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Two Uncertain Programming Models for Inverse Minimum Spanning Tree Problem
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 Title & Authors
Two Uncertain Programming Models for Inverse Minimum Spanning Tree Problem
Zhang, Xiang; Wang, Qina; Zhou, Jian;
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An inverse minimum spanning tree problem makes the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In this paper, the concept of uncertain -minimum spanning tree is initiated for minimum spanning tree problem with uncertain edge weights. Using different decision criteria, two uncertain programming models are presented to formulate a specific inverse minimum spanning tree problem with uncertain edge weights involving a sum-type model and a minimax-type model. By means of the operational law of independent uncertain variables, the two uncertain programming models are transformed to their equivalent deterministic models which can be solved by classic optimization methods. Finally, some numerical examples on a traffic network reconstruction problem are put forward to illustrate the effectiveness of the proposed models.
Minimum Spanning Tree;Uncertain Minimum Spanning Tree;Inverse Optimization;Uncertain Programming;
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Ahuja, R. K., Magnanti, T. L., and Orlin, J. B. (1993), Network Flows: Theory, Algorithms, and Applications, Prentice Hall, Englewood Cliffs, NJ.

Ahuja, R. K. and Orlin, J. B. (2000), A faster algorithm for the inverse spanning tree problem, Journal of Algorithms, 34(1), 177-193. crossref(new window)

Chen, X. (2011), American option pricing formula for uncertain financial market, International Journal of Operations Research, 8(2), 27-32.

Farago, A., Szentesi, A., and Szviatovszki, B. (2003), Inverse optimization in high-speed networks, Discrete Applied Mathematics, 129(1), 83-98. crossref(new window)

Guan, X. and Zhang, J. (2007), Inverse constrained bottleneck problems under weighted $l_{{\infty}}$ norm, Computers and Operations Research, 34(11), 3243-3254. crossref(new window)

He, Y., Zhang, B., and Yao, E. (2005), Weighted inverse minimum spanning tree problems under Hamming distance, Journal of Combinatorial Optimization, 9(1), 91-100. crossref(new window)

Kershenbaum, A. (1993), Telecommunication Network Design Algorithms, McGraw-Hill, New York, NY.

Li, S. and Peng, J. (2012), A new approach to risk comparison via uncertain measure, Industrial Engineering & Management Systems, 11(2), 176-182. crossref(new window)

Liu, B. (2007), Uncertainty Theory (2nd ed.), Springer-Verlag, Berlin.

Liu, B. (2009), Some research problems in uncertainty theory, Journal of Uncertain Systems, 3(1), 3-10.

Liu, B. (2010), Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer- Verlag, Berlin.

Peng, J. and Li, S. (2011), Spanning tree problem of uncertain network, Proceedings of the 3rd International Conference on Computer Design and Applications, Xi'an, Shaanxi, China.

Peng, Z. and Iwamura, K. (2010), A sufficient and necessary condition of uncertainty distribution, Journal of Interdisciplinary Mathematics, 13(3), 277-285. crossref(new window)

Sheng, Y. and Yao K. (2012), Fixed charge transportation problem and its uncertain programming model, Industrial Engineering and Management Systems, 11(2), 183-187. crossref(new window)

Sokkalingam, P. T., Ahuja, R. K., and Orlin, J. B. (1999), Solving inverse spanning tree problems through network flow techniques, Operations Research, 47(2), 291-298. crossref(new window)

Wang, Q., Yang, X., and Zhang, J. (2006), A class of inverse dominant problems under weighted $l_{{\infty}}$ norm and an improved complexity bound for Radzik's algorithm, Journal of Global Optimization, 34(4), 551-567. crossref(new window)

Xu, X. and Zhu, Y. (2012), Uncertain bang-bang control for continuous time model, Cybernetics and Systems, 43(6), 515-527. crossref(new window)

Yang, X. and Zhang, J. (2007), Some inverse min-max network problems under weighted l1 and $l_{{\infty}}$ norms with bound constraints on changes, Journal of Combinatorial Optimization, 13(2), 123-135.

Zhang, B., Zhang, J., and He, Y. (2006), Constrained inverse minimum spanning tree problems under the bottleneck-type Hamming distance, Journal of Global Optimization, 34(3), 467-474. crossref(new window)

Zhang, J., Liu. Z., and Ma, Z. (1996), On the inverse problem of minimum spanning tree with partition constraints, Mathematical Methods of Operations Research, 44(2), 171-187. crossref(new window)

Zhang, J. and Zhou, J. (2006), Models and hybrid algorithms for inverse minimum spanning tree problem with stochastic edge weights, World Journal of Modelling and Simulation, 2(5), 297-311.

Zhou, C. and Peng, J. (2011), Models and algorithm ofmaximum flow problem in uncertain network, Proceedingsof the 3rd International Conference on-Artificial Intelligence and Computational Intelligence,Taiyuan, Shanxi, China, 101-109.