Evolution and Optimum Seeking

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224 Comparison of Direct Search Strategies for Parameter Optimization Table 6.10 continued : SIMP - Simplex method of Nelder <strong>and</strong> Mead (with restart rule) time OFC restarts case time OFC restarts case time OFC restarts case time OFC restarts case time OFC restarts case Probl. n = 135 (max) n = 100 n = 30 n = 10 n = 3 5270 1 5142 1 4 4 - - - 862 1789 0 1 0 1 1 1 - 37.4 664 0 1 1.49 138 0 1 1 1 1 1 1 0.09 28 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1.1 25800 6190 42099 10082 1.56 1 0 1514 95.2 3.54 1 0 1277 79.7 12.10 1 1 12936 8130.0 1.62 1 7 17357 1100.0 206.00 2 547 101142 4030.0 1.68 1 7 17357 1140.0 39.10 1 181 21387 1020.0 152 300 163 163 22362 163 3968 0 0 0 0 185 0 48 0.10 0.12 34 40 3.1 3.2 4 - 0.28 0.08 0.08 32 25 32 3.3 3.4 3.5 - - 4 4 1 1 0.08 0.08 25 28 1 1 3.6 3.7 COMP - Complex method of Box ( no. of vertices = 2n ) time OFC case time CFC OFC case time CFC OFC case time CFC OFC case Probl. n = 95 (max) n = 30 n = 10 n = 3 11000 13100 14902 17397 13300 17431 32196 25300 1.1 1 69 0.22 1 535 6.72 1 2621 211 1 3.1 1 76 0.28 1 691 9.30 1 2770 247 1 3.2 1 83 0.28 1 527 6.99 1 3092 259 1 3.3 1 58 0.55 1 966 74.30 2(4) 19407 12100 - 3.4 1 74 0.24 1(2) 529 6.71 1(2) 4722 402 4 3.5 1 57 0.23 1 1266 17.20 2(4) 16936 1450 4 3.6 1 85 0.32 1 556 7.34 1(2) 9011 781 4 3.7 1 76 0.30 1 587 7.68 1 9537 840 1 3.8 1 40 186 0.33 1 207 4680 8.32 1 1041 75867 240 4 3.9 1 35 44 0.19 1 384 600 8.46 2 2622 4508 357 - 3.10 1 33 208 0.25 1(4) 486 8919 12.10 4 -
Numerical Comparison of Strategies 225 Table 6.10 continued : EVOL - (1+1) evolution strategy time CFC OFC mutations case time CFC OFC mutations case time CFC OFC mutations case Probl. n = 30 n = 3 n = 10 1 630 14.0 1 730 16.6 1 1041 26.5 1 7103 4060.0 1 10939 244.0 2 1 15769 365.0 1 1154 26.7 1 668 300 24629 46.2 1 1435 579 1436 34.5 4 1 224 1.74 1 221 1.88 1 537 4.46 1 2244 156.00 1 257 2.18 2 200 1.82 1 325 2.87 1 206 1.74 1 319 136 3980 5.80 1 388 148 389 3.33 1 59757 39076 802511 824.00 1 49 0.17 1 67 0.22 1 179 0.52 1 61 0.50 1 66 0.20 1 74 0.36 1 89 0.32 1 63 0.20 1 99 45 301 0.54 1 78 31 79 0.29 1 925 592 3913 4.06 1.1 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 time CFC OFC mutations case time CFC OFC mutations case time CFC OFC mutations case Probl. n = 100 n = 300 n = 1000 15600 17100 17200 23607 23374 23819 1 1 1 - - 2 - 4 - - - 1 6666 1310 1 7638 1700 1 6916 1480 - 4 2 4 1 14818 3060 1 3161 3129 1883309 14100 1 13035 5374 13036 2830 - 1 2192 149 1 2185 164 1 2208 188 - 1 47720 3320 2 1 37985 2710 1 5145 389 1 1696 998 255392 803 1 4633 1870 4634 336 - 1.1 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10
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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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Page 245 and 246: Summary and Outlook 237 numerical o
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Page 257 and 258: Chapter 8 References Glossary of ab
Page 259 and 260: References 251 Anscombe, F.J. (1959
Page 261 and 262: References 253 Bandler, J.W. (1969b
Page 263 and 264: References 255 Bendin, F. (1992), E
Page 265 and 266: References 257 Booth, A.D. (1955),
Page 267 and 268: References 259 Brent, R.P. (1971),
Page 269 and 270: References 261 Carroll, C.W. (1961)
Page 271 and 272: References 263 Courant, R., D. Hilb
Page 273 and 274: References 265 Davies, M., I.J. Whi
Page 275 and 276: References 267 Dvoretzky, A. (1956)
Page 277 and 278: References 269 Fiacco, A.V. (1974),
Page 279 and 280: References 271 Fogel, L.J., A.J. Ow
Page 281 and 282: 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
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356 Appendix A Problem 2.44 As Prob
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358 Appendix A Figure A.29: Graphic
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360 Appendix A Start: Figure A.31:
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362 Appendix A Problem 3.2 (analogo
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364 Appendix A Problem 3.6 (analogo
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366 Appendix A Minimum: x i =0 for
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368 Appendix B LF (integer) Return
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370 Appendix B 4. Convergence crite
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372 Appendix B 8. Function Z(S,R) T
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374 Appendix B 25 L(K)=L(K+1) L(10)
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376 Appendix B LF=2 (continued) No
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378 Appendix B man), vol. 15 of Pro
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380 Appendix B instead of T, as a p
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382 Appendix B 15 CONTINUE 16 FF=F(
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384 Appendix B SK(KS)=AMAX1(SM(I),A
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386 Appendix B B.3 ( + ) Evolution
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388 Appendix B EPSILO (one dimensio
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390 Appendix B GLEICH (real functio
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392 Appendix B GLEICH, and TKONTR d
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394 Appendix B 1 NL=1+N-NS NM=N-1 N
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396 Appendix B ZSTERN=ZBEST K=LBEST
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398 Appendix B C NEGATIVE (LETHAL M
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400 Appendix B C C PREPARE FINAL DA
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402 Appendix B 2 IF(.NOT.BKOMMA.OR.
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404 Appendix B 32 WRITE(KANAL,126)
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406 Appendix B DO 4 I=1,NX KI=KI1 I
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408 Appendix B Subroutine MINMAX MI
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410 Appendix B 2 IF(U.LT..965487131
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412 Appendix B parameters by multip
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414 Appendix B
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416 Appendix C - SIMP Simplex strat
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418 Appendix C C.3.2 How to Install
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420 Appendix C { } return(0.26*(x[0
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422 Appendix C 1 No recombination 2
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424 Appendix C 8e-07 8e-07 Initial
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426 Index Banach, S., 10 Bandler, J
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428 Index Coordinate strategy, 41{4
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430 Index Evolution strategy, 3, 6,
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432 Index Graves, R.L., 23 Great de
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434 Index Khurgin, Ya.I., 89 Kiefer
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436 Index Michie, D., 102 Mickey, M
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438 Index Parkinson, J.M., 61 Parta
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440 Index Rotating coordinates meth
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442 Index Storey, C., 23, 50, 54 St
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444 Index Wilson, S.W., 103 Witt, U
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