Stability and Robustness: Reliability in the World of Uncertainty

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ExampleProblemFormulation1.0Stability andAccuracyFunctions0.750.50.250.00.00.250.5rho0.751.0Figure 1: Stability functions S(C 0 , J, x 1 , ρ) and S(C 0 , J, x 2 , ρ)for ρ ∈ [0, 1).Graphics for S(C 0 , J, x 1 , ρ) (continuous line) and S(C 0 , J, x 2 , ρ)(dotted line) are depicted in figure 1.Sensitivity Analysis in Game Theory Yury Nikulin - p. 28/29
Concluding remarksProblemFormulationStability andAccuracyFunctionsThe accuracy and stability functions describe the quality ofequilibrium in the game with uncertain coefficients in payoffs.The definitions of these functions are directly connected withgiven optimality principles. While the stability and accuracyradii determine only maximum values of independentperturbations preserving the property of being equilibrium for agiven solution, the stability and accuracy functions willadditionally give the answer what happens with the solutionafter it becomes non-optimal in terms of quantitative measureof stability reflecting the speed of relative deterioration of thegiven solution.Sensitivity Analysis in Game Theory Yury Nikulin - p. 29/29
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OutlineThe World of UncertaintyRobu
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OutlineOutlineThe World of Uncertai
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Interval UncertaintyOutlineThe Worl
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ExampleOutlineThe World of Uncertai
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ExampleOutlineThe World of Uncertai
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Introduction: Sensitivity analysis
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Dealing with uncertainty16/04/2009
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Classical approachKouvelis P. and Y
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Telecommunication and MST16/04/2009
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Multicommodity reformulation formin
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Dual problem16/04/2009 Yury Nikulin
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Interval data and scenariosG = ( E,
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RST problem reformulation as mixedi
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Robust Spanning Tree Problem within
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Example: weak edgesweaknon-weak12-5
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Example: Strong edgesstrong12-553-4
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CPLEX results on complete graphs16/
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Branching strategyNode d with the s
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Lower bound16/04/2009 Yury Nikulin,
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SA: preprocessing, initial solution
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SA: neighborhood search moveCase2.1
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Running time16/04/2009 Yury Nikulin
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SA summary• In spite of SA is gen
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16/04/2009 Yury Nikulin, Sensitivit
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Heuristics for Central Tree Problem
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Distance MeasureThe Central TreePro
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Distance MeasureThe Central TreePro
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The Central Tree ProblemThe Central
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The CTP vs. MDTPThe Central TreePro
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The CTP vs. MDTPThe Central TreePro
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Short ExampleThe Central TreeProble
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Complexity of the CTPThe Central Tr
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Complexity of the CTPThe Central Tr
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Equivalence between 0 − 1 RSTP an
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One more evidence of NP-hardnessThe
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MILP FormulationCorollary from the
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Approximation for the CTPThe Centra
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Stability and Robustness: Reliability in the World of Uncertainty

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