Evolution and Optimum Seeking

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( + ) Evolution Strategy KORR 407 RETURN 20 DO 21 I=1,NX 21 XX(I)=XX(I)+(Y((L1+IFIX(IELTER*GLEICH(D)))*NZ+NN+I) 1+Y((L1+IFIX(IELTER*GLEICH(D)))*NZ+NN+I))*.5 RETURN END --------------------------------------------------------- Subroutine SPEICH SPEICH transfers to the data pool Y for the parents of the next generation the data of a descendant representing a successful mutation (the object variables X and the strategy parameters S (and P, if used) together with the corresponding value of the objective function). A check is made that S (and P) fall within speci ed bounds. J is the address in array Y from which pointonwards the data are to be written and is provided by KORR. ZZ represents ZSTERN or Z, XX represents XSTERN or X. --------------------------------------------------------- SUBROUTINE SPEICH 1(J,BKORRL,EPSILO,N,NS,NP,NY,ZZ,XX,S,P,Y) LOGICAL BKORRL DIMENSION EPSILO(4),XX(N),S(NS),P(NP),Y(NY) COMMON/PIDATA/PIHALB,PIEINS,PIZWEI K=J DO 1 I=1,N K=K+1 1 Y(K)=XX(I) DO 2 I=1,NS K=K+1 2 Y(K)=AMAX1(S(I),EPSILO(1)) IF(.NOT.BKORRL) GOTO 4 DO 3 I=1,NP K=K+1 PI=P(I) IF(ABS(PI).GT.PIEINS) PI=PI-SIGN(PIZWEI,PI) 3 Y(K)=PI 4 K=K+1 Y(K)=ZZ RETURN END ---------------------------------------------------------
408 Appendix B Subroutine MINMAX MINMAX searches for the smallest or largest value in a series of values of the objective function held in an array. KORR calls this subroutine to determine the best or worst parent, in the rst case in order to transfer its data to the location ZBEST (and perhaps also ZSTERN and XSTERN) and in the other case in order to give space for a better descendant. C=1.0 initiates a search for the best (smallest) value of the function, while C=;1.0 does the same for the worst (largest) value. LL and NZ are auxiliary quantities used to transmit information on the position of the required values within array Y. ZM and LM contain the best (or worst) values of the objective function and the number of the corresponding parent minus one. --------------------------------------------------------- SUBROUTINE MINMAX 1(C,LL,NZ,ZM,LM,IELTER,NY,Y) DIMENSION Y(NY) LM=LL K1=LL*NZ+NZ ZM=Y(K1) IF(IELTER.EQ.1) RETURN K1=K1+NZ K2=(LL+IELTER)*NZ KM=LL DO 1 K=K1,K2,NZ KM=KM+1 ZZ=Y(K) IF((ZZ-ZM)*C.GT.0.) GOTO 1 ZM=ZZ LM=KM 1 CONTINUE RETURN END --------------------------------------------------------- Subroutine ABSCHA ABSCHA tests the convergence criterion. If KONVKR = 1 has been selected, the difference between the objective function values representing the best and worst parents (ZBEST and ZSCHL) must be less than the limits set by EPSILO(3) (absolute) or EP- SILO(4) (relative). Then the assignment BKONVG =.TRUE. is made. Alternatively, the current di erence ZSCHL-ZBEST is replaced by the change Z1;Z2 in the sum of all the parent objective function values occurring after KONVKR generations divided by IELTER. The Boolean variable BKONVG transmits the result of the convergence test to KORR.
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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
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344 Appendix A Start: x (0) i =10 f
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346 Appendix A on the interval 0 y
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348 Appendix A Problem 2.32 after B
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350 Appendix A Constraints: Gj(x) =
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352 Appendix A The constraints form
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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 and 402: 394 Appendix B 1 NL=1+N-NS NM=N-1 N
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: 406 Appendix B DO 4 I=1,NX KI=KI1 I
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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