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21Yearwood, John
20Ugon, Julien
14Barton, Andrew
14Rubinov, Alex
12Mala-Jetmarova, Helena
10Ghosh, Ranadhir
10Taheri, Sona
9Ghosh, Moumita
9Karmitsa, Napsu
7Mohebi, Ehsan
7Sultanova, Nargiz
6Webb, Dean
5Al Nuaimat, Alia
5Beliakov, Gleb
5Makela, Marko
5Ozturk, Gurkan
4Karasozen, Bulent
4Kasimbeyli, Refail
4Mammadov, Musa

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39Nonsmooth optimization
330103 Numerical and Computational Mathematics
280102 Applied Mathematics
190802 Computation Theory and Mathematics
17Optimisation
14Nonconvex optimization
120801 Artificial Intelligence and Image Processing
12Classification
12Cluster analysis
11Algorithms
11Subdifferential
10Data mining
8Global optimization
8Optimization
8Water distribution systems
7Discrete gradient
7Discrete gradient method
60806 Information Systems
60906 Electrical and Electronic Engineering
6Derivative-free optimization

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Piecewise linear classifiers based on nonsmooth optimization approaches

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

**Authors:**Bagirov, Adil , Kasimbeyli, Refail , Ozturk, Gurkan , Ugon, Julien**Date:**2014**Type:**Text , Book chapter**Relation:**Optimization in Science and Engineering p. 1-32**Full Text:**false**Reviewed:****Description:**Nonsmooth optimization provides efficient algorithms for solving many machine learning problems. In particular, nonsmooth optimization approaches to supervised data classification problems lead to the design of very efficient algorithms for their solution. In this chapter, we demonstrate how nonsmooth optimization algorithms can be applied to design efficient piecewise linear classifiers for supervised data classification problems. Such classifiers are developed using a max–min and a polyhedral conic separabilities as well as an incremental approach. We report results of numerical experiments and compare the piecewise linear classifiers with a number of other mainstream classifiers.

- Bagirov, Adil, Miettinen, Kaisa, Weber, Gerhard-Wilhelm

**Authors:**Bagirov, Adil , Miettinen, Kaisa , Weber, Gerhard-Wilhelm**Date:**2014**Type:**Text , Journal article**Relation:**Journal of Global Optimization Vol. 60, no. 1 (June 2014), p. 1-3**Full Text:**false**Reviewed:****Description:**C1

A new modification of Kohonen neural network for VQ and clustering problems

- Mohebi, Ehsan, Bagirov, Adil

**Authors:**Mohebi, Ehsan , Bagirov, Adil**Date:**2013**Type:**Text , Conference paper**Relation:**Proceedings of the 11-th Australasian Data Mining Conference (AusDM'13) Vol. 146, p. 81-88**Full Text:**false**Reviewed:****Description:**Vector Quantization (VQ) and Clustering are significantly important in the field of data mining and pattern recognition. The Self Organizing Maps has been widely used for clustering and topology visualization. The topology of the SOM and its initial neurons play an important role in the convergence of the Kohonen neural network. In this paper, in order to improve the convergence of the SOM we introduce an algorithm based on the split and merging of clusters to initialize neurons. We also introduce a topology based on this initialization to optimize the vector quantization error. Such an approach allows one to find global or near global solution to the vector quantization and consequently clustering problem. The numerical results on 4 small to large real-world data sets are reported to demonstrate the performance of the proposed algorithm.

- 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:**2013**Type:**Text , Journal article**Relation:**Mathematical and Computer Modelling Vol. 57, no. 3-4 (2013), p. 873-886**Relation:**http://purl.org/au-research/grants/arc/LP0990908**Full Text:**false**Reviewed:****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 explicit pump scheduling to minimize energy consumption by pumps is introduced which uses the pump start/end run times as continuous variables, and binary integer variables to describe the pump status at the beginning of the scheduling period. 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 mixed integer 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. © 2012 Elsevier Ltd.**Description:**2003010583

Capped K-NN Editing in definition lacking environments

- Stranieri, Andrew, Yatsko, Andrew, Golden, Isaac, Mammadov, Musa, Bagirov, Adil

**Authors:**Stranieri, Andrew , Yatsko, Andrew , Golden, Isaac , Mammadov, Musa , Bagirov, Adil**Date:**2013**Type:**Text , Journal article**Relation:**Journal of Pattern Recognition Research Vol. 8, no. 1 (2013), p. 39-58**Full Text:**false**Reviewed:****Description:**While any input may be contributing, imprecise specification of class of data subdivided into classes identifies as rather common a source of noise. The misrepresentation may be characteristic of the data or be caused by forcing of a regression problem into the classification type. Consideration is given to examples of this nature, and an alternative is proposed. In the main part, the approach is based on a well-known technique of data treatment for noise using k-NN. The paper advances an editing technique designed around idea of variable number of authenticating instances. Test runs performed on publicly available and proprietary data demonstrate high retention ability of the new procedure without loss of classification accuracy. Noise reduction methods in a broader classification context are extensively surveyed.

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**Full Text:**false**Reviewed:****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**Full Text:**false**Reviewed:****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

- Mala-Jetmarova, Helena, Bagirov, Adil, Barton, Andrew

**Authors:**Mala-Jetmarova, Helena , Bagirov, Adil , Barton, Andrew**Date:**2013**Type:**Text , Conference paper**Relation:**Proceedings of the 35th IAHR World Congress**Full Text:**false**Reviewed:**

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.**Full Text:**false**Reviewed:****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**Full Text:**false**Reviewed:****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

- 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**Full Text:**false**Reviewed:****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**Full Text:**false**Reviewed:****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**Full Text:**false**Reviewed:****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

- Mala-Jetmarova, Helena, Bagirov, Adil, Barton, Andrew

**Authors:**Mala-Jetmarova, Helena , Bagirov, Adil , Barton, Andrew**Date:**2012**Type:**Text , Conference paper**Relation:**10th International conference on Hydroinformatics**Full Text:**false**Reviewed:**

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**Full Text:**false**Reviewed:****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**Full Text:**false**Reviewed:****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.

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

**Authors:**Barton, Andrew , Mala-Jetmarova, Helena , Nuamat, Alia Mari Al , Bagirov, Adil , Sultanova, Nargiz , Ahmed, Shams Tabrez**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**Full Text:**false**Reviewed:****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**Full Text:**false**Reviewed:****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**Full Text:**false**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**Full Text:**false**Reviewed:****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.

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