Stability and Robustness: Reliability in the World of Uncertainty

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ApplicationsThe Central TreeProblemHeuristics for theCTPFinal RemarksThe CTP can find its application in many real-life models. For example,in computer networking, spanning tree topologies can beefficiently used to model network configurations.Similar network problems have many applications in telecommunications,circuit analysis, facility allocation, and related domainsin electric, gas, and sewer networks.Heuristics for the Central Tree Problem Yury Nikulin - p. 8/33
Equivalence between 0 − 1 RSTP and CTPThe Central TreeProblemThe following theorem establishes equivalence between 0 − 1RSTP and CTP.Heuristics for theCTPFinal RemarksHeuristics for the Central Tree Problem Yury Nikulin - p. 9/33
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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
Page 63 and 64: Classical approachKouvelis P. and Y
Page 65 and 66: Telecommunication and MST16/04/2009
Page 67 and 68: Multicommodity reformulation formin
Page 69 and 70: Dual problem16/04/2009 Yury Nikulin
Page 71 and 72: Interval data and scenariosG = ( E,
Page 73 and 74: RST problem reformulation as mixedi
Page 75 and 76: Robust Spanning Tree Problem within
Page 77 and 78: Example: weak edgesweaknon-weak12-5
Page 79 and 80: Example: Strong edgesstrong12-553-4
Page 81 and 82: CPLEX results on complete graphs16/
Page 83 and 84: Branching strategyNode d with the s
Page 85 and 86: Lower bound16/04/2009 Yury Nikulin,
Page 87 and 88: SA: preprocessing, initial solution
Page 89 and 90: SA: neighborhood search moveCase2.1
Page 91 and 92: Running time16/04/2009 Yury Nikulin
Page 93 and 94: SA summary• In spite of SA is gen
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Page 97 and 98: Heuristics for Central Tree Problem
Page 99 and 100: Distance MeasureThe Central TreePro
Page 101 and 102: Distance MeasureThe Central TreePro
Page 103 and 104: The Central Tree ProblemThe Central
Page 105 and 106: The CTP vs. MDTPThe Central TreePro
Page 107 and 108: The CTP vs. MDTPThe Central TreePro
Page 109 and 110: Short ExampleThe Central TreeProble
Page 111 and 112: Complexity of the CTPThe Central Tr
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Page 121 and 122: Approximation for the CTPThe Centra
Page 123 and 124: The Central TreeProblemHeuristics f
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Page 127 and 128: ExampleThe Central TreeProblemHeuri
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Page 147 and 148: Sensitivity Analysis in Game Theory
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Page 157 and 158: ExampleProblemFormulationStability
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Sketch of the proofProblemFormulati
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Formula for Stability RadiusProblem
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Independent players, no bansProblem
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Accuracy Function and RadiusProblem
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ExampleProblemFormulationStability
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Concluding remarksProblemFormulatio
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Fuzziness: one more way of dealingw
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Crisp and Fuzzy Numbers28/04/2009 Y
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Geometrical interpretation: Union28
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Geometrical interpretation:Intersec
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Fuzzy sets28/04/2009 Yury Nikulin,
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Comparison of fuzzy numbers:strong
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Maximal and Minimalfuzzy numbersμ(
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Fuzzy maximum and minimum28/04/2009
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Statistical data about flight delay
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Possibility distribution28/04/2009
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Fuzzy Number representing delays28/
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Stability and Robustness: Reliability in the World of Uncertainty

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