Abstract
This paper considers how to increase the capacities of the elements in a set E efficiently so that probability of the total cost for the increment of capacity can be under an upper limit to maximum extent while the final expansion capacity of a given family F of subsets of E is with a given limit bound. The paper supposes the cost w is a stochastic variable according to some distribution. Network bottleneck capacity expansion problem with stochastic cost is originally formulated as Dependent-chance programming model according to some criteria. For solving the stochastic model efficiently, network bottleneck capacity algorithm, stochastic simulation, neural network(NN) and genetic algorithm(GA) are integrated to produce a hybrid intelligent algorithm. Finally a numerical example is presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Prentice-Hall, Englewood Cliffs (1993)
Averbakh, I., Berman, O., Punnen, A.P.: Constrained Matroidal Bottleneck Problem. Discrete Applied Mathematics 63, 201–214 (1995)
Krumke, S.O., Marthe, M.V., Ravi, R., Ravi, S.S.: Approximation Algorithms for Certain Network Improvement. Journal of Combinatorial Optimization 2, 257–288 (1998)
Zhang, J., Yang, C., Lin, Y.: A Class of Bottleneck Expansion Problems. Computer and Operational Research 124, 77–88 (2000)
Yang, C., Liu, J.: A Capacity Expansion Problem with Budget Constraint and Bottleneck Limitation. Acta Mathematica Scientia 22, 207–212 (2002)
Hongguo, W., Shaohan, M.: Capacity Expansion Problem on Undirected Network. Journal of Shangdong University 35, 418–424 (2000)
Hongguo, W., Shaohan, M.: Capacity Expansion Problem on Directed Network. Application Mathematics Journal of Chinese University 16, 471–473 (2001)
Yang, X.G., Zhang, J.Z.: A Network Improvement Problem under Different Norms. Computational Optimization and Applications 27, 305–319 (2004)
Charnes, A., Cooper, W.W.: Management Models and Industrial Applications of Linear Programming. Prentice-Hall, Englewood Cliffs (1961)
Liu, B.: Dependent-Chance Programming: a class of stochastic programming. Computers & Mathematics with Applications 34, 89–104 (1997)
Iwamura, K., Liu, B.: Dependent-Chance Integer Programming Applied to Capital Budgeting. Journal of the Operations Research Society of Japan 42, 117–127 (1999)
Ryan, S.M.: Capacity Expansion for Random Exponential Demand Growth. Working Paper No.00-109, Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, IA (August 2000)
Katagiri, H., Ishii, H.: Chance Constrained Bottleneck Spanning Tree Problem with Fuzzy Random Edge Costs. Journal of the Operations Research Society of Japan 43, 128–137 (2000)
Katagiri, H., Sakawa, M., Ishii, H.: Fuzzy Random Bottleneck Spanning Tree Problem Using Possibility and Necessity Measures. European Journal of Operational Research 152, 88–95 (2004)
Liu, B.: Uncertain Programming. Wiley, New York (1999)
Venkatech, S.: Computation and Learning in the Context of Neural Network Capacity. Neural Networks for Perception 2, 173–327 (1992)
Castellano, G., Fanelli, A.M., Pelillo, M.: An Iterative Pruning Algorithm for FeedForward Neural Networks. IEEE Transactions on Neural Network 8, 519–537 (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wu, Y., Zhou, J., Yang, J. (2005). Dependent-Chance Programming Model for Stochastic Network Bottleneck Capacity Expansion Based on Neural Network and Genetic Algorithm. In: Wang, L., Chen, K., Ong, Y.S. (eds) Advances in Natural Computation. ICNC 2005. Lecture Notes in Computer Science, vol 3612. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11539902_14
Download citation
DOI: https://doi.org/10.1007/11539902_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28320-1
Online ISBN: 978-3-540-31863-7
eBook Packages: Computer ScienceComputer Science (R0)