Stability and Robustness: Reliability in the World of Uncertainty

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OutlineThe World of UncertaintyRobust OptimizationStability AnalysisConclusionStability AnalysisFuture Research Perspectivesdeveloping heuristics to calculate stability function and stabilityradiusspecifying attainable lower and upper boundsconsidering problems with non-linear objectivesextending the results for problems with various optimalityprinciplesand many others...Yury NikulinStability and Robustness: Reliability in the World of Uncertainty
OutlineOutlineThe World of UncertaintyRobust OptimizationStability AnalysisConclusion1 The World of UncertaintyReasons for UncertaintyExtreme Consequences of UncertaintyEfficient Use of UncertaintyModeling Uncertainty2 Robust Optimization3 Stability Analysis4 ConclusionYury NikulinStability and Robustness: Reliability in the World of Uncertainty
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OutlineThe World of UncertaintyRobu
Page 3 and 4: OutlineOutlineThe World of Uncertai
Page 5 and 6: OutlineThe World of UncertaintyRobu
Page 13 and 14: Interval UncertaintyOutlineThe Worl
Page 15 and 16: OutlineOutlineThe World of Uncertai
Page 51 and 52: ExampleOutlineThe World of Uncertai
Page 53: ExampleOutlineThe World of Uncertai
Page 59 and 60: Introduction: Sensitivity analysis
Page 61 and 62: 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
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
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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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Game descriptionProblemFormulationS
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Forming a coalition, bansProblemFor
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EquilibriaProblemFormulationStabili
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Original problemProblemFormulationS
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ExampleProblemFormulationStability
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Stability FunctionProblemFormulatio
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SufficiencyProblemFormulationStabil
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Formula for Stability FunctionProbl
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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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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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