A hybrid neural learning algorithm combining evolutionary algorithm with discrete gradient method
- Authors: Ghosh, Ranadhir , Yearwood, John , Bagirov, Adil
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at the Second International Conference on Software Computing and Intelligent Systems, Yokahama, Japan : 21st October, 2004
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003000860
Improving risk grouping rules for prostate cancer patients with optimization
- Authors: Churilov, Leonid , Bagirov, Adil , Schwartz, Daniel , Smith, Kate , Dally, Michael
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at the 37th Annual Hawaii International Conference on System Sciences, Big Island, Hawaii : 5th January, 2004
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- Description: Data mining techniques provide a popular and powerful toolset to address both clinical and management issues in the area of health care. This paper describes the study of assigning prostate cancer patients into homogenous groups with the aim to support future clinical treatment decisions. The cluster analysis based model is suggested and an application of non-smooth non-convex optimization techniques to solve this model is discussed. It is demonstrated that using the optimization based approach to data mining of a prostate cancer patients database can lead to generation of a significant amount of new knowledge that can be effectively utilized to enhance clinical decision making.
- Description: E1
- Description: 2003000846
Optimization of feed forward MLPs using the discrete gradient method
- Authors: Bagirov, Adil , Yearwood, John , Ghosh, Ranadhir
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at CIMCA 2004: International Conference on Computational Intelligence for Modelling, Control & Automation, Gold Coast, Queensland : 12th July, 2004
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003000845
Solving Euclidian travelling salesman problem using discrete-gradient based clustering and kohonen neural network
- Authors: Ghosh, Moumita , Ugon, Julien , Ghosh, Ranadhir , Bagirov, Adil
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at ICOTA6: 6th International Conference on Optimization - Techniques and Applications, Ballarat, Victoria : 9th December, 2004
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003000864
An algorithm for clustering based on non-smooth optimization techniques
- Authors: Bagirov, Adil , Rubinov, Alex , Sukhorukova, Nadezda , Yearwood, John
- Date: 2003
- Type: Text , Journal article
- Relation: International Transactions in Operational Research Vol. 10, no. 6 (2003), p. 611-617
- Full Text: false
- Reviewed:
- Description: The problem of cluster analysis is formulated as a problem of non-smooth, non-convex optimization, and an algorithm for solving the cluster analysis problem based on non-smooth optimization techniques is developed. We discuss applications of this algorithm in large databases. Results of numerical experiments are presented to demonstrate the effectiveness of this algorithm.
- Description: C1
- Description: 2003000422
An optimization-based approach to patient grouping for acute healthcare in Australia
- Authors: Bagirov, Adil , Churilov, Leonid
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at Computational Science - ICCS 2003 Conference, Melbourne : 2nd June, 2003
- Full Text: false
- Reviewed:
- Description: The problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization, and an algorithm for solving the cluster analysis problem based on the nonsmooth optimization techniques is developed. The issues of applying this algorithm to large data sets are discussed and a feature selection procedure is demonstrated. The algorithm is then applied to a hospital data set to generate new knowledge about different patterns of patients resource consumption.
- Description: E1
- Description: 2003000434
Comparative analysis of the cutting angle and simulated annealing methods in global optimization
- 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
Continuous subdifferential approximations and their applications
- Authors: Bagirov, Adil
- Date: 2003
- Type: Text , Journal article
- Relation: Journal of Mathematical Sciences Vol. 115, no. 5 (2003), p. 2567-2609
- Full Text: false
- Reviewed:
- Description: In this paper, we study continuous approximations to the Clarke subdifferential and the Demyanov– Rubinov quasidifferential. Different methods have been proposed and discussed for the construction of the continuous approximations. Numerical methods for minimization of the locally Lipschitzian functions which are based on the continuous approximations are described and their convergence is studied. To test the proposed methods, numerical experiments have been carried out and discussed in the paper.
- Description: C1
- Description: 2003000423
Cutting angle method and a local search
- 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
- Full Text: false
- Reviewed:
- 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
Lagrange-type functions in constrained optimization
- Authors: Rubinov, Alex , Yang, Xiao , Bagirov, Adil , Gasimov, Rafail
- Date: 2003
- Type: Text , Journal article
- Relation: Journal of Mathematical Sciences Vol. 115, no. 4 (2003), p. 2437-2505
- Full Text: false
- Reviewed:
- Description: We examine various kinds of nonlinear Lagrange-type functions for constrained optimization problems. In particular, we study the weak duality, the zero duality gap property, and the existence of an exact parameter for these functions. The paper contains a detailed survey of results in these directions and comparison of different methods proposed by different authors. Some new results are also given.
- Description: C1
- Description: 2003000358
New algorithms for multi-class cancer diagnosis using tumor gene expression signatures
- Authors: Bagirov, Adil , Ferguson, Brent , Ivkovic, Sasha , Saunders, Gary , Yearwood, John
- Date: 2003
- Type: Text , Journal article
- Relation: Bioinformatics Vol. 19, no. 14 (2003), p. 1800-1807
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- Description: Motivation: The increasing use of DNA microarray-based tumor gene expression profiles for cancer diagnosis requires mathematical methods with high accuracy for solving clustering, feature selection and classification problems of gene expression data. Results: New algorithms are developed for solving clustering, feature selection and classification problems of gene expression data. The clustering algorithm is based on optimization techniques and allows the calculation of clusters step-by-step. This approach allows us to find as many clusters as a data set contains with respect to some tolerance. Feature selection is crucial for a gene expression database. Our feature selection algorithm is based on calculating overlaps of different genes. The database used, contains over 16 000 genes and this number is considerably reduced by feature selection. We propose a classification algorithm where each tissue sample is considered as the center of a cluster which is a ball. The results of numerical experiments confirm that the classification algorithm in combination with the feature selection algorithm perform slightly better than the published results for multi-class classifiers based on support vector machines for this data set.
- Description: C1
- Description: 2003000439
Optimization based clustering algorithms in multicast group hierarchies
- Authors: Jia, Long , Ouveysi, Iradj , Rubinov, Alex , Bagirov, Adil
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at the 2003 Australian Telecommunications Networks and Applications Conference, Melbourne : 8th - 10th December, 2003
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- Reviewed:
- Description: In this paper we propose the use of optimization based clustering algorithms to determine hierarchical multicast trees. This problem is formulated as an optimization problem with a non-smooth, non-convex objective function. Different algorithms are examined for solving this problem. Results of numerical experiments using some artificial and real-world databases are reported. We compare several optimization based clustering methods and their combinations with the k- means method. The results demonstrate the effectiveness of these algorithms.
- Description: E1
- Description: 2003000382
Parallelization of the discrete gradient method of non-smooth optimization and its applications
- Authors: Beliakov, Gleb , Tobon, Monsalve , Bagirov, Adil
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at Computational Science ICCS 2003 Conference, Melbourne : 2nd June, 2003
- Full Text: false
- Reviewed:
- Description: We investigate parallelization and performance of the discrete gradient method of nonsmooth optimization. This derivative free method is shown to be an effective optimization tool, able to skip many shallow local minima of nonconvex nondifferentiable objective functions. Although this is a sequential iterative method, we were able to parallelize critical steps of the algorithm, and this lead to a significant improvement in performance on multiprocessor computer clusters. We applied this method to a difficult polyatomic clusters problem in computational chemistry, and found this method to outperform other algorithms.
- Description: E1
- Description: 2003000435
Penalty functions with a small penalty parameter : Numerical experiments
- Authors: Bagirov, Adil , Rubinov, Alex
- Date: 2003
- Type: Text , Conference paper
- Relation: Paper presented at Industrial Optimization Conference 2003, Perth : 30th September, 2002
- Full Text: false
- Reviewed:
- Description: E1
- Description: 2003000432
The discrete gradient evolutionary strategy method for global optimization
- 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
- Full Text:
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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
Unsupervised and supervised data classification via nonsmooth and global optimisation
- Authors: Bagirov, Adil , Rubinov, Alex , Sukhorukova, Nadezda , Yearwood, John
- Date: 2003
- Type: Text , Journal article
- Relation: Top Vol. 11, no. 1 (2003), p. 1-92
- Full Text:
- Reviewed:
- Description: We examine various methods for data clustering and data classification that are based on the minimization of the so-called cluster function and its modications. These functions are nonsmooth and nonconvex. We use Discrete Gradient methods for their local minimization. We consider also a combination of this method with the cutting angle method for global minimization. We present and discuss results of numerical experiments.
- Description: C1
- Description: 2003000421
A global optimization approach to classification
- Authors: Bagirov, Adil , Rubinov, Alex , Yearwood, John
- Date: 2002
- Type: Text , Journal article
- Relation: Optimization and Engineering Vol. 9, no. 7 (2002), p. 129-155
- Full Text: false
- Reviewed:
- Description: In this paper is presented an hybrid algorithm for finding the absolute extreme point of a multimodal scalar function of many variables. The algorithm is suitable when the objective function is expensive to compute, the computation can be affected by noise and/or partial derivatives cannot be calculated. The method used is a genetic modification of a previous algorithm based on the Prices method. All information about behavior of objective function collected on previous iterates are used to chose new evaluation points. The genetic part of the algorithm is very effective to escape from local attractors of the algorithm and assures convergence in probability to the global optimum. The proposed algorithm has been tested on a large set of multimodal test problems outperforming both the modified Prices algorithm and classical genetic approach.
- Description: C1
- Description: 2003000061
A method for minimization of quasidifferentiable functions
- Authors: Bagirov, Adil
- Date: 2002
- Type: Text , Journal article
- Relation: Optimization Methods and Software Vol. 17, no. 1 (2002), p. 31-60
- Full Text: false
- Reviewed:
- Description: In this paper, we propose a new method for the unconstrained minimization of a function presented as a difference of two convex functions. This method is based on continuous approximations to the Demyanov-Rubinov quasidifferential. First, a terminating algorithm for the computation of a descent direction of the objective function is described. Then we present a minimization algorithm and study its convergence. An implementable version of this algorithm is discussed. Finally, we report the results of preliminary numerical experiments.
- Description: C1
- Description: 2003000064
A method of truncated codifferential with application to some problems of cluster analysis
- Authors: Demyanov, Vladimir , Bagirov, Adil , Rubinov, Alex
- Date: 2002
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 23, no. 1 (May 2002), p. 63-80
- Full Text: false
- Reviewed:
- Description: A method of truncated codifferential descent for minimizing continuously codifferentiable functions is suggested. The convergence of the method is studied. Results of numerical experiments are presented. Application of the suggested method for the solution of some problems of cluster analysis are discussed. In numerical experiments Wisconsin Diagnostic Breast Cancer database was used.
- Description: 2003000062
Penalty functions with a small penalty parameter
- Authors: Rubinov, Alex , Yang, Xiao , Bagirov, Adil
- Date: 2002
- Type: Text , Journal article
- Relation: Optimization Methods and Software Vol. 17, no. 5 (2002), p. 931-964
- Full Text: false
- Reviewed:
- Description: In this article, we study the nonlinear penalization of a constrained optimization problem and show that the least exact penalty parameter of an equivalent parametric optimization problem can be diminished. We apply the theory of increasing positively homogeneous (IPH) functions so as to derive a simple formula for computing the least exact penalty parameter for the classical penalty function through perturbation function. We establish that various equivalent parametric reformulations of constrained optimization problems lead to reduction of exact penalty parameters. To construct a Lipschitz penalty function with a small exact penalty parameter for a Lipschitz programming problem, we make a transformation to the objective function by virtue of an increasing concave function. We present results of numerical experiments, which demonstrate that the Lipschitz penalty function with a small penalty parameter is more suitable for solving some nonconvex constrained problems than the classical penalty function.
- Description: 2003000116