Skip to main content
SpringerLink
Log in

Uncertain random shortest path problem

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The shortest path is an important problem in network optimization theory. This paper considers the shortest path problem under the situation where weights of edges in a network include both uncertainty and randomness and focuses on the case that the weights of edges are expressed by uncertain random variables. Some optimization models based on chance theory are proposed in order to find the shortest path which fully reflects uncertain and random information. This paper proposes also an intelligent algorithm to calculate the shortest path for an uncertain random network. A numerical example is given to illustrate its effectiveness.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Balinski ML (1961) Fixed cost transportation problem. Nav Res Logist Q 8(1):41–54

    MATH  Google Scholar 

  • Bellman E (1958) On a routing problem. Q Appl Math 16(1):87–90

    MATH  Google Scholar 

  • Dijkstra EW (1959) A note on two problems in connection with graphs. Numer Math 1(1):269–271

    MathSciNet  MATH  Google Scholar 

  • Ding SB (2014) Uncertain minimum cost flow problem. Soft Comput 18(11):2201–2207

    MATH  Google Scholar 

  • Dreyfus S (1969) An appraisal of some shortest path algorithms. Oper Res 17(3):359–412

    MATH  Google Scholar 

  • Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York

    MATH  Google Scholar 

  • Floyd RW (1962) Algorithm-97-shortest path. Comm Assoc Comput Mach 5(6):345

    Google Scholar 

  • Frank H (1969) Shortest paths in probability graphs. Oper Res 17(4):583–599

    MATH  Google Scholar 

  • Frank H, Hakimi SL (1965) Probabilistic flows through a communication network. IEEE Trans Circuit Theory 12:413–414

    Google Scholar 

  • Fu L, Rilett LR (1998) Expected shortest paths in dynamic and stochastic traffic networks. Transp Res Part B Methodol 32(7):499–516

    Google Scholar 

  • Gao X (2009) Some properties of continuous uncertain measure. Int J Uncertain Fuzziness Knowl Based Syst 17(3):419–426

    MathSciNet  MATH  Google Scholar 

  • Gao Y (2011) Shortest path problem with uncertain arc lengths. Comput Math Appl 62:2591–2610

    MathSciNet  MATH  Google Scholar 

  • Guo HY, Wang XS (2014) Variance of uncertain random variables. J Uncertain Anal Appl 2:6

    Google Scholar 

  • Hall R (1986) The fastest path through a network with random time-dependent travel time. Transp Sci 20(3):182–188

    MathSciNet  Google Scholar 

  • Han SW, Peng ZX, Wang SQ (2014) The maximum flow problem of uncertain network. Inf Sci 265:167–175

    MathSciNet  MATH  Google Scholar 

  • Hou YC (2014) Subadditivity of chance measure. J Uncertain Anal Appl 2:14

    Google Scholar 

  • Jia LF, Yang XF, Gao X (2018) A new definition of cross entropy for uncertain random variables and its application. J Intell Fuzzy Syst 35(1):1193–1204

    Google Scholar 

  • Ke H, Su TY (2015) Uncertain random multilevel programming with application to product control problem. Soft Comput 19(6):1739–1746

    MATH  Google Scholar 

  • Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  • Liu B (2009a) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10

    Google Scholar 

  • Liu B (2009b) Theory and practice of uncertain programming, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  • Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty, 2nd edn. Springer, Berlin

    Google Scholar 

  • Liu B (2012) Why is there a need for uncertainty theory. J Uncertain Syst 6(1):3–10

    Google Scholar 

  • Liu YH (2013a) Uncertain random variables: a mixture of uncertainty and randomness. Soft Comput 17(4):625–634

    MATH  Google Scholar 

  • Liu YH (2013b) Uncertain random programming with applications. Fuzzy Optim Decis Mak 12(2):153–169

    MathSciNet  MATH  Google Scholar 

  • Liu B (2014) Uncertain random graph and uncertain random network. J Uncertain Syst 8(1):3–12

    Google Scholar 

  • Liu YH, Ha MH (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181–186

    Google Scholar 

  • Liu YH, Ralescu DA (2014) Risk index in uncertain random risk analysis. Int J Uncertain Fuzziness Knowl Based Syst 22(4):491–504

    MathSciNet  MATH  Google Scholar 

  • Loui P (1983) Optimal paths in graphs with stochastic or multidimensional weights. Commun Assoc Comput Mach 26(9):670–676

    MathSciNet  MATH  Google Scholar 

  • Mirchandani PB (1976) Shortest distance and reliability of probabilistic networks. Comput Oper Res 3(4):347–676

    Google Scholar 

  • Okada S (2004) Fuzzy shortest path problems incorporating interactivity among paths. Fuzzy Sets Syst 142(3):335–357

    MathSciNet  MATH  Google Scholar 

  • Peng ZX, Iwamura K (2010) A sufficient and necessary condition of uncertainty distribution. J Interdiscip Math 13(3):277–285

    MathSciNet  MATH  Google Scholar 

  • Qin ZF (2018) Uncertain random goal programming. Fuzzy Optim Decis Mak 17:375–386

    MathSciNet  MATH  Google Scholar 

  • Sheng YH, Gao JW (2014) Chance distribution of the maximum flow of uncertain random network. J Uncertain Anal Appl 2:15

    Google Scholar 

  • Sheng YH, Gao Y (2016) Shortest path problem of uncertain random network. Comput Ind Eng 99:97–105

    Google Scholar 

  • Sheng YH, Yao K (2014) Some formulas of variance of uncertain random variable. J Uncertain Anal Appl 2:12

    Google Scholar 

  • Sheng YH, Qin ZF, Shi G (2017) Minimum spanning tree problem of uncertain random network. J Intell Manuf 28(3):565–574

    Google Scholar 

  • Shi G, Sheng YH, Cui Q (2015) Relative entropy model of uncertain random shortest path. Int J e-Navig Marit Econ 2:87–100

    Google Scholar 

  • Sigal CL, Pritsker AAB, Solberg JJ (1980) The stochastic shortest route problem. Oper Res 5(28):1122–1129

    MathSciNet  MATH  Google Scholar 

  • Yang XF, Gao JW, Ni YD (2018) Resolution principle in uncertain random environment. IEEE Trans Fuzzy Syst 26(3):1578–1588

    Google Scholar 

  • Zhang B, Peng J (2012) Uncertain programming model for Chinese postman problem with uncertain weights. Ind Eng Manag Syst 11(1):18–25

    Google Scholar 

  • Zhou J, Yang F, Wang K (2014) Multi-objective optimization in uncertain random environments. Fuzzy Optim Decis Mak 13(4):397–413

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grants No. 61563050), Joint Key Program of National Natural Science Foundation of China (Grants No. U1703262), Innovation Team Research Program of Universities in Xinjiang Uyghur Autonomous Region (Grants No. XJEDU2017 T001), and this work was granted by China Scholarship Council (Grants 201708 655050).

Author information

Authors and Affiliations

  1. College of Mathematical and System Sciences, Xinjiang University, Ürümqi, 830046, China

    Yuhong Sheng & Xuehui Mei

Authors
  1. Yuhong Sheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xuehui Mei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuhong Sheng.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Additional information

Communicated by Y. Ni.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sheng, Y., Mei, X. Uncertain random shortest path problem. Soft Comput 24, 2431–2440 (2020). https://doi.org/10.1007/s00500-018-03714-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-018-03714-5

Keywords

Search

Navigation