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The discrete gradient evolutionary strategy method for global optimization

- Abbas, Hussein, Bagirov, Adil, Zhang, Jiapu

  • Authors: Abbas, Hussein , Bagirov, Adil , Zhang, Jiapu
  • Date: 2003
  • Type: Text , Conference paper
  • Relation: Paper presented at the Congress on Evolutionary Computation CEC 2003, Canberra : 8th December, 2003
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  • Description: Global optimization problems continue to be a challenge in computational mathematics. The field is progressing in two streams: deterministic and heuristic approaches. In this paper, we present a hybrid method that uses the discrete gradient method, which is a derivative free local search method, and evolutionary strategies. We show that the hybridization of the two methods is better than each of them in isolation.
  • Description: E1
  • Description: 2003000440

Batch clustering algorithm for big data sets

- Alguliyev, Rasim, Aliguliyev, Ramiz, Bagirov, Adil, Karimov, Rafael

  • Authors: Alguliyev, Rasim , Aliguliyev, Ramiz , Bagirov, Adil , Karimov, Rafael
  • Date: 2017
  • Type: Text , Conference proceedings
  • Relation: 10th IEEE International Conference on Application of Information and Communication Technologies, AICT 2016; Baku, Azerbaijan; 12th-14th October 2016 p. 1-4
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  • Description: Vast spread of computing technologies has led to abundance of large data sets. Today tech companies like, Google, Facebook, Twitter and Amazon handle big data sets and log terabytes, if not petabytes, of data per day. Thus, there is a need to find similarities and define groupings among the elements of these big data sets. One of the ways to find these similarities is data clustering. Currently, there exist several data clustering algorithms which differ by their application area and efficiency. Increase in computational power and algorithmic improvements have reduced the time for clustering of big data sets. But it usually happens that big data sets can't be processed whole due to hardware and computational restrictions. In this paper, the classic k-means clustering algorithm is compared to the proposed batch clustering (BC) algorithm for the required computation time and objective function. The BC algorithm is designed to cluster large data sets in batches but maintain the efficiency and quality. Several experiments confirm that batch clustering algorithm for big data sets is more efficient in using computational power, data storage and results in better clustering compared to k-means algorithm. The experiments are conducted with the data set of 2 (two) million two-dimensional data points. © 2016 IEEE.

Global optimization in the summarization of text documents

- Alyguliev, R. M., Bagirov, Adil

  • Authors: Alyguliev, R. M. , Bagirov, Adil
  • Date: 2005
  • Type: Text , Journal article
  • Relation: Automatic Control and Computer Sciences Vol. 39, no. 6 (2005), p. 42-47
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  • Description: In order to ensure minimal redundancy in the summary of a document and the greatest possible coverage of its content a method for the construction of summaries (summarization) based on the clustering of sentences is proposed in the article. Clustering of sentences reduces to a determination of cluster centroids the mathematical realization of which relies on a problem of global optimization. A determination of the number of clusters is one of the complex problems in the clustering procedure. Therefore, an algorithm of stepwise determination of the number of clusters is also proposed in the present study. © 2006 by Allerton Press, Inc.
  • Description: C1

Piecewise partially separable functions and a derivative-free algorithm for large scale nonsmooth optimization

- Bagirov, Adil, Ugon, Julien

  • Authors: Bagirov, Adil , Ugon, Julien
  • Date: 2006
  • Type: Text , Journal article
  • Relation: Journal of Global Optimization Vol. 35, no. 2 (Jun 2006), p. 163-195
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  • Description: This paper introduces the notion of piecewise partially separable functions and studies their properties. We also consider some of many applications of these functions. Finally, we consider the problem of minimizing of piecewise partially separable functions and develop an algorithm for its solution. This algorithm exploits the structure of such functions. We present the results of preliminary numerical experiments.
  • Description: 2003001532

Nonsmooth optimisation approach to data classification

- Bagirov, Adil, Soukhoroukova, Nadejda

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 © 2010 Watam Press.

Alexander Rubinov - An outstanding scholar

- Bagirov, Adil

Modified global k-means algorithm for clustering in gene expression data sets

- Bagirov, Adil, Mardaneh, Karim

  • Authors: Bagirov, Adil , Mardaneh, Karim
  • Date: 2006
  • Type: Text , Conference paper
  • Relation: Paper presented at Intelligent Systems for Bioinformatics 2006, proceedings of the AI 2006 Workshop on Intelligent Systems of Bioinformatics, Hobart, Tasmania : 4th December, 2006
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  • Description: Clustering in gene expression data sets is a challenging problem. Different algorithms for clustering of genes have been proposed. However due to the large number of genes only a few algorithms can be applied for the clustering of samples. k-means algorithm and its different variations are among those algorithms. But these algorithms in general can converge only to local minima and these local minima are significantly different from global solutions as the number of clusters increases. Over the last several years different approaches have been proposed to improve global search properties of k-means algorithm and its performance on large data sets. One of them is the global k-means algorithm. In this paper we develop a new version of the global k-means algorithm: the modified global k-means algorithm which is effective for solving clustering problems in gene expression data sets. We present preliminary computational results using gene expression data sets which demonstrate that the modified k-means algorithm improves and sometimes significantly results by k-means and global k-means algorithms.
  • Description: E1
  • Description: 2003001713

A new modified global k-means algorithm for clustering large data sets

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

  • Authors: Bagirov, Adil , Ugon, Julien , Webb, Dean
  • Date: 2009
  • Type: Text , Conference paper
  • Relation: Paper presented at XIIIth International Conference : Applied Stochastic Models and Data Analysis, ASMDA 2009, Vilnius, Lithuania : 30th June - 3rd July 2009 p. 1-5
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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 inefficient for solving clustering problems in large data sets. Recently, in order to resolve difficulties with the choice of starting points, incremental approaches have been developed. The modified global k-means algorithm is based on such an approach. It iteratively adds one cluster center at a time. Numerical experiments show that this algorithm considerably improve the k-means algorithm. However, this algorithm is not suitable for clustering very large data sets. 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 spanning different parts of the data set. We exploit information gathered in previous iterations of the incremental algorithm to reduce its complexity.
  • Description: 2003007558

Using global optimization to improve classification for medical diagnosis and prognosis

- Bagirov, Adil, Rubinov, Alex, Yearwood, John

  • Authors: Bagirov, Adil , Rubinov, Alex , Yearwood, John
  • Date: 2001
  • Type: Text , Journal article
  • Relation: Topics in health information management Vol. 22, no. 1 (2001), p. 65-74
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  • Description: Global optimization-based techniques are studied in order to increase the accuracy of medical diagnosis and prognosis with data from various databases. First, we discuss feature selection, the problem of determining the most informative features for classification in the databases under consideration. Then, we apply a technique based on convex and global optimization for classification in these databases. The third application of this technique is a method that calculates centers of clusters to predict when breast cancer is likely to recur in patients for which cancer has been removed. The technique achieves high accuracy with these databases. Better classifiers will lead to improved assistance in making medical diagnostic and prognostic decisions.
  • Description: 2003003662

Cutting angle method and a local search

- Bagirov, Adil, Rubinov, Alex

  • Authors: Bagirov, Adil , Rubinov, Alex
  • Date: 2003
  • Type: Text , Journal article
  • Relation: Journal of Global Optimization Vol. 27, no. 2-3 (Nov 2003), p. 193-213
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  • Description: The paper deals with combinations of the cutting angle method in global optimization and a local search. We propose to use special transformed objective functions for each intermediate use of the cutting angle method. We report results of numerical experiments which demonstrate that the proposed approach is very beneficial in the search for a global minimum.
  • Description: C1
  • Description: 2003000438

DC programming algorithm for clusterwise linear L1 regression

- Bagirov, Adil, Taheri, Sona

  • Authors: Bagirov, Adil , Taheri, Sona
  • Date: 2017
  • Type: Text , Journal article
  • Relation: Journal of the Operations Research Society of China Vol. 5, no. 2 (2017), p. 233-256
  • Relation: http://purl.org/au-research/grants/arc/DP140103213
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  • Description: The aim of this paper is to develop an algorithm for solving the clusterwise linear least absolute deviations regression problem. This problem is formulated as a nonsmooth nonconvex optimization problem, and the objective function is represented as a difference of convex functions. Optimality conditions are derived by using this representation. An algorithm is designed based on the difference of convex representation and an incremental approach. The proposed algorithm is tested using small to large artificial and real-world data sets. © 2017, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.

Optimization of feed forward MLPs using the discrete gradient method

- Bagirov, Adil, Yearwood, John, Ghosh, Ranadhir

Comparative analysis of the cutting angle and simulated annealing methods in global optimization

- Bagirov, Adil, Zhang, Jiapu

  • Authors: Bagirov, Adil , Zhang, Jiapu
  • Date: 2003
  • Type: Text , Journal article
  • Relation: Optimization Vol. 52, no. 4-5 (2003), p. 363-378
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  • Description: This article presents a comparative analysis of two methods of global optimization: the simulated annealing method and a method based on a combination of the cutting angle method and a local search. This analysis is carried out using results of numerical experiments. These results demonstrate that the combined method is more effective than the simulated annealing method.
  • Description: C1
  • Description: 2003000436

Optimisation of operations of a water distribution system for reduced power usage

- Bagirov, Adil, Ugon, Julien, Barton, Andrew, Briggs, Steven

  • Authors: Bagirov, Adil , Ugon, Julien , Barton, Andrew , Briggs, Steven
  • Date: 2008
  • Type: Text , Conference paper
  • Relation: Paper presented at 9th National Conference on Hydraulics in Water Engineering: Hydraulics 2008, Darwin, Northern Territory : 22nd-26th September 2008
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  • Description: There are many improvements to operation that can be made to a water distribution system once it has been constructed and placed in ground. Pipes and associated storages and pumps are typically designed to meet average peak daily demands, offer some capacity for growth, and also allow for some deterioration of performance over time. However, the 'as constructed' performance of the pipeline is invariably different to what was designed on paper, and this is particularly so for anything other than design flows, such as during times of water restrictions when there are significantly reduced flows. Because of this, there remain significant benefits to owners and operators for the adaptive and global optimisation of such systems. The present paper uses the Ouyen subsystem of the Northern Mallee Pipeline, in Victoria, as a case study for the development of an optimisation model. This has been done with the intent of using this model to reduce costs and provide better service to customers on this system. The Ouyen subsystem consists of 1600 km of trunk and distribution pipeline servicing an area of 456,000 Ha. The system includes 2 fixed speed pumps diverting water from the Murray River at Liparoo into two 150 ML balancing storages at Ouyen, 4 variable speed pumps feeding water from the balancing storages into the pipeline system, 2 variable speed pressure booster pumps and 5 town balancing storages. When considering all these components of the system, power consumption becomes an important part of the overall operation. The present paper considers a global optimisation model to minimise power consumption while maintaining reasonable performance of the system. The main components of the model are described including the network structure and the costs functions associated with the system. The final model presents the cost functions associated with the pump scheduling, including the penalties descriptions associated with maintaining appropriate storages levels and pressure bounds within the water distribution network.
  • Description: 2003006758

Penalty functions with a small penalty parameter : Numerical experiments

- Bagirov, Adil, Rubinov, Alex

Application of derivative free methods for production optimization

- Bagirov, Adil, Mason, T. L., Ghosh, Moumita

  • Authors: Bagirov, Adil , Mason, T. L. , Ghosh, Moumita
  • Date: 2006
  • Type: Text , Journal article
  • Relation: Applied and Computational Mathematics Vol. 5, no. 1 (2006), p. 94-105
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  • Description: Continuous gas lift is a high value optimization proposition, where high-pressure gas is injected at various depths, into oil production well to lightened the fluid column and so improve production and recovery. Gas lift optimization models as a surrogate for optimization planning, are usually nonconvex and even nonsmooth. Moreover, in many situations the objective and/or constraint functions in these problems are not known analytically. Most of traditional methods of optimization cannot be applied to solve such problems. Derivative free methods seem to be better choice for solving such problems. In this paper, we compare two different derivative free methods, our variant of the discrete gradient method and the generalized descent method for solving nonlinear gas lift optimization problems. We consider two different gas lift optimization problems. The objective functions in these problems are separable, nonsmooth and nonconvex. Although both algorithms produce satisfactory results, however the discrete gradient method better deals with noisy data and produces better results.
  • Description: C1
  • Description: 2003001714

The cutting angle method and its applications

- Bagirov, Adil

  • Authors: Bagirov, Adil
  • Date: 2001
  • Type: Text , Thesis , PhD
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  • Description: "The main objective of this thesis is to develop and study new techniques for solving global optimization problems and to apply them to solving data classification problems."

Introduction to Nonsmooth Optimization : Theory, practice and software

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

  • Authors: Bagirov, Adil , Karmitsa, Napsu , Makela, Marko
  • Date: 2014
  • Type: Text , Book
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  • Description: This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily differentiable optimization). Soving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining, ecomonics, and computational chemistry and physics. The book covers both the theory and the numerical methods used in NSO, and provides an overview of different problems arising in the field. It is organized into three parts: 1. convex and nonconvex analysis and the theory of NSO; 2. test problems and practical applications; 3. a guide to NSO software. The book is ideal for anyone teaching or attending NSO courses. As an accessible introduction to the field, it is also well suited as an independent learning guide for practitioners already familiar with the basics of optimization.

Modified global k-means algorithm for minimum sum-of-squares clustering problems

- Bagirov, Adil

  • Authors: Bagirov, Adil
  • Date: 2008
  • Type: Text , Journal article
  • Relation: Pattern Recognition Vol. 41, no. 10 (2008), p. 3192-3199
  • Relation: http://purl.org/au-research/grants/arc/DP0666061
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  • Description: k-Means algorithm and its variations are known to be fast clustering algorithms. However, they are sensitive to the choice of starting points and inefficient for solving clustering problems in large data sets. Recently, a new version of the k-means algorithm, the global k-means algorithm has been developed. It is an incremental algorithm that dynamically adds one cluster center at a time and uses each data point as a candidate for the k-th cluster center. Results of numerical experiments show that the global k-means algorithm considerably outperforms the k-means algorithms. In this paper, a new version of the global k-means algorithm is proposed. A starting point for the k-th cluster center in this algorithm is computed by minimizing an auxiliary cluster function. Results of numerical experiments on 14 data sets demonstrate the superiority of the new algorithm, however, it requires more computational time than the global k-means algorithm.
  • Description: k-Means algorithm and its variations are known to be fast clustering algorithms. However, they are sensitive to the choice of starting points and inefficient for solving clustering problems in large data sets. Recently, a new version of the k-means algorithm, the global k-means algorithm has been developed. It is an incremental algorithm that dynamically adds one cluster center at a time and uses each data point as a candidate for the k-th cluster center. Results of numerical experiments show that the global k-means algorithm considerably outperforms the k-means algorithms. In this paper, a new version of the global k-means algorithm is proposed. A starting point for the k-th cluster center in this algorithm is computed by minimizing an auxiliary cluster function. Results of numerical experiments on 14 data sets demonstrate the superiority of the new algorithm, however, it requires more computational time than the global k-means algorithm. © 2008 Elsevier Ltd. All rights reserved.
  • Description: 2003001713