Stability and Robustness: Reliability in the World of Uncertainty

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Computational ExperimentsThe Central TreeProblemHeuristics for theCTPFinal Remarks|V | = 10 Instance A Instance B Instance C Instance DGCH 75 90 80 73GCH+FLSI 92 95 94 90Table 7: Average (over 100 runs) performance of GCHand.GCH+FLSI on instances with 10 vertices|V | = 15 Instance A Instance B Instance C Instance DGCH 7 9 8 7GCH+FLSI 9 9 9 8Table 8: Average (over 50 runs) performance of GCH andGCH+FLSI on instances with 15 verticesHeuristics for the Central Tree Problem Yury Nikulin - p. 28/33
Computational ExperimentsThe Central TreeProblemHeuristics for theCTPFinal Remarks|V | 50 100 150 200Instance A 15sec 1h 2h 6hInstance B 40sec 3h 6h 19hInstance C 13sec 50min 2h 6hInstance D 25sec 2h30min 7h 20hTable 9: Average (over 10 runs) running time of GCH+FLSI onlarge instances.Heuristics for the Central Tree Problem Yury Nikulin - p. 29/33
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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
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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
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
Page 95 and 96: 16/04/2009 Yury Nikulin, Sensitivit
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 115 and 116: Equivalence between 0 − 1 RSTP an
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Page 119 and 120: MILP FormulationCorollary from the
Page 121 and 122: Approximation for the CTPThe Centra
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Page 127 and 128: ExampleThe Central TreeProblemHeuri
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Page 145 and 146: ConclusionThe Central TreeProblemHe
Page 147 and 148: Sensitivity Analysis in Game Theory
Page 149 and 150: Game descriptionProblemFormulationS
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Page 153 and 154: EquilibriaProblemFormulationStabili
Page 155 and 156: Original problemProblemFormulationS
Page 157 and 158: ExampleProblemFormulationStability
Page 159 and 160: Stability FunctionProblemFormulatio
Page 161 and 162: SufficiencyProblemFormulationStabil
Page 163 and 164: Formula for Stability FunctionProbl
Page 165 and 166: Sketch of the proofProblemFormulati
Page 167 and 168: Formula for Stability RadiusProblem
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Page 171 and 172: Accuracy Function and RadiusProblem
Page 173 and 174: ExampleProblemFormulationStability
Page 175 and 176: Concluding remarksProblemFormulatio
Page 177 and 178: Fuzziness: one more way of dealingw
Page 179 and 180: Crisp and Fuzzy Numbers28/04/2009 Y
Page 181 and 182: Geometrical interpretation: Union28
Page 183 and 184: Geometrical interpretation:Intersec
Page 185 and 186: Fuzzy sets28/04/2009 Yury Nikulin,
Page 187 and 188: Comparison of fuzzy numbers:strong
Page 189 and 190: 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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