Industrial Engineering and Management Systems

  • 제12권1호
  • /
  • Pages.9-15
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  • 2013
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  • 1598-7248(pISSN)
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  • 2234-6473(eISSN)
대한산업공학회 (Korean Institute of Industrial Engineers)
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Two Uncertain Programming Models for Inverse Minimum Spanning Tree Problem

  • Zhang, Xiang (School of Management, Shanghai University) ;
  • Wang, Qina (School of Management, Shanghai University) ;
  • Zhou, Jian (School of Management, Shanghai University)
  • 투고 : 2012.08.15
  • 심사 : 2013.03.05
  • 발행 : 2013.03.31
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초록

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 ${\alpha}$-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.

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피인용 문헌

  1. Multi-objective optimization in uncertain random environments vol.13, pp.4, 2014, https://doi.org/10.1007/s10700-014-9183-3
  2. Uncertain Quadratic Minimum Spanning Tree Problem pp.17962021, 2014, https://doi.org/10.12720/jcm.9.5.385-390
  3. Entropy of Uncertain Random Variables wi h Application to Minimum Spanning Tree Problem vol.25, pp.04, 2017, https://doi.org/10.1142/S0218488517500210
  4. An interactive satisficing approach for multi-objective optimization with uncertain parameters vol.28, pp.3, 2017, https://doi.org/10.1007/s10845-014-0998-0
  5. Minimum spanning tree problem of uncertain random network vol.28, pp.3, 2017, https://doi.org/10.1007/s10845-014-1015-3
  6. Uncertain risk aversion vol.28, pp.3, 2017, https://doi.org/10.1007/s10845-014-1013-5
  7. The covariance of uncertain variables: definition and calculation formulae pp.1573-2908, 2017, https://doi.org/10.1007/s10700-017-9270-3
  8. Path Optimality Conditions for Minimum Spanning Tree Problem with Uncertain Edge Weights vol.23, pp.1, 2013, https://doi.org/10.1142/s0218488515500038
  9. A new definition of cross entropy for uncertain random variables and its application vol.35, pp.1, 2013, https://doi.org/10.3233/jifs-18268