Global Optimization Toolbox User's Guide - MathWorks

More documents

Recommendations

Info

3 Using <strong>Global</strong>Search and MultiStart 3-84 Create 200 data points and responses. Use the values a =–3,b =1/4,c =1/2, and d = 1. Include random noise in the response. rng default % for reproducibility N = 200; % number of data points preal = [-3,1/4,1/2,1]; % real coefficients xdata = 5*rand(N,2); % data points ydata = fitfcn(preal,xdata) + 0.1*randn(N,1); % response data with noise Step 3. Set bounds and initial point. Set bounds for lsqcurvefit. There is no reason for d to exceed π in absolute value, because the sine function takes values in its full range over any interval of width 2π. Assume that the coefficient c must be smaller than 20 in absolute value, because allowing a very high frequency can cause unstable responses or spurious convergence. lb = [-Inf,-Inf,-20,-pi]; ub = [Inf,Inf,20,pi]; Set the initial point arbitrarily to (5,5,5,0). p0 = 5*ones(1,4); % Arbitrary initial point p0(4) = 0; % so the initial point satisfies the bounds Step 4. Find the best local fit. Fit the parameters to the data, starting at p0. [xfitted,errorfitted] = lsqcurvefit(fitfcn,p0,xdata,ydata,lb,ub) Local minimum possible. lsqcurvefit stopped because the final change in the sum of squares relative its initial value is less than the default value of the function tolerance. xfitted = -2.6149 -0.0238 6.0191 -1.6998 errorfitted = 28.2524
<strong>Global</strong>Search and MultiStart Examples lsqcurvefit found a local solution that is not particularly close to the model parameter values (–3,1/4,1/2,1). Step 5. Set up the problem for MultiStart. Create a problem structure so MultiStart can solve the same problem. problem = createOptimProblem('lsqcurvefit','x0',p0,'objective',fitfcn,... 'lb',lb,'ub',ub,'xdata',xdata,'ydata',ydata); Step6. Findaglobalsolution. Solve the fitting problem using MultiStart with 50 iterations. Plot the smallest error as the number of MultiStart iterations. ms = MultiStart('PlotFcns',@gsplotbestf); [xmulti,errormulti] = run(ms,problem,50) MultiStart completed the runs from all start points. All 50 local solver runs converged with a positive local solver exit flag. xmulti = -2.9852 -0.2472 -0.4968 -1.0438 errormulti = 1.6464 3-85
Page 1 and 2:
Global Optimization Toolbox User’
Page 3:
Revision History January 2004 Onlin
Page 6 and 7:
vi Contents 3 How to Write a Functi
Page 8 and 9:
viii Contents An Unsuccessful Poll
Page 10 and 11:
x Contents 6 Genetic Algorithm Usin
Page 12 and 13:
xii Contents 8 9 Bibliography .....
Page 14 and 15:
11 12 A Getting Started xiv Content
Page 16 and 17:
1 Introducing Global Optimization T
Page 18 and 19:
Page 20 and 21:
Page 22 and 23:
Page 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
2 Write Files for Optimization Func
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
3 Using GlobalSearch and MultiStart
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87: 3 Using GlobalSearch and MultiStart
Page 150 and 151: 4 Using Direct Search 4-2 What Is D
Page 152 and 153: 4 Using Direct Search 4-4 Choose so
Page 154 and 155: 4 Using Direct Search 4-6 Optimize
Page 156 and 157: 4 Using Direct Search 4-8 The reaso
Page 158 and 159: 4 Using Direct Search 4-10 Pattern
Page 160 and 161: 4 Using Direct Search 4-12 The algo
Page 162 and 163: 4 Using Direct Search 4-14 The prob
Page 164 and 165: 4 Using Direct Search 4-16 Note By
Page 166 and 167: 4 Using Direct Search 4-18 8*[0 -1]
Page 168 and 169: 4 Using Direct Search 4-20 2 1.5 1
Page 170 and 171: 4 Using Direct Search 4-22 The dist
Page 172 and 173: 4 Using Direct Search 4-24 Update c
Page 174 and 175: 4 Using Direct Search 4-26 Search T
Page 176 and 177: 4 Using Direct Search 4-28 3 Set th
Page 178 and 179: 4 Using Direct Search 4-30 Referenc
Page 180 and 181: 4 Using Direct Search 4-32 Pattern
Page 182 and 183: 4 Using Direct Search 4-34 - Set Ae
Page 184 and 185: 4 Using Direct Search 4-36 The uppe
Page 186 and 187:
4 Using Direct Search 4-38 if optim
Page 188 and 189:
4 Using Direct Search 4-40 Now, whe
Page 190 and 191:
4 Using Direct Search 4-42 Custom P
Page 192 and 193:
4 Using Direct Search 4-44 x = -4.7
Page 194 and 195:
4 Using Direct Search 4-46 MaxFunEv
Page 196 and 197:
4 Using Direct Search 4-48 You can
Page 198 and 199:
4 Using Direct Search 4-50 [-100...
Page 200 and 201:
4 Using Direct Search 4-52 0 −5
Page 202 and 203:
4 Using Direct Search 4-54 mesh and
Page 204 and 205:
4 Using Direct Search 4-56 Example:
Page 206 and 207:
4 Using Direct Search 4-58 2 Choose
Page 208 and 209:
4 Using Direct Search 4-60 Algorith
Page 210 and 211:
4 Using Direct Search 4-62 The most
Page 212 and 213:
4 Using Direct Search 4-64 To see t
Page 214 and 215:
4 Using Direct Search 4-66 With the
Page 216 and 217:
4 Using Direct Search 4-68 3 Run th
Page 218 and 219:
4 Using Direct Search 4-70 The firs
Page 220 and 221:
4 Using Direct Search 4-72 When you
Page 222 and 223:
4 Using Direct Search 4-74 Note For
Page 224 and 225:
4 Using Direct Search 4-76 Iter f-c
Page 226 and 227:
4 Using Direct Search 4-78 3 Run th
Page 228 and 229:
4 Using Direct Search 4-80 This tim
Page 230 and 231:
4 Using Direct Search 4-82 The patt
Page 232 and 233:
4 Using Direct Search 4-84 Best Obj
Page 234 and 235:
4 Using Direct Search 4-86 If x0 is
Page 236 and 237:
4 Using Direct Search 4-88 The same
Page 238 and 239:
4 Using Direct Search 4-90 The init
Page 240 and 241:
4 Using Direct Search 4-92 ylabel('
Page 242 and 243:
4 Using Direct Search 4-94 distance
Page 244 and 245:
4 Using Direct Search 4-96 if nargi
Page 246 and 247:
4 Using Direct Search 4-98 You can
Page 248 and 249:
4 Using Direct Search 4-100 outpt =
Page 250 and 251:
5 Using the Genetic Algorithm 5-2 W
Page 252 and 253:
5 Using the Genetic Algorithm 5-4 U
Page 254 and 255:
5 Using the Genetic Algorithm 5-6 T
Page 256 and 257:
5 Using the Genetic Algorithm 5-8 G
Page 258 and 259:
5 Using the Genetic Algorithm 5-10
Page 260 and 261:
Page 262 and 263:
Page 264 and 265:
Page 266 and 267:
Page 268 and 269:
Page 270 and 271:
Page 272 and 273:
Page 274 and 275:
Page 276 and 277:
Page 278 and 279:
Page 280 and 281:
Page 282 and 283:
Page 284 and 285:
Page 286 and 287:
Page 288 and 289:
Page 290 and 291:
Page 292 and 293:
Page 294 and 295:
Page 296 and 297:
Page 298 and 299:
Page 300 and 301:
Page 302 and 303:
Page 304 and 305:
Page 306 and 307:
Page 308 and 309:
Page 310 and 311:
Page 312 and 313:
Page 314 and 315:
Page 316 and 317:
Page 318 and 319:
Page 320 and 321:
Page 322 and 323:
Page 324 and 325:
Page 326 and 327:
Page 328 and 329:
Page 330 and 331:
Page 332 and 333:
Page 334 and 335:
Page 336 and 337:
Page 338 and 339:
Page 340 and 341:
Page 342 and 343:
Page 344 and 345:
Page 346 and 347:
Page 348 and 349:
Page 350 and 351:
Page 352 and 353:
Page 354 and 355:
Page 356 and 357:
Page 358 and 359:
Page 360 and 361:
Page 362 and 363:
Page 364 and 365:
Page 366 and 367:
6 Using Simulated Annealing 6-2 Wha
Page 368 and 369:
6 Using Simulated Annealing 6-4 Usi
Page 370 and 371:
6 Using Simulated Annealing 6-6 To
Page 372 and 373:
6 Using Simulated Annealing 6-8 Man
Page 374 and 375:
6 Using Simulated Annealing 6-10 Si
Page 376 and 377:
6 Using Simulated Annealing 6-12 Ho
Page 378 and 379:
6 Using Simulated Annealing 6-14 T
Page 380 and 381:
6 Using Simulated Annealing 6-16 Us
Page 382 and 383:
6 Using Simulated Annealing 6-18 op
Page 384 and 385:
6 Using Simulated Annealing 6-20 x,
Page 386 and 387:
6 Using Simulated Annealing 6-22
Page 388 and 389:
7 Multiobjective Optimization 7-2 W
Page 390 and 391:
7 Multiobjective Optimization 7-4 F
Page 392 and 393:
7 Multiobjective Optimization 7-6 U
Page 394 and 395:
7 Multiobjective Optimization 7-8 3
Page 396 and 397:
7 Multiobjective Optimization 7-10
Page 398 and 399:
Page 400 and 401:
Page 402 and 403:
8 Parallel Processing 8-2 Backgroun
Page 404 and 405:
8 Parallel Processing 8-4 Suppose,
Page 406 and 407:
8 Parallel Processing 8-6 reaches a
Page 408 and 409:
8 Parallel Processing 8-8 Implement
Page 410 and 411:
8 Parallel Processing 8-10 Run gamu
Page 412 and 413:
8 Parallel Processing 8-12 MultiSta
Page 414 and 415:
8 Parallel Processing 8-14 After yo
Page 416 and 417:
8 Parallel Processing 8-16 Parallel
Page 418 and 419:
8 Parallel Processing 8-18
Page 420 and 421:
9 Options Reference 9-2 GlobalSearc
Page 422 and 423:
9 Options Reference 9-4 run when th
Page 424 and 425:
9 Options Reference 9-6 If you spec
Page 426 and 427:
9 Options Reference 9-8 If MaxWaitC
Page 428 and 429:
9 Options Reference 9-10 In this se
Page 430 and 431:
9 Options Reference 9-12 - TolX —
Page 432 and 433:
9 Options Reference 9-14 the number
Page 434 and 435:
9 Options Reference 9-16 Note If yo
Page 436 and 437:
9 Options Reference 9-18 The search
Page 438 and 439:
9 Options Reference 9-20 Off or On
Page 440 and 441:
9 Options Reference 9-22 Specify
Page 442 and 443:
9 Options Reference 9-24 - TolFun
Page 444 and 445:
9 Options Reference 9-26 When Evalu
Page 446 and 447:
9 Options Reference 9-28 Option Ava
Page 448 and 449:
9 Options Reference 9-30 Option Ava
Page 450 and 451:
9 Options Reference 9-32 See “Set
Page 452 and 453:
9 Options Reference 9-34 To display
Page 454 and 455:
9 Options Reference 9-36 Selection
Page 456 and 457:
9 Options Reference 9-38 The functi
Page 458 and 459:
9 Options Reference 9-40 - Set Scal
Page 460 and 461:
9 Options Reference 9-42 The input
Page 462 and 463:
9 Options Reference 9-44 options =
Page 464 and 465:
9 Options Reference 9-46 - Selects
Page 466 and 467:
9 Options Reference 9-48 Your cross
Page 468 and 469:
9 Options Reference 9-50 space (gen
Page 470 and 471:
9 Options Reference 9-52 Enter @myf
Page 472 and 473:
9 Options Reference 9-54 Max Constr
Page 474 and 475:
9 Options Reference 9-56 Simulated
Page 476 and 477:
9 Options Reference 9-58 optimvalue
Page 478 and 479:
9 Options Reference 9-60 - @anneali
Page 480 and 481:
9 Options Reference 9-62 Stopping C
Page 482 and 483:
9 Options Reference 9-64 - 'iter'
Page 484 and 485:
9 Options Reference 9-66
Page 486 and 487:
10 Function Reference 10-2 GlobalSe
Page 488 and 489:
10 Function Reference 10-4 Genetic
Page 490 and 491:
10 Function Reference 10-6 Simulate
Page 492 and 493:
11 Class Reference 11-2
Page 494 and 495:
createOptimProblem 12-2 Purpose Cre
Page 496 and 497:
createOptimProblem 12-4 Output Argu
Page 498 and 499:
CustomStartPointSet 12-6 Get the fo
Page 500 and 501:
ga 12-8 x = ga(fitnessfcn,nvars,A,b
Page 502 and 503:
ga 12-10 If the problem has m linea
Page 504 and 505:
ga 12-12 where constraintfile.m is
Page 506 and 507:
ga 12-14 Exit Flag Meaning 1 Withou
Page 508 and 509:
ga 12-16 Examples Given the followi
Page 510 and 511:
gamultiobj 12-18 Purpose Find minim
Page 512 and 513:
gamultiobj 12-20 rngstate Optional
Page 514 and 515:
gamultiobj 12-22 end y(i,1) = x(i)
Page 516 and 517:
gamultiobj 12-24 See Also ga | gaop
Page 518 and 519:
gaoptimset 12-26 Purpose Create gen
Page 520 and 521:
gaoptimset 12-28 Option Description
Page 522 and 523:
Page 524 and 525:
Page 526 and 527:
GlobalOptimSolution 12-34 Copy Sema
Page 528 and 529:
GlobalSearch 12-36 'off' —Nodispl
Page 530 and 531:
GlobalSearch 12-38 Default: [] Star
Page 532 and 533:
CustomStartPointSet.list 12-40 Purp
Page 534 and 535:
RandomStartPointSet.list 12-42 Algo
Page 536 and 537:
MultiStart 12-44 OutputFcns A funct
Page 538 and 539:
MultiStart 12-46 Methods Copy Seman
Page 540 and 541:
patternsearch 12-48 Ax ≤ b Aeq
Page 542 and 543:
patternsearch 12-50 Exit Flag 1 Mea
Page 544 and 545:
patternsearch 12-52 x = 0.6667 1.33
Page 546 and 547:
psoptimget 12-54 Purpose Obtain val
Page 548 and 549:
psoptimset 12-56 Option Description
Page 550 and 551:
psoptimset 12-58 Option Description
Page 552 and 553:
GlobalSearch.run 12-60 Purpose Find
Page 554 and 555:
GlobalSearch.run 12-62 funcCount Nu
Page 556 and 557:
MultiStart.run 12-64 Purpose Run lo
Page 558 and 559:
MultiStart.run 12-66 output 2 At le
Page 560 and 561:
RandomStartPointSet 12-68 Purpose R
Page 562 and 563:
saoptimget 12-70 Purpose Values of
Page 564 and 565:
saoptimset 12-72 AnnealingFcn: @ann
Page 566 and 567:
saoptimset 12-74 Option Description
Page 568 and 569:
simulannealbnd 12-76 solver 'simula
Page 570 and 571:
simulannealbnd 12-78 x = 0.0392 -31
Page 572 and 573:
simulannealbnd 12-80 See Also ga |
Page 574 and 575:
A Examples A-2 GlobalSearch and Mul
Page 576 and 577:
A Examples A-4 Genetic Algorithm
Page 578 and 579:
A Examples A-6
Page 580 and 581:
Index global 5-97 local 5-97 minimi
show all

Global Optimization Toolbox User's Guide - MathWorks

Create successful ePaper yourself

Delete template?

Save as template?