Stability and Robustness: Reliability in the World of Uncertainty

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OutlineThe World of UncertaintyRobust OptimizationStability AnalysisConclusionModeling UncertaintyReasons for UncertaintyExtreme Consequences of UncertaintyEfficient Use of UncertaintyModeling UncertaintyUncertainty can be modeled by means of:possible scenarios (parameter realizations)fuzzy numbers and fuzzy objective functionsvarious probabilistic measuresinterval dataYury NikulinStability and Robustness: Reliability in the World of Uncertainty
Interval UncertaintyOutlineThe World of UncertaintyRobust OptimizationStability AnalysisConclusionReasons for UncertaintyExtreme Consequences of UncertaintyEfficient Use of UncertaintyModeling UncertaintyAdvantagesLower and upper interval bounds are easy to specifyNo statistical observations needed for the modelEasy implementation and practical useDisadvantagesInfinite number of problem input parameter realization -scenarios (can be overcome for some models!)Yury NikulinStability and Robustness: Reliability in the World of Uncertainty
Page 1 and 2: OutlineThe World of UncertaintyRobu
Page 3 and 4: OutlineOutlineThe World of Uncertai
Page 11: OutlineThe World of UncertaintyRobu
Page 51 and 52: ExampleOutlineThe World of Uncertai
Page 53 and 54: ExampleOutlineThe World of Uncertai
Page 59 and 60: Introduction: Sensitivity analysis
Page 61 and 62: 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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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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Stability and Robustness: Reliability in the World of Uncertainty

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