Evolution and Optimum Seeking

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( + ) <strong>Evolution</strong> Strategy KORR 395 C 8 DO 8 I=1,N X(I)=X(I)+Y(I) IF(IFALLK.GT.0) GOTO 9 C C IF THE STARTING POINT IS NOT FEASIBLE, EACH C MUTATION IS CHECKED AT ONCE TO SEE WHETHER A C FEASIBLE VECTOR HAS BEEN FOUND. THE SEARCH ENDS C C WITH IFALLK = 0 IF THIS IS SO. Z=ZULASS(N,M,X,RESTRI) IF(Z)40,40,12 9 IF(M.EQ.0) GOTO 11 IF(.NOT.BLETAL(N,M,X,RESTRI)) GOTO 11 C C IF A MUTATION FROM A FEASIBLE STARTING POINT C RESULTS IN A NON-FEASIBLE X VECTOR, THEN THE STEP C SIZES ARE REDUCED (ON THE ASSUMPTION THAT THEY WERE C INITIALLY TOO LARGE) IN ORDER TO AVOID THE C THE CONSUMPTION OF EXCESSIVE TIME IN DEFINING THE C C THE FIRST PARENT GENERATION. DO 10 I=1,NS 10 S(I)=S(I)*.5 GOTO 5 11 Z=ZIELFU(N,X) 12 IF(Z.GT.ZBEST) GOTO 13 ZBEST=Z LBEST=L-1 DSMAXI=DSMAXI*ALOG(2.) 13 CALL SPEICH 1((L-1)*NZ,BKORRL,EPSILO,N,NS,NP,NY,Z,X,S,P,Y) C C C STORE PARENT DATA IN ARRAY Y. IF(KONVKR.GT.1) Z1=Z1+Z 14 C CONTINUE C THE INITIAL PARENT GENERATION IS NOW COMPLETE. C ZSTERN AND XSTERN, WHICH HOLD THE BEST VALUES, ARE C OVERWRITTEN WHEN AN IMPROVEMENT OF THE INITIAL C C SITUATION IS OBTAINED. IF(LBEST.EQ.0) GOTO 16
396 Appendix B ZSTERN=ZBEST K=LBEST*NZ DO 15 I=1,N 15 XSTERN(I)=Y(K+I) 16 L1=IELTER L2=0 IF(KONVKR.GT.1) KONVZ=0 C C ALL INITIALIZATION STEPS COMPLETED AT THIS POINT. C EACH FRESH GENERATION NOW STARTS AT LABEL 17. C 17 L3=L2 L2=L1 L1=L3 IF(M.GT.0) L3=0 LMUTAT=0 C C LMUTAT IS THE MUTATION COUNTER WITHIN A GENERATION, C WHILE L3 IS THE COUNTER FOR LETHAL MUTATIONS WHEN C THE PROBLEM INVOLVES CONSTRAINTS. C IF(BKOMMA) GOTO 18 C C IF BKOMMA=.FALSE. HAS BEEN SELECTED, THE PARENTS C MUST BE INCORPORATED IN THE SELECTION. THE DATA FOR C THESE ARE TRANSFERRED FROM THE FIRST (OR SECOND) C PART OF THE ARRAY Y TO THE SECOND (OR FIRST) PART. C IN THIS CASE THE WORST INDIVIDUAL MUST ALSO BE C KNOWN, THIS IS REPLACED BY THE FIRST BETTER C DESCENDANT. C CALL UMSPEI 1(L1*NZ,L2*NZ,IELTER*NZ,NY,Y) CALL MINMAX 1(-1.,L2,NZ,ZSCHL,LSCHL,IELTER,NY,Y) C C THE GENERATION OF EACH DESCENDANT STARTS AT LABEL 18 C 18 K1=L1+IELTER*GLEICH(D) C C RANDOM CHOICE OF A PARENT OR OF A PAIR OF PARENTS C IN ACCORDANCE WITH THE VALUE CHOSEN FOR IREKOM. IF C IREKOM=3 OR IREKOM=5, THE CHOICE OF PARENTS IS MADE C WITHIN GNPOOL.
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Evolution and Optimum Seeking Hans-
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vi Multiple Data) machines with man
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viii 3.2.1.6 Complex Strategy of Bo
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Chapter 1 Introduction There is sca
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Introduction 3 simple matter to col
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Chapter 2 Problems and Methods of O
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Particular Problems and Methods of
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Other Special Cases 19 with expecta
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Other Special Cases 21 parts of the
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Chapter 3 Hill climbing Strategies
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One Dimensional Strategies 25 then
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One Dimensional Strategies 27 Even
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One Dimensional Strategies 29 The b
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One Dimensional Strategies 31 F(x)
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One Dimensional Strategies 33 For t
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One Dimensional Strategies 35 It is
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One Dimensional Strategies 37 F P F
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Multidimensional Strategies 39 the
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Multidimensional Strategies 41 asch
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Multidimensional Strategies 43 e 2
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Multidimensional Strategies 45 Step
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Multidimensional Strategies 47 Numb
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Multidimensional Strategies 49 wher
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Multidimensional Strategies 53 Numb
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Multidimensional Strategies 55 The
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Multidimensional Strategies 57 Anum
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Multidimensional Strategies 61 Iter
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Multidimensional Strategies 63 (If
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Multidimensional Strategies 65 eval
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Multidimensional Strategies 67 The
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Multidimensional Strategies 69 devi
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Multidimensional Strategies 71 spec
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Multidimensional Strategies 73 othe
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Multidimensional Strategies 75 anot
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Multidimensional Strategies 77 3.2.
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Multidimensional Strategies 81 Brow
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Multidimensional Strategies 83 (197
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Multidimensional Strategies 85 meth
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Chapter 4 Random Strategies One gro
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Random Strategies 89 parts is taken
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Random Strategies 91 Pardalos and R
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Random Strategies 93 to write the n
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Random Strategies 95 the expectatio
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Random Strategies 97 maintained at
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Random Strategies 99 works entirely
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Random Strategies 101 the principle
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Random Strategies 103 out, a limite
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Chapter 5 Evolution Strategies for
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The Two Membered Evolution Strategy
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A Multimembered Evolution Strategy
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Genetic Algorithms 151 too is the c
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Genetic Algorithms 153 mean objecti
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Genetic Algorithms 155 p( ∆x) 1 1
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Genetic Algorithms 157 out any chan
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Genetic Algorithms 159 Average Numb
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Simulated Annealing 161 There are t
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Tabu Search and Other Hybrid Concep
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Chapter 6 Comparison of Direct Sear
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Theoretical Results 167 Oettli, 196
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Theoretical Results 169 where 0
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Theoretical Results 171 tions. Simi
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Numerical Comparison of Strategies
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Core storage required 233 term \cor
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Chapter 7 Summary and Outlook So, i
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Summary and Outlook 237 numerical o
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Summary and Outlook 239 considerabl
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Summary and Outlook 241 is called t
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Summary and Outlook 243 to the prod
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Summary and Outlook 245 tition betw
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Summary and Outlook 247 the experim
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Chapter 8 References Glossary of ab
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References 251 Anscombe, F.J. (1959
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References 253 Bandler, J.W. (1969b
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References 255 Bendin, F. (1992), E
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References 257 Booth, A.D. (1955),
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References 259 Brent, R.P. (1971),
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References 261 Carroll, C.W. (1961)
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References 263 Courant, R., D. Hilb
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References 265 Davies, M., I.J. Whi
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References 267 Dvoretzky, A. (1956)
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References 269 Fiacco, A.V. (1974),
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References 271 Fogel, L.J., A.J. Ow
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References 273 Gill, P.E., W. Murra
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References 275 Graves, R.L., P. Wol
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References 277 Heckler, R., H.-P. S
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References 279 Ho meister, F., H.-P
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References 281 Idelsohn, J.M. (1964
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References 283 Karnopp, D.C. (1966)
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References 285 Kochen, M., H.M. Has
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References 287 Kunzi, H.P., H.G. Tz
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References 289 LeCam, L.M., J. Neym
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References 291 Mamen, R., D.Q. Mayn
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294 References Miele, A., H.Y. Huan
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296 References Murray, W. (Ed.) (19
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298 References Oldenburger, R. (Ed.
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300 References Peschel, M. (1980),
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302 References Powell, M.J.D. (1970
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304 References Rechenberg, I. (1989
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306 References Rybashov, M.V. (1969
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308 References Schmidt, J.W., K. Ve
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310 References Shedler, G.S. (1967)
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312 References Steinbuch, K. (1971)
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314 References Tabak, D. (1970), Ap
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316 References Varela, F.J., P. Bou
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318 References White, L.J., R.G. Da
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320 References Youden, W.J., O. Kem
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322 References Glossary of Abbrevia
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324 References
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326 Appendix A Problem 1.2 Objectiv
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328 Appendix A Minimum: x =(3 0:5)
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330 Appendix A Figure A.3: Graphica
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332 Appendix A Several of the searc
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338 Appendix A Minimum: Start: Prob
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340 Appendix A Problem 2.20 Objecti
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342 Appendix A Problem 2.23 Objecti
Page 351 and 352: 344 Appendix A Start: x (0) i =10 f
Page 353 and 354: 346 Appendix A on the interval 0 y
Page 355 and 356: 348 Appendix A Problem 2.32 after B
Page 357 and 358: 350 Appendix A Constraints: Gj(x) =
Page 359 and 360: 352 Appendix A The constraints form
Page 361 and 362: 354 Appendix A Start: x (0) =(250 2
Page 363 and 364: 356 Appendix A Problem 2.44 As Prob
Page 365 and 366: 358 Appendix A Figure A.29: Graphic
Page 367 and 368: 360 Appendix A Start: Figure A.31:
Page 369 and 370: 362 Appendix A Problem 3.2 (analogo
Page 371 and 372: 364 Appendix A Problem 3.6 (analogo
Page 373 and 374: 366 Appendix A Minimum: x i =0 for
Page 375 and 376: 368 Appendix B LF (integer) Return
Page 377 and 378: 370 Appendix B 4. Convergence crite
Page 379 and 380: 372 Appendix B 8. Function Z(S,R) T
Page 381 and 382: 374 Appendix B 25 L(K)=L(K+1) L(10)
Page 383 and 384: 376 Appendix B LF=2 (continued) No
Page 385 and 386: 378 Appendix B man), vol. 15 of Pro
Page 387 and 388: 380 Appendix B instead of T, as a p
Page 389 and 390: 382 Appendix B 15 CONTINUE 16 FF=F(
Page 391 and 392: 384 Appendix B SK(KS)=AMAX1(SM(I),A
Page 393 and 394: 386 Appendix B B.3 ( + ) Evolution
Page 395 and 396: 388 Appendix B EPSILO (one dimensio
Page 397 and 398: 390 Appendix B GLEICH (real functio
Page 399 and 400: 392 Appendix B GLEICH, and TKONTR d
Page 401: 394 Appendix B 1 NL=1+N-NS NM=N-1 N
Page 405 and 406: 398 Appendix B C NEGATIVE (LETHAL M
Page 407 and 408: 400 Appendix B C C PREPARE FINAL DA
Page 409 and 410: 402 Appendix B 2 IF(.NOT.BKOMMA.OR.
Page 411 and 412: 404 Appendix B 32 WRITE(KANAL,126)
Page 413 and 414: 406 Appendix B DO 4 I=1,NX KI=KI1 I
Page 415 and 416: 408 Appendix B Subroutine MINMAX MI
Page 417 and 418: 410 Appendix B 2 IF(U.LT..965487131
Page 419 and 420: 412 Appendix B parameters by multip
Page 421 and 422: 414 Appendix B
Page 423 and 424: 416 Appendix C - SIMP Simplex strat
Page 425 and 426: 418 Appendix C C.3.2 How to Install
Page 427 and 428: 420 Appendix C { } return(0.26*(x[0
Page 429 and 430: 422 Appendix C 1 No recombination 2
Page 431 and 432: 424 Appendix C 8e-07 8e-07 Initial
Page 433 and 434: 426 Index Banach, S., 10 Bandler, J
Page 435 and 436: 428 Index Coordinate strategy, 41{4
Page 437 and 438: 430 Index Evolution strategy, 3, 6,
Page 439 and 440: 432 Index Graves, R.L., 23 Great de
Page 441 and 442: 434 Index Khurgin, Ya.I., 89 Kiefer
Page 443 and 444: 436 Index Michie, D., 102 Mickey, M
Page 445 and 446: 438 Index Parkinson, J.M., 61 Parta
Page 447 and 448: 440 Index Rotating coordinates meth
Page 449 and 450: 442 Index Storey, C., 23, 50, 54 St
Page 451: 444 Index Wilson, S.W., 103 Witt, U
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Evolution and Optimum Seeking

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