Stability and Robustness: Reliability in the World of Uncertainty

More documents

Recommendations

Info

OutlineThe World of UncertaintyRobust OptimizationStability AnalysisConclusionThe Robust Spanning Tree ProblemMethodologyMIP, CPLEXYaman et al., 2001Branch and BoundAron and Van Hentenryck, 2002Improved Branch and BoundMontemanni and Gambardella, 20052-Approximation AlgorithmKasperski and Zielinski, 2006Yury NikulinStability and Robustness: Reliability in the World of Uncertainty
OutlineThe World of UncertaintyRobust OptimizationStability AnalysisConclusionThe Robust Spanning Tree ProblemFuture Research Perspectivesdeveloping new fast heuristicsconsidering biobjective modelsfinding approximation algorithmsand many others...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 13 and 14: Interval UncertaintyOutlineThe Worl
Page 33: 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
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
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
Page 115 and 116:
Equivalence between 0 − 1 RSTP an
Page 117 and 118:
One more evidence of NP-hardnessThe
Page 119 and 120:
MILP FormulationCorollary from the
Page 121 and 122:
Approximation for the CTPThe Centra
Page 123 and 124:
The Central TreeProblemHeuristics f
Page 125 and 126:
Greedy Construction HeuristicThe Ce
Page 127 and 128:
ExampleThe Central TreeProblemHeuri
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Computational ExperimentsThe Centra
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
ConclusionThe Central TreeProblemHe
Page 147 and 148:
Sensitivity Analysis in Game Theory
Page 149 and 150:
Game descriptionProblemFormulationS
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
Page 169 and 170:
Independent players, no bansProblem
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/
Page 199 and 200:
Page 201:
show all

Stability and Robustness: Reliability in the World of Uncertainty

Create successful ePaper yourself

Delete template?

Save as template?