41-46
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Description: Abstract - Computational methods have become an important tool in the analysis of medical data sets. In this paper, we apply three optimisation-based data mining methods to the following data sets: (i) a cystic fibrosis data set and (ii) a tobacco control data set. Three algorithms used in the analysis of these data sets include: the modified linear least square fit, an optimization based heuristic algorithm for feature selection and an optimization based clustering algorithm. All these methods explore the relationship between features and classes, with the aim of determining contribution of specific features to the class outcome. However, the three algorithms are based on completely different approaches. We apply these methods to solve feature selection and classification problems. We also present comparative analysis of the algorithms using computational results. Results obtained confirm that these algorithms may be effectively applied to the analysis of other (bio)medical data sets

Comparing different nonsmooth minimization methods and software

- Karmitsa, Napsu, Bagirov, Adil, Makela, Marko

Authors: Karmitsa, Napsu , Bagirov, Adil , Makela, Marko
Date: 2012
Type: Text , Journal article
Relation: Optimization Methods and Software Vol. 27, no. 1 (2012), p. 131-153
Relation: http://purl.org/au-research/grants/arc/DP0666061
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Description: Most nonsmooth optimization (NSO) methods can be divided into two main groups: subgradient methods and bundle methods. In this paper, we test and compare different methods from both groups as well as some methods which may be considered as hybrids of these two and/or some others. All the solvers tested are so-called general black box methods which, at least in theory, can be applied to solve almost all NSO problems. The test set includes a large number of unconstrained nonsmooth convex and nonconvex problems of different size. In particular, it includes piecewise linear and quadratic problems. The aim of this work is not to foreground some methods over the others but to get some insight on which method to select for certain types of problems. © 2012 Taylor and Francis Group, LLC.

Comparison of metaheuristic algorithms for pump operation optimization

- Bagirov, Adil, Ahmed, S. T., Barton, Andrew, Mala-Jetmarova, Helena, Al Nuaimat, Alia, Sultanova, Nargiz

Authors: Bagirov, Adil , Ahmed, S. T. , Barton, Andrew , Mala-Jetmarova, Helena , Al Nuaimat, Alia , Sultanova, Nargiz
Date: 2012
Type: Text , Conference paper
Relation: 14th Water Distribution Systems Analysis Conference 2012, WDSA 2012 Vol. 2; Adelaide, Australia; 24th-27th September 2012; p. 886-896
Relation: http://purl.org/au-research/grants/arc/LP0990908
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Description: Pumping cost constitutes the main part of the overall operating cost of water distribution systems. There are different optimization formulations of the pumping cost minimization problem including those with application of continuous and integer programming approaches. To date mainly various metaheuristics have been applied to solve this problem. However, the comprehensive comparison of those metaheuristics has not been done. Such a comparison is important to identify strengths and weaknesses of different algorithms which reflects on their performance. In this paper, we present a methodology for comparative analysis of widely used metaheuristics for solving the pumping cost minimization problem. This methodology includes the following comparison criteria: (a) the "optimal solution" obtained; (b) the efficiency; and (c) robustness. Algorithms applied are: particle swarm optimization, artificial bee colony and firefly algorithms. These algorithms were applied to one test problem available in the literature. The results obtained demonstrate that the artificial bee colony is the most robust and the firefly is the most efficient and accurate algorithm for this test problem. Funding :ARC

Limited memory discrete gradient bundle method for nonsmooth derivative-free optimization

- Karmitsa, Napsu, Bagirov, Adil

Authors: Karmitsa, Napsu , Bagirov, Adil
Date: 2012
Type: Text , Journal article
Relation: Optimization Vol. 61, no. 12 (2012), p. 1491-1509
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Description: Typically, practical nonsmooth optimization problems involve functions with hundreds of variables. Moreover, there are many practical problems where the computation of even one subgradient is either a difficult or an impossible task. In such cases derivative-free methods are the better (or only) choice since they do not use explicit computation of subgradients. However, these methods require a large number of function evaluations even for moderately large problems. In this article, we propose an efficient derivative-free limited memory discrete gradient bundle method for nonsmooth, possibly nonconvex optimization. The convergence of the proposed method is proved for locally Lipschitz continuous functions and the numerical experiments to be presented confirm the usability of the method especially for medium size and large-scale problems. © 2012 Copyright Taylor and Francis Group, LLC.
Description: 2003010398

Machine learning algorithms for analysis of DNA data sets

- Yearwood, John, Bagirov, Adil, Kelarev, Andrei

Authors: Yearwood, John , Bagirov, Adil , Kelarev, Andrei
Date: 2012
Type: Text , Book chapter
Relation: Machine Learning Algorithms for Problem Solving in Computational Applications: Intelligent Techniques p. 47-58
Relation: http://purl.org/au-research/grants/arc/LP0990908
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Description: The applications of machine learning algorithms to the analysis of data sets of DNA sequences are very important. The present chapter is devoted to the experimental investigation of applications of several machine learning algorithms for the analysis of a JLA data set consisting of DNA sequences derived from non-coding segments in the junction of the large single copy region and inverted repeat A of the chloroplast genome in Eucalyptus collected by Australian biologists. Data sets of this sort represent a new situation, where sophisticated alignment scores have to be used as a measure of similarity. The alignment scores do not satisfy properties of the Minkowski metric, and new machine learning approaches have to be investigated. The authors' experiments show that machine learning algorithms based on local alignment scores achieve very good agreement with known biological classes for this data set. A new machine learning algorithm based on graph partitioning performed best for clustering of the JLA data set. Our novel k-committees algorithm produced most accurate results for classification. Two new examples of synthetic data sets demonstrate that the authors' k-committees algorithm can outperform both the Nearest Neighbour and k-medoids algorithms simultaneously.

Minimization of pumping costs in water distribution systems using explicit and implicit pump scheduling

- Barton, Andrew, Mala-Jetmarova, Helena, Nuamat, Alia Mari Al, Bagirov, Adil, Sultanova, Nargiz, Ahmed, Shams

Authors: Barton, Andrew , Mala-Jetmarova, Helena , Nuamat, Alia Mari Al , Bagirov, Adil , Sultanova, Nargiz , Ahmed, Shams
Date: 2012
Type: Text , Conference paper
Relation: 34th Hydrology and Water Resources Symposium, HWRS 2012; Sydney, Australia; 19th-22nd November 2012; p. 1298-1305
Relation: http://purl.org/au-research/grants/arc/LP0990908
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Description: The operation of a water distribution system is a complex task which involves scheduling of pumps, regulating water levels of storages, and providing satisfactory water quality to customers at required flow and pressure. Pump scheduling is one of the most important tasks of the operation of a water distribution system as it represents the major part of its operating costs. In this paper, a novel approach for modeling of pump scheduling to minimize energy consumption by pumps is introduced which uses pump's start/end run times. We separate two types of pumps, one is operated based on the water level in a storage and another one is operated based on downstream pressure. For the first type of pumps both the explicit and implicit pump scheduling can be used, whereas the second type pumps can be optimized only using implicit pump scheduling. The problem is formulated as an optimization problem and an algorithm is developed for its solution. The performance of the algorithm is evaluated using a literature test problem applying the hydraulic simulation model EPANet.

Subgradient Method for Nonconvex Nonsmooth Optimization

- Bagirov, Adil, Jin, L., Karmitsa, Napsu, Al Nuaimat, A., Sultanova, Nargiz

Authors: Bagirov, Adil , Jin, L. , Karmitsa, Napsu , Al Nuaimat, A. , Sultanova, Nargiz
Date: 2012
Type: Text , Journal article
Relation: Journal of Optimization Theory and Applications Vol.157, no.2 (2012), p.416–435
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Description: In this paper, we introduce a new method for solving nonconvex nonsmooth optimization problems. It uses quasisecants, which are subgradients computed in some neighborhood of a point. The proposed method contains simple procedures for finding descent directions and for solving line search subproblems. The convergence of the method is studied and preliminary results of numerical experiments are presented. The comparison of the proposed method with the subgradient and the proximal bundle methods is demonstrated using results of numerical experiments. © 2012 Springer Science+Business Media, LLC.

A novel hybrid neural learning algorithm using simulated annealing and quasisecant method

- Yearwood, John, Bagirov, Adil, Seifollahi, Sattar

Authors: Yearwood, John , Bagirov, Adil , Seifollahi, Sattar
Date: 2011
Type: Text , Conference proceedings
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Description: In this paper, we propose a hybrid learning algorithm for the single hidden layer feedforward neural networks (SLFNs) for data classification. The proposed hybrid algorithm is a two-phase learning algorithm and is based on the quasisecant and the simulated annealing methods. First, the weights between the hidden layer and the output layer nodes (output layer weights) are adjusted by the quasisecant algorithm. Then the simulated annealing is applied for global attribute weighting. The weights between the input layer and the hidden layer nodes are fixed in advance and are not included in the learning process. The proposed two-phase learning of the network is a novel idea and is different from that of the existing ones. The numerical results on some benchmark data sets are also reported and these results are promising. © 2011, Australian Computer Society, Inc.
Description: 2003009507

A novel piecewise linear classifier based on polyhedral conic and max-min separabilities

- Bagirov, Adil, Ugon, Julien, Webb, Dean, Ozturk, Gurkan, Kasimbeyli, Refail

Authors: Bagirov, Adil , Ugon, Julien , Webb, Dean , Ozturk, Gurkan , Kasimbeyli, Refail
Date: 2011
Type: Text , Journal article
Relation: TOP Vol.21, no.1 (2011), p. 1-22
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Description: In this paper, an algorithm for finding piecewise linear boundaries between pattern classes is developed. This algorithm consists of two main stages. In the first stage, a polyhedral conic set is used to identify data points which lie inside their classes, and in the second stage we exclude those points to compute a piecewise linear boundary using the remaining data points. Piecewise linear boundaries are computed incrementally starting with one hyperplane. Such an approach allows one to significantly reduce the computational effort in many large data sets. Results of numerical experiments are reported. These results demonstrate that the new algorithm consistently produces a good test set accuracy on most data sets comparing with a number of other mainstream classifiers. Â© 2011 Sociedad de EstadÃstica e InvestigaciÃ³n Operativa.

An efficient algorithm for the incremental construction of a piecewise linear classifier

- Bagirov, Adil, Ugon, Julien, Webb, Dean

Authors: Bagirov, Adil , Ugon, Julien , Webb, Dean
Date: 2011
Type: Text , Journal article
Relation: Information Systems Vol. 36, no. 4 (2011), p. 782-790
Relation: http://purl.org/au-research/grants/arc/DP0666061
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Description: In this paper the problem of finding piecewise linear boundaries between sets is considered and is applied for solving supervised data classification problems. An algorithm for the computation of piecewise linear boundaries, consisting of two main steps, is proposed. In the first step sets are approximated by hyperboxes to find so-called "indeterminate" regions between sets. In the second step sets are separated inside these "indeterminate" regions by piecewise linear functions. These functions are computed incrementally starting with a linear function. Results of numerical experiments are reported. These results demonstrate that the new algorithm requires a reasonable training time and it produces consistently good test set accuracy on most data sets comparing with mainstream classifiers. Â© 2010 Elsevier B.V. All rights reserved.

Classification through incremental max-min separability

- Bagirov, Adil, Ugon, Julien, Webb, Dean, Karasozen, Bulent

Authors: Bagirov, Adil , Ugon, Julien , Webb, Dean , Karasozen, Bulent
Date: 2011
Type: Text , Journal article
Relation: Pattern Analysis and Applications Vol. 14, no. 2 (2011), p. 165-174
Relation: http://purl.org/au-research/grants/arc/DP0666061
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Description: Piecewise linear functions can be used to approximate non-linear decision boundaries between pattern classes. Piecewise linear boundaries are known to provide efficient real-time classifiers. However, they require a long training time. Finding piecewise linear boundaries between sets is a difficult optimization problem. Most approaches use heuristics to avoid solving this problem, which may lead to suboptimal piecewise linear boundaries. In this paper, we propose an algorithm for globally training hyperplanes using an incremental approach. Such an approach allows one to find a near global minimizer of the classification error function and to compute as few hyperplanes as needed for separating sets. We apply this algorithm for solving supervised data classification problems and report the results of numerical experiments on real-world data sets. These results demonstrate that the new algorithm requires a reasonable training time and its test set accuracy is consistently good on most data sets compared with mainstream classifiers. © 2010 Springer-Verlag London Limited.

Codifferential method for minimizing nonsmooth DC functions

- Bagirov, Adil, Ugon, Julien

Authors: Bagirov, Adil , Ugon, Julien
Date: 2011
Type: Text , Journal article
Relation: Journal of Global Optimization Vol. 50, no. 1 (2011), p. 3-22
Relation: http://purl.org/au-research/grants/arc/DP0666061
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Description: In this paper, a new algorithm to locally minimize nonsmooth functions represented as a difference of two convex functions (DC functions) is proposed. The algorithm is based on the concept of codifferential. It is assumed that DC decomposition of the objective function is known a priori. We develop an algorithm to compute descent directions using a few elements from codifferential. The convergence of the minimization algorithm is studied and its comparison with different versions of the bundle methods using results of numerical experiments is given. © 2010 Springer Science+Business Media, LLC.

Fast modified global k-means algorithm for incremental cluster construction

- Bagirov, Adil, Ugon, Julien, Webb, Dean

Authors: Bagirov, Adil , Ugon, Julien , Webb, Dean
Date: 2011
Type: Text , Journal article
Relation: Pattern Recognition Vol. 44, no. 4 (2011), p. 866-876
Relation: http://purl.org/au-research/grants/arc/DP0666061
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Description: The k-means algorithm and its variations are known to be fast clustering algorithms. However, they are sensitive to the choice of starting points and are inefficient for solving clustering problems in large datasets. Recently, incremental approaches have been developed to resolve difficulties with the choice of starting points. The global k-means and the modified global k-means algorithms are based on such an approach. They iteratively add one cluster center at a time. Numerical experiments show that these algorithms considerably improve the k-means algorithm. However, they require storing the whole affinity matrix or computing this matrix at each iteration. This makes both algorithms time consuming and memory demanding for clustering even moderately large datasets. In this paper, a new version of the modified global k-means algorithm is proposed. We introduce an auxiliary cluster function to generate a set of starting points lying in different parts of the dataset. We exploit information gathered in previous iterations of the incremental algorithm to eliminate the need of computing or storing the whole affinity matrix and thereby to reduce computational effort and memory usage. Results of numerical experiments on six standard datasets demonstrate that the new algorithm is more efficient than the global and the modified global k-means algorithms. Â© 2010 Elsevier Ltd. All rights reserved.

A generalized subgradient method with piecewise linear subproblem

- Bagirov, Adil, Ganjehlou, Asef Nazari, Tor, Hakan, Ugon, Julien

Authors: Bagirov, Adil , Ganjehlou, Asef Nazari , Tor, Hakan , 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. 621-638
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Description: In this paper, a new version of the quasisecant method for nonsmooth nonconvex optimization is developed. Quasisecants are overestimates to the objective function in some neighborhood of a given point. Subgradients are used to obtain quasisecants. We describe classes of nonsmooth functions where quasisecants can be computed explicitly. We show that a descent direction with suffcient decrease must satisfy a set of linear inequalities. In the proposed algorithm this set of linear inequalities is solved by applying the subgradient algorithm to minimize a piecewise linear function. We compare results of numerical experiments between the proposed algorithm and subgradient method. Copyright Â© 2010 Watam Press.

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