ILOG CPLEX 11.0 User's Manual

More documents

Recommendations

Info

Reminder: It may help you understand the signatures of these functions to recall thefamiliar Cartesian representation of a line or segment in two dimensions, x and y:y=ax+bwhere a represents the slope of the line or segment and b represents the height at which theline theoretically crosses the y-axis at the point (0, b).Discontinuous Piecewise Linear FunctionsThus far, you have seen a piecewise linear function where the segments are continuous.Intuitively, in a continuous piecewise linear function, the endpoint of one segment has thesame coordinates as the initial point of the next segment, as in Figure 18.1.There are piecewise linear functions, however, where the endpoint of one segment and theinitial point of the next segment may have the same x coordinate but differ in the value off(x). Such a difference is known as a step in the piecewise linear function, and such afunction is known as discontinuous. Figure 18.2 shows a discontinuous piecewise linearfunction with two steps.Syntactically, a step is represented in this way:◆ The x-coordinate of the breakpoint where the step occurs is repeated in the array of thebreakpoint.◆The value of the first point of a step in the array of slopes is the height of the step.◆ The value of the second point of the step in the array of slopes is the slope of the functionafter the step.By convention, a breakpoint belongs in both segments associated with the step. For example,in Figure 18.2, at the breakpoint x=3, the points (3,1) and (3,3) are both admissible.Similarly, when x = 5, the points (5,4) and (5,5) are both admissible.However, isolated points, as explained in Isolated Points in Piecewise Linear Functions onpage 341, are not allowed, neither in continuous nor in discontinuous piecewise linearfunctions. In fact, only one step is allowed at a given point.In Concert Technology, a discontinuous piecewise linear function is represented as aninstance of the class IloPiecewiseLinear (the same class as used for continuouspiecewise linear functions). For example, the function in Figure 18.2 is declared in this way:IloPiecewiseLinear(x,IloNumArray(env, 4, 3. ,3. ,5. ,5.),IloNumArray(env, 5, 0., 2., 0.5, 1., -1.),0, 1);340 ILOG CPLEX 11.0 — USER’ S MANUAL
Figure 18.25f(x)4321x01 2 3 4 5 6 7 8Figure 18.2 A discontinuous piecewise linear function with stepsReminder: It may help to understand the signature of the function in this example to recallthat in Cartesian coordinates, the slope of a horizontal line (that is, a line or segmentparallel to the x-axis) is 0 (zero), and the slope of a vertical line (that is, a line or segmentparallel to the y-axis) is undefined in the conventional representation:y=ax+bIn the signature of the function, the undefined slope of the vertical segment at the point ofdiscontinuity is represented as the height of the step.Isolated Points in Piecewise Linear FunctionsWhen you specify the same point more than twice as you declare a piecewise linear function,you inadvertently create an isolated point. ILOG CPLEX does not support isolated points.When it encounters an isolated point in the declaration of a piecewise linear function,ILOG CPLEX issues a warning and ignores the isolated point. An isolated point may appearas a visible point in the graph of a discontinues piecewise linear function. For example, thepoint (3, 2) would be an isolated point in Figure 18.2 and consequently ignored byILOG CPLEX. Isolated points may also be less conspicuously visible; for example, if theheight of a step in a discontinuous piecewise linear function is 0 (zero), the isolated pointILOG CPLEX 11.0 — USER’ S MANUAL 341
Page 1 and 2:
ILOG CPLEX 11.0User’s ManualSepte
Page 3 and 4:
C O N T E N T STable of ContentsILO
Page 5 and 6:
Building the Model by Column . . .
Page 8:
Program Description . . . . . . . .
Page 13 and 14:
Cholesky Factor in the Log File . .
Page 15:
Examples: QCP . . . . . . . . . . .
Page 19 and 20:
Chapter 18 Using Piecewise Linear F
Page 21 and 22:
Representing the Data. . . . . . .
Page 23 and 24:
Reading and Writing MPS Files . . .
Page 25 and 26:
Protected Variables in Presolve Red
Page 27 and 28:
P R E F A C EMeet ILOG CPLEXILOG CP
Page 29 and 30:
When a linear optimization problem
Page 31 and 32:
◆◆◆◆implemented in ILOG CPL
Page 33 and 34:
Solution Pool: Generating and Keepi
Page 35:
Table 1ExamplesExample Source File
Page 38 and 39:
◆◆◆◆◆◆Overview of the A
Page 40 and 41:
Wolsey, Laurence A., Integer Progra
Page 43 and 44:
C H A P T E R1ILOG Concert Technolo
Page 45 and 46:
Compiling and LinkingCompilation an
Page 47 and 48:
The class IloNumVar provides method
Page 49 and 50:
IloModel object itself and added to
Page 51 and 52:
Table 1.1 Concert Technology Modeli
Page 53 and 54:
Choosing an OptimizerSolving the ex
Page 55 and 56:
Table 1.4 on page 55 summarizes the
Page 57 and 58:
Dynamic control of the solution pro
Page 59 and 60:
However, querying solution values v
Page 61 and 62:
parameter for the getQuality method
Page 63 and 64:
model2.add(model1);model2.add(IloCo
Page 65 and 66:
Example: Optimizing the Diet Proble
Page 67 and 68:
Concert Technology, as demonstrated
Page 69 and 70:
method IloModel::add returns the mo
Page 71 and 72:
Page 73 and 74:
Licenses in a Java ApplicationILOG
Page 75 and 76:
Models that consist only of such co
Page 77 and 78:
The special case of linear expressi
Page 79 and 80:
IloObjective obj = cplex.add(cplex.
Page 81 and 82:
Solving the ModelOnce you have crea
Page 83 and 84:
IloCplex cplex = new IloCplex();Ilo
Page 85 and 86:
IloCplex.setParam(IloCplex.IntParam
Page 87 and 88:
Thus, the suggested method for sett
Page 89 and 90:
Basis InformationWhen solving an LP
Page 91 and 92:
where A is a sparse matrix. A spars
Page 93 and 94:
The example starts by evaluating th
Page 95 and 96:
IloMPModeler.setLinearCoefs, and Il
Page 97 and 98:
Page 99 and 100:
◆What is the purpose (the objecti
Page 101 and 102:
Step 3Create the modelGo to the com
Page 103 and 104:
Step 9Add nutritional constraintsGo
Page 105 and 106:
Step 14Display the solutionGo to th
Page 107 and 108:
Step 18Enclose the application in t
Page 109 and 110:
C H A P T E R4ILOG CPLEX Callable L
Page 111 and 112:
◆◆file reading and writing rout
Page 113 and 114:
◆◆If data already exist in MPS,
Page 115 and 116:
For example, let’s look at the sy
Page 117 and 118:
As you modify a problem object thro
Page 119 and 120:
However, ILOG CPLEX updates the nam
Page 121 and 122:
whether an optimization should be a
Page 123 and 124:
Callable Library have names greater
Page 125 and 126:
◆CPXsetstrparam accepts arguments
Page 127 and 128:
Here’s another way to visualize a
Page 129 and 130:
program—can discover the length o
Page 131:
Part IIProgramming ConsiderationsTh
Page 134 and 135:
◆ Test Data on page 135◆ Choose
Page 136 and 137:
◆ Use the MIP optimizer if the pr
Page 138 and 139:
Choose Clarity First, Efficiency La
Page 140 and 141:
1. If you can reproduce the behavio
Page 142 and 143:
indices, errors will occur. Therefo
Page 144 and 145:
Understanding File FormatsThe refer
Page 146 and 147:
definitions that it finds. The firs
Page 148 and 149:
◆◆IloXmlReader creates a reader
Page 150 and 151:
Controlling Message ChannelsIn both
Page 152 and 153:
more calls to the message handling
Page 154 and 155:
Concert Technology Message Channels
Page 156 and 157:
Types of ILM Runtime LicensesILM ru
Page 158 and 159:
char *inststr = NULL;char *envstr =
Page 160 and 161:
The registerLicense Method for Java
Page 162 and 163:
not correct that problem either. In
Page 164 and 165:
In the Interactive Optimizer, you c
Page 166 and 167:
For models not in the current worki
Page 168 and 169:
◆◆In the .NET API, pass an inst
Page 171 and 172:
C H A P T E R9Solving LPs: Simplex
Page 173 and 174:
The symbolic names for these settin
Page 175 and 176:
When no candidates are present, the
Page 177 and 178:
solution; but examination of soluti
Page 179 and 180:
Then to later read an advanced basi
Page 181 and 182:
Table 9.5 PPriInd Parameter Setting
Page 183 and 184:
ILOG CPLEX ignores the coefficients
Page 185 and 186:
Numeric DifficultiesILOG CPLEX is d
Page 187 and 188:
esult is the same as would be obtai
Page 189 and 190:
automatically perturbs the variable
Page 191 and 192:
4. Consider alternate scalings.You
Page 193 and 194:
smaller in absolute value than the
Page 195 and 196:
exceptions are caught as well, and
Page 197 and 198:
C H A P T E R10Solving LPs: Barrier
Page 199 and 200:
The ILOG CPLEX Barrier Optimizer is
Page 201 and 202:
And then you call the solution rout
Page 203 and 204:
Here is an example of a log file fo
Page 205 and 206:
If solution values are large in abs
Page 207 and 208:
Normalized errors, for example, rep
Page 209 and 210:
◆ workmem in the Interactive Opti
Page 211 and 212:
est order. It may require more time
Page 213 and 214:
choice of starting-point heuristic
Page 215 and 216:
To see the current value of the col
Page 217 and 218:
C H A P T E R11Solving Network-Flow
Page 219 and 220:
◆◆l a , the lower bound, sets t
Page 221 and 222:
of the objective function calculate
Page 223 and 224:
then ILOG CPLEX will carry out such
Page 225 and 226:
-a 1 + a 2 - a 8 - a 9 + a 14 = 0-
Page 227 and 228:
C H A P T E R12Solving Problems wit
Page 229 and 230:
convex QPs, Q must be positive semi
Page 231 and 232:
A similar Java program using Concer
Page 233 and 234:
◆ qp indicates that you want ILOG
Page 235 and 236:
RootAlg parameter (QPMETHOD in the
Page 237 and 238:
ilolpex1.cpp counterpart. Here the
Page 239 and 240:
C H A P T E R13Solving Problems wit
Page 241 and 242:
Figure 13.2y(0, 1)(-1, 0)d(1, 0)xc(
Page 243 and 244:
Detecting Problem TypeILOG CPLEX de
Page 245 and 246:
COLUMNSMARK0000 'MARKER''INTORG'C15
Page 247 and 248:
C180 R100 159C180 R119 200C180 R120
Page 249 and 250:
QMATRIXC158 C158 1C158 C189 0.5C189
Page 251 and 252:
◆From the Callable Library, use t
Page 253:
Part IVDiscrete OptimizationThis pa
Page 256 and 257:
Stating a MIP ProblemA mixed intege
Page 258 and 259:
sections does not matter. To enter
Page 260 and 261:
◆milp, miqp, or miqcpindicating t
Page 262 and 263:
1. finding a succession of improvin
Page 264 and 265:
easonable amount of computation tim
Page 266 and 267:
If the solution to the relaxation s
Page 268 and 269:
anches taken so far in this dive. S
Page 270 and 271:
directives about the order in which
Page 272 and 273:
◆ Parameters Affecting Cuts on pa
Page 274 and 275:
◆●●IloCplex.getNcuts in the J
Page 276 and 277:
Relaxation Induced Neighborhood Sea
Page 278 and 279:
Table 14.10Parameters for Controlli
Page 280 and 281:
Library). If this process succeeds,
Page 282 and 283:
After you have solved a MIP, you wi
Page 284 and 285:
Table 14.13Settings of the MIP Disp
Page 286 and 287:
ILOG CPLEX also logs its addition o
Page 288 and 289:
◆ Parent specifies the NodeID of
Page 290 and 291: parameter settings are also worth c
Page 292 and 293: When you set a MIP cutoff value, IL
Page 294 and 295: memory. It also includes several op
Page 296 and 297: ◆◆●●at problem modification
Page 298 and 299: ◆In the Callable Library, use the
Page 300 and 301: ●●Then call CPXprimopt to optim
Page 302 and 303: ◆ The Incumbent and the Solution
Page 304 and 305: c17: x1 - y11 >= 0c18: x1 - y21 >=
Page 306 and 307: Populating the Solution PoolILOG CP
Page 308 and 309: NodesCuts/Node Left Objective IInf
Page 310 and 311: Note: The parameter to limit the nu
Page 312 and 313: Example: Using Populate after MIP O
Page 314 and 315: Limitations Due to Numeric Difficul
Page 316 and 317: Examining the Solution PoolIn the I
Page 318 and 319: For a sample of these methods or ro
Page 320 and 321: ◆◆In the Callable Library (C AP
Page 322 and 323: Then display the objective value of
Page 324 and 325: ◆ If you want to filter solutions
Page 326 and 327: ●●●In the C++ API, use the me
Page 328 and 329: NAME locationRNGFILTER f2 -inf 0tra
Page 330 and 331: continuous, a model containing one
Page 332 and 333: ◆The routine setPriorities sets t
Page 334 and 335: What Are Semi-Continuous Variables?
Page 336 and 337: With that model, now the applicatio
Page 338 and 339: Piecewise Linearity in ILOG CPLEXSo
Page 342 and 343: overlaps with an endpoint of two ot
Page 344 and 345: Figure 18.4400003000020000100000Fig
Page 346 and 347: in demand; in terms of this model,
Page 348 and 349: 348 ILOG CPLEX 11.0 — USER’ S M
Page 350 and 351: What Are Logical Constraints?For IL
Page 352 and 353: ◆◆Cplex.NotCplex.IfThenAgain, t
Page 356 and 357: In Concert Technology applications,
Page 360 and 361: Describing the ProblemThe problem i
Page 362 and 363: Notice that how much to use and buy
Page 364 and 365: Then use a for-loop to add the cons
Page 366 and 367: These lines (the action of the if-s
Page 368 and 369: Describing the ProblemThe problem i
Page 370 and 371: Stating Precedence ConstraintsIn ea
Page 372 and 373: Solving the ProblemAn emphasis on f
Page 374 and 375: What Is Column Generation?In colloq
Page 376 and 377: Solving this model with all columns
Page 378 and 379: Likewise, the application adds an a
Page 380 and 381: Pattern Generator ModelThe submodel
Page 382 and 383: Complete ProgramYou can see the ent
Page 384 and 385: your problem formulation caused thi
Page 386 and 387: To control the types of reductions
Page 388 and 389: What Is Unboundedness?Any class of
Page 390 and 391:
Callable Library use the advanced r
Page 392 and 393:
the conflict to arrive at a minimal
Page 394 and 395:
the IIS finder can, and often more.
Page 396 and 397:
Then you will see results like thes
Page 398 and 399:
Now view the entire conflict with t
Page 400 and 401:
The constraints in conflict with th
Page 402 and 403:
If a model contains more than one c
Page 404 and 405:
Immediately after that statement, i
Page 406 and 407:
◆ Groups in the Conflict Refiner
Page 408 and 409:
408 ILOG CPLEX 11.0 — USER’ S M
Page 410 and 411:
The infeasibility on which FeasOpt
Page 412 and 413:
Now the following lines invoke Feas
Page 414 and 415:
suggests decreasing the upper bound
Page 416 and 417:
416 ILOG CPLEX 11.0 — USER’ S M
Page 419 and 420:
C H A P T E R28User-Cut and Lazy-Co
Page 421 and 422:
However, there is an important dist
Page 423 and 424:
◆◆Through the routine CPXreadco
Page 425 and 426:
Here is an example of an MPS file e
Page 427 and 428:
C H A P T E R29Using GoalsThis chap
Page 429 and 430:
How Goals Are Implemented in Branch
Page 431 and 432:
In the Java API, a Fail goal is ret
Page 433 and 434:
This return statement returns an An
Page 435 and 436:
The Goal StackTo understand how goa
Page 437 and 438:
soon as they are enclosed in a goal
Page 439 and 440:
The global cut goal for lhs[i] ≤
Page 441 and 442:
If a node has multiple evaluators a
Page 443 and 444:
As this example is an extension of
Page 445 and 446:
C H A P T E R30Using Optimization C
Page 447 and 448:
Reference Documents about Informati
Page 449 and 450:
Query or Diagnostic CallbacksQuery
Page 451 and 452:
● Cplex.DisjunctiveCutCallback in
Page 453 and 454:
◆◆●●Cplex.HeuristicCallback
Page 455 and 456:
It is not customary to write such a
Page 457 and 458:
IloCplex::Callback mycallback = cpl
Page 459 and 460:
Here is the previous sample of code
Page 461 and 462:
◆◆cbdata, a pointer to ILOG CPL
Page 463 and 464:
conventions of the Interactive Opti
Page 465 and 466:
een added, it can be deleted by cal
Page 467 and 468:
Interaction Between Callbacks and I
Page 469 and 470:
C H A P T E R31Goals and Callbacks:
Page 471 and 472:
The only functionality that is not
Page 473 and 474:
C H A P T E R32Advanced Presolve Ro
Page 475 and 476:
once. All of the node relaxation so
Page 477 and 478:
- 5x1, + x2 ≤ 0 2y1, + y2, ≥ 1x
Page 479 and 480:
problem, the problem has a presolve
Page 481 and 482:
Modifying a ProblemThis section bri
Page 483 and 484:
C H A P T E R33Advanced MIP Control
Page 485 and 486:
value strictly greater than one. It
Page 487 and 488:
Cut CallbackThe next example we con
Page 489 and 490:
problem. Since branching involves a
Page 491 and 492:
C H A P T E R34Parallel OptimizersT
Page 493 and 494:
Threads and Performance Considerati
Page 495 and 496:
3. Call the parallel optimizer with
Page 497 and 498:
optimizer turns out to be the faste
Page 499 and 500:
0 0 3383.7784 16 4505.0000 Cuts: 35
Page 501 and 502:
I N D E XIndexAabsolute objective d
Page 503 and 504:
ole in converting LP to network flo
Page 505 and 506:
emoving from basis (C++ API) 62repr
Page 507 and 508:
CPX_PARAM_PCPX_PARAM_POLISHTIMEsolu
Page 509 and 510:
CPXcreateprob 467CPXcreateprob rout
Page 511 and 512:
CPXwcpxwarning message channel 151C
Page 513 and 514:
empty goal 431, 435end methodIloEnv
Page 515 and 516:
getDuals method (Java API) 88getMax
Page 517 and 518:
emove method (Java API) 94IloModele
Page 519 and 520:
ecords singularities 188relocating
Page 521 and 522:
from 218head 218sink 219source 219s
Page 523 and 524:
control callbacks and 453query call
Page 525 and 526:
primal reduction 385primal simplex
Page 527 and 528:
eturn statusBounded (Java API) 81Er
Page 529 and 530:
solvingdiet problem (Java API) 82mo
Page 531 and 532:
arrier 208WorkMem 293WorkMem parame
show all

ILOG CPLEX 11.0 User's Manual

Create successful ePaper yourself

Delete template?

Save as template?