Evolution and Optimum Seeking

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( + ) Evolution Strategy KORR 393 ready-made timing software. If this is given as a function, only its name needs to be supplied to KORR instead of TKONTR as a parameter. GLEICH Function for generating a uniform random number distribution in the range (0,1]. The structure must be: REAL FUNCTION GLEICH(D) where D is arbitrary. GLEICH is the value of the random number. The standard library usually includes a suitable program, in which case only the appropriate name has to be supplied to KORR. The other subroutines and functions are explained brie y in the program itself. --------------------------------------------------------- SUBROUTINE KORR 1(IELTER,BKOMMA,NACHKO,IREKOM,BKORRL,KONVKR,IFALLK, 2TGRENZ,EPSILO,DELTAS,DELTAI,DELTAP,N,M,NS,NP,NY, 3ZSTERN,XSTERN,ZBEST,X,S,P,Y,ZIELFU,RESTRI,GAUSSN, 4GLEICH,TKONTR,KANAL) LOGICAL BKOMMA,BKORRL,BFATAL,BKONVG,BLETAL DIMENSION EPSILO(4),XSTERN(N),X(N),S(NS),P(NP), 1Y(NY) COMMON/PIDATA/PIHALB,PIEINS,PIZWEI EXTERNAL RESTRI,GAUSSN,GLEICH IREKOX = IREKOM / 100 IREKOS = (IREKOM - IREKOX*100) / 10 IREKOP = IREKOM - IREKOX*100 - IREKOS*10 D = 0. CALL PRUEFG 1(IELTER,BKOMMA,NACHKO,IREKOM,BKORRL,KONVKR,TGRENZ, 2EPSILO,DELTAS,DELTAI,DELTAP,N,M,NS,NP,NY,KANAL, 3BFATAL) C C CHECK INPUT PARAMETERS FOR FORMAL ERRORS. C IF(BFATAL) RETURN C C PREPARE AUXILIARY QUANTITIES. TIMING MONITORED IN C ACCORDANCE WITH THE TKONTR FUNCTION FROM HERE C ONWARDS. C TMAXIM=TGRENZ+TKONTR(D) IF(.NOT.BKORRL) GOTO 1 PIHALB=2.*ATAN(1.) PIEINS=PIHALB+PIHALB PIZWEI=PIEINS+PIEINS
394 Appendix B 1 NL=1+N-NS NM=N-1 NZ=NY/(IELTER+IELTER) IF(M.EQ.0) GOTO 2 C C C CHECK FEASIBILITY OF INITIAL VECTOR XSTERN. IFALLK=-1 ZSTERN=ZULASS(N,M,XSTERN,RESTRI) IF(ZSTERN.GT.0.) GOTO 3 2 IFALLK=1 ZSTERN=ZIELFU(N,XSTERN) 3 CALL SPEICH 1(0,BKORRL,EPSILO,N,NS,NP,NY,ZSTERN,XSTERN,S,P,Y) C C THE INITIAL VALUES SUPPLIED BY THE USER ARE STORED C C C IN FIELD Y AS THE DATA OF THE FIRST PARENT. IF(KONVKR.GT.1) Z1=ZSTERN ZBEST=ZSTERN LBEST=0 IF(IELTER.EQ.1) GOTO 16 DSMAXI=DELTAS DPMAXI=AMIN1(DELTAP*10.,PIHALB) DO 14 L=2,IELTER C IF IELTER > 1, THE OTHER IELTER - 1 INITIAL VECTORS C ARE DERIVED FROM THE VECTOR FOR THE FIRST PARENT BY C MUTATION (WITHOUT SELECTION). THE STRATEGY C C PARAMETERS ARE WIDELY SPREAD. DO 4 I=1,NS 4 S(I)=Y(N+I) 5 IF(TKONTR(D).LT.TMAXIM) GOTO 501 IFALLK=-3 GOTO 42 501 IF(.NOT.BKORRL) GOTO 7 DO 6 I=1,NP 6 P(I)=Y(N+NS+I) 7 C CALL MUTATI 1(NL,NM,BKORRL,DSMAXI,DELTAI,DPMAXI,N,NS,NP,X,S,P, 2GAUSSN,GLEICH) C MUTATION IN ALL OBJECT AND STRATEGY PARAMETERS.
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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
Page 349 and 350: 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: 392 Appendix B GLEICH, and TKONTR d
Page 403 and 404: 396 Appendix B ZSTERN=ZBEST K=LBEST
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
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444 Index Wilson, S.W., 103 Witt, U
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