# Stability Radius for the Shortest Path Problem

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In stability theory, a quantitative characteristic called the stability radius is defined as the limit level of perturbations of problem parameters preserving optimality of a single solution (or of the solution set). These perturbations are caused by the various factors of uncertainty and randomness, such as inadequacy of mathematical models to real processes, rounding errors, calculation errors, and so on.

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Contributed by: Olia Karelkina (February 2016)

Open content licensed under CC BY-NC-SA

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References

[1] N. Chakravarti and A. P. M. Wagelmans, "Calculation of Stability Radii for Combinatorial Optimization Problems," *Operations Research Letters*, 23(1–2), 1998 pp. 1–7. doi:10.1016/S0167-6377(98)00031-5.

[2] V. Emelichev and D. Podkopaev, "Quantitative Stability Analysis for Vector Problems of 0-1 Programming,"* Discrete Optimization*, 7(1-2), 2010 pp. 48–63. doi:10.1016/j.disopt.2010.02.001.

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