Stability and Robustness: Reliability in the World of Uncertainty

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ConclusionsThere is no unique understanding of dealing with uncertainty.There are several approaches, each of them hasown advantages and disadvantages.Which one to choose for a particular problemis a very difficult question which has to be solved bythe decision maker based on own preferences,expectations and managing experience!28/04/2009 Yury Nikulin, Sensitivity analysis 25
28/04/2009 Yury Nikulin, Sensitivity analysis 26
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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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The Central TreeProblemHeuristics f
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Greedy Construction HeuristicThe Ce
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ExampleThe Central TreeProblemHeuri
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Computational ExperimentsThe Centra
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ConclusionThe Central TreeProblemHe
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Sensitivity Analysis in Game Theory
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Page 151 and 152: Forming a coalition, bansProblemFor
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(
Page 191 and 192: Fuzzy maximum and minimum28/04/2009
Page 193 and 194: Statistical data about flight delay
Page 195 and 196: Possibility distribution28/04/2009
Page 197 and 198: Fuzzy Number representing delays28/
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Stability and Robustness: Reliability in the World of Uncertainty

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