Abstract
Minimum spanning tree problem is a typical and fundamental problem in combinatorial optimization. Most of the existing literature is devoted to the case with deterministic or random weights. However, due to lack of data, a proportion of edge weights have to be estimated according to experts’ evaluations, which may be considered as uncertain variables. This paper focuses on the case where some weights are random variables and the others are uncertain variables. The concept of an ideal chance distribution is introduced and its expression is given based on the uncertainty distributions and probability distributions. A model is formulated to find a minimum spanning tree whose chance distribution is the closest to the ideal one. Finally, a numerical example is given to illustrate the modelling idea of the study.
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This work was supported by National Natural Science Foundation of China Grant Nos. 61273044, 61262023 and 71371019.
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Sheng, Y., Qin, Z. & Shi, G. Minimum spanning tree problem of uncertain random network. J Intell Manuf 28, 565–574 (2017). https://doi.org/10.1007/s10845-014-1015-3
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DOI: https://doi.org/10.1007/s10845-014-1015-3