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Reseach Article

Multifacility Location Problem using Scaled Conjugate Gradient Algorithm under Triangular Area Constraints

by G.M. Nasira, T.S.S. Balaji
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 1 - Number 22
Year of Publication: 2010
Authors: G.M. Nasira, T.S.S. Balaji
10.5120/435-664

G.M. Nasira, T.S.S. Balaji . Multifacility Location Problem using Scaled Conjugate Gradient Algorithm under Triangular Area Constraints. International Journal of Computer Applications. 1, 22 ( February 2010), 99-103. DOI=10.5120/435-664

@article{ 10.5120/435-664,
author = { G.M. Nasira, T.S.S. Balaji },
title = { Multifacility Location Problem using Scaled Conjugate Gradient Algorithm under Triangular Area Constraints },
journal = { International Journal of Computer Applications },
issue_date = { February 2010 },
volume = { 1 },
number = { 22 },
month = { February },
year = { 2010 },
issn = { 0975-8887 },
pages = { 99-103 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume1/number22/435-664/ },
doi = { 10.5120/435-664 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T19:47:55.149712+05:30
%A G.M. Nasira
%A T.S.S. Balaji
%T Multifacility Location Problem using Scaled Conjugate Gradient Algorithm under Triangular Area Constraints
%J International Journal of Computer Applications
%@ 0975-8887
%V 1
%N 22
%P 99-103
%D 2010
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The problem of finding the multiple locations for new facilities with respect to the multiple existing facilities in a given environment is known as Multifacility Location Problem (MLP).Every location problem is normally bounded by some sort of area constraint. But the fact that much of the work carried out in the literature has almost neglected the area constraint which has motivated us to work on Multifacility Location Problem taking the area constraint into consideration. The mathematical model of the multifacility location problem with area constraint has been developed and the solution has been obtained using Kuhn-Tucker theory. This mathematical analysis and solution procedure is highly complex and time consuming. Hence, an attempt has been made to get the solution of a complex, constrained multifacility location problem using Scaled Conjugate Gradient Algorithm (SCGA) in Artificial Neural Networks (ANN). With the help of Numerical examples, it has been established that the solution obtained through ANN model compares well within the acceptable limits with those obtained through analytical method.

References
  1. Cabot A.V., Francis R.L. and Stary M.A., AIIE Transactions, Vol. 2, No. 2, June 1970 p.132.
  2. Pritsker A.A.B., and Ghare P.M., AIIE Transactions, Vol. 2, No. 4, December 1970, p.290.
  3. Kuhn H.W., and Kuenne R.E., Journal of Regional Science, 4, p. 21-33, (1962).
  4. Eyster J.W., and White J.A., AIIE Transactions, Vol. 5, No. 3, p. 275. (September 1973).
  5. McHose A.H., The journal of Industrial Engineering, Vol. 12, No. 5, Sept. - Oct., 1961, p. 334.
  6. Moller, M.F., “Learning by Conjugate Gradients”, the 6th International Meeting of Young Computer Scientists, Czechoslovakia, in press, 1990
  7. Rumelhart, D.E., G.E. Hinton, R.J. Williams “Learning Internal Representations by Error Propagation”, in: Parallel Distributed Processing: Exploration in the Microstructure of Cognition, Eds. D.E. Rumelhart, J.L. McClelland, MIT Press, Cambridge, MA., pp. 318– 362, 1986.
  8. Da-Zheng Feng , Xian-Da Zhang, and Zheng Bao, “A Neural Network Learning for Adaptively Extracting Cross-Correlation Features between two High- Dimensional Data Streams”, Neural Networks, IEEE, Vol. 15, No. 6, pp. 1541-1554, 2004.
  9. Fok Hing Chi Tivive, and A. Bouzerdoum, “Efficient Training Algorithms for a Class of Shunting Inhibitory Convolutional Neural Networks”, Neural Networks, IEEE, Vol. 16, No. 3, pp. 541-556, 2005.
Index Terms

Computer Science
Information Sciences

Keywords

Multifacility Location Problem Area Constraint Kuhn-Tucker theory Artificial Neural Networks (ANN) Scaled Conjugate Gradient Algorithm (SCGA)