Stability and Robustness: Reliability in the World of Uncertainty

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Computational ExperimentsThe Central TreeProblemHeuristics for theCTPFinal RemarksGCH 10 15 20 40Distance 6 6 11 33Running time (in sec.) 0.10 0.16 0.46 8.46GCH+FLSI 10 15 20 40Distance 5 6 11 31Running time (in sec.) 0.11 0.17 0.48 8.92SLS 10 15 20 40Distance 6 7 13 36Running time (in sec.) 0.32 0.94 30.64 1175.0ES 10 15 20 40Distance 5 6 - -Running time (in sec.) 14.92 486.0 - -Table 3: Instance sample A.Heuristics for the Central Tree Problem Yury Nikulin - p. 24/33
Computational ExperimentsThe Central TreeProblemHeuristics for theCTPFinal RemarksGCH 10 15 20 40Distance 6 12 17 87Running time (in sec.) 0.07 0.34 0.82 38.35GCH+FLSI 10 15 20 40Distance 6 12 17 37Running time (in sec.) 0.07 0.37 0.88 38.72SLS 10 15 20 40Distance 7 13 19 39Running time (in sec.) 0.46 0.62 52.33 2888.0ES 10 15 20 40Distance 6 - - -Running time (in sec.) 195.0 - - -Table 4: Instance sample B.Heuristics for the Central Tree Problem Yury Nikulin - p. 25/33
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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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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
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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
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Page 167 and 168: Formula for Stability RadiusProblem
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Page 173 and 174: ExampleProblemFormulationStability
Page 175 and 176: Concluding remarksProblemFormulatio
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Page 179 and 180: Crisp and Fuzzy Numbers28/04/2009 Y
Page 181 and 182: Geometrical interpretation: Union28
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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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