Implementation of Cutting Plane Separators for Mixed Integer ... - ZIB

More documents

Recommendations

Info

List of Figures 3.1 MIR function Fα for α = 0.5 . . . . . . . . . . . . . . . . . . . . . . 17 3.2 CPS for the class of c-MIR inequalities: MAXAGGR – Summary . . . . 35 3.3 CPS for the class of c-MIR inequalities: MAXROUNDS – Summary . . . 42 4.1 Functions f and g for Example 4.10 . . . . . . . . . . . . . . . . . . 53 5.1 0-1 single node flow set . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7.1 Comparison with Cplex and Cbc– Summary . . . . . . . . . . . . . 118 7.2 Impact of the overall performance of Scip: Enabling – Summary . . 123 7.3 Impact of the overall performance of Scip: Disabling – Summary . . 126 vii
Page 1: Implementation of Cutting Plane Sep
Page 5 and 6: Contents 1 Introduction 1 2 Prelimi
Page 7: List of Algorithms 3.1 Separation a
Page 11 and 12: List of Tables 3.1 CPS for the clas
Page 13 and 14: B.55 CPS for the 0-1 single node fl
Page 15 and 16: Chapter 1 Introduction A mixed inte
Page 17 and 18: Chapter 3, 4, and 5 form the main p
Page 19 and 20: Chapter 2 Preliminaries In this cha
Page 21 and 22: 2.2 Lifting Theory 7 1. If there ex
Page 23 and 24: 2.2 Lifting Theory 9 be an arbitrar
Page 25 and 26: 2.3 Computational Study 11 Obviousl
Page 27 and 28: 2.3 Computational Study 13 separato
Page 29 and 30: Chapter 3 Cutting Plane Separator f
Page 31 and 32: PSfrag replacements −3 −3+α
Page 33 and 34: 3.3 Algorithmic Aspects 19 where α
Page 35 and 36: 3.3 Algorithmic Aspects 21 Input :
Page 37 and 38: original MIP row corresponding to c
Page 39 and 40: 3.3 Algorithmic Aspects 25 resultin
Page 41 and 42: 3.3 Algorithmic Aspects 27 use the
Page 43 and 44: 3.3 Algorithmic Aspects 29 As for t
Page 45 and 46: 3.3 Algorithmic Aspects 31 Input :
Page 47 and 48: 3.4 Computational Study 33 have to
Page 49 and 50: 18 16 14 12 10 8 6 (4.68) 4 (2.1) 2
Page 51 and 52: 3.4 Computational Study 37 is also
Page 53 and 54: 3.4 Computational Study 39 Cut gene
Page 55 and 56: 3.4 Computational Study 41 For our
Page 57 and 58: Chapter 4 Cutting Plane Separator f
Page 59 and 60:
4.2 Strong Valid Inequalities for t
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Then xj + is valid for X BK . 4.2
Page 67 and 68:
PSfrag replacements 3 2 1 4.2 Stron
Page 69 and 70:
4.3 Algorithmic Aspects 55 Separati
Page 71 and 72:
4.3 Algorithmic Aspects 57 Input :
Page 73 and 74:
4.3 Algorithmic Aspects 59 (see [37
Page 75 and 76:
4.3 Algorithmic Aspects 61 if the r
Page 77 and 78:
4.3 Algorithmic Aspects 63 of varia
Page 79 and 80:
4.3 Algorithmic Aspects 65 Consider
Page 81 and 82:
Page 83 and 84:
4.4 Computational Study 4.4 Computa
Page 85 and 86:
4.4 Computational Study 71 Gap Clos
Page 87 and 88:
4.4 Computational Study 73 of the n
Page 89 and 90:
4.4 Computational Study 75 Input :
Page 91 and 92:
4.4 Computational Study 77 the init
Page 93 and 94:
4.4 Computational Study 79 Input :
Page 95 and 96:
4.4 Computational Study 81 possible
Page 97 and 98:
4.5 Conclusion 83 classes of LMCI1
Page 99 and 100:
Chapter 5 Cutting Plane Separator f
Page 101 and 102:
z f(z)=g(z) 1 2 3 5 7 12 13 18 22 N
Page 103 and 104:
5.2 Valid Inequalities for the 0-1
Page 105 and 106:
and by Theorem 5.1, we obtain the S
Page 107 and 108:
5.3 Algorithmic Aspects 93 In the l
Page 109 and 110:
Page 111 and 112:
5.3 Algorithmic Aspects 97 To find
Page 113 and 114:
5.3 Algorithmic Aspects 99 Let j
Page 115 and 116:
5.4 Computational Study 101 Gap Clo
Page 117 and 118:
5.4 Computational Study 103 As it w
Page 119 and 120:
5.4 Computational Study 105 Gap Clo
Page 121 and 122:
5.4 Computational Study 107 the sep
Page 123 and 124:
5.5 Conclusion 5.5 Conclusion 109 T
Page 125 and 126:
Chapter 6 Further Cutting Plane Sep
Page 127 and 128:
6.3 Cutting Plane Separator for the
Page 129 and 130:
Chapter 7 Computational Results In
Page 131 and 132:
7.1 Comparison with Cplex and Cbc 1
Page 133 and 134:
7.1 Comparison with Cplex and Cbc 1
Page 135 and 136:
7.2 Impact on the Overall Performan
Page 137 and 138:
Sfrag replacements f(z) g(z) z f(z)
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Appendix A Zusammenfassung In diese
Page 145 and 146:
Appendix B Tables B.1 Cutting Plane
Page 147 and 148:
B.1 Cutting Plane Separator for the
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Page 199 and 200:
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
Page 221 and 222:
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
B.4 Comparison with Cplex and Cbc 2
Page 237 and 238:
SCIP 0.81 CPLEX 10.01 Cbc 1.01.00 G
Page 239 and 240:
SCIP 0.81 CPLEX 10.01 Cbc 1.01.00 G
Page 241 and 242:
SCIP 0.81 CPLEX 10.01 Cbc 1.01.00 G
Page 243 and 244:
SCIP 0.81 CPLEX 10.01 Cbc 1.01.00 G
Page 245 and 246:
SCIP 0.81 CPLEX 10.01 Cbc 1.01.00 G
Page 247 and 248:
SCIP 0.81 CPLEX 10.01 Cbc 1.01.00 G
Page 249 and 250:
SCIP 0.81 CPLEX 10.01 Cbc 1.01.00 G
Page 251 and 252:
SCIP 0.81 CPLEX 10.01 Cbc 1.01.00 G
Page 253 and 254:
B.5 Impact on the Overall Performan
Page 255 and 256:
No Cuts Only GMI Only C-MIR Only Kn
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
All Cuts No GMI No C-MIR No Knapsac
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Bibliography [1] T. Achterberg. SCI
Page 273 and 274:
259 [30] Z. Gu, G.L. Nemhauser, and
Page 275 and 276:
[62] E. Zemel. Easily computable fa
Page 277:
Die selbständige und eigenhändige
show all

Implementation of Cutting Plane Separators for Mixed Integer ... - ZIB

Create successful ePaper yourself

Delete template?

Save as template?