Stability and Robustness: Reliability in the World of Uncertainty

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ExampleThe Central TreeProblemHeuristics for theCTPFinal RemarksHeuristics for the Central Tree Problem Yury Nikulin - p. 19/33
ExampleThe Central TreeProblemHeuristics for theCTPFinal RemarksHeuristics for the Central Tree Problem Yury Nikulin - p. 19/33
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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
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
Page 95 and 96: 16/04/2009 Yury Nikulin, Sensitivit
Page 97 and 98: Heuristics for Central Tree Problem
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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
Page 113 and 114: Complexity of the CTPThe Central Tr
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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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Page 167 and 168: Formula for Stability RadiusProblem
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Page 175 and 176: Concluding remarksProblemFormulatio
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Page 179 and 180: 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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28/04/2009 Yury Nikulin, Sensitivit
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28/04/2009 Yury Nikulin, Sensitivit
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Stability and Robustness: Reliability in the World of Uncertainty

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