Evolution and Optimum Seeking

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222 Comparison of Direct Search Strategies for Parameter Optimization Table 6.10 continued : DSCG - Davies-Swann-Campey method with Gram-Schmidt orthonormalization time OFC lin. search orth. case time OFC lin. search orth. case time OFC lin. search orth. case time OFC lin. search orth. case Probl. n = 75 (max) n = 30 n = 10 n = 3 6.10 338 75 0 1 1 1 1 1 - 1 1 1 1 1.18 136 30 0 1 3 28 0 0 0 0 1 1 1 2 1 1 1 1 0.20 56 10 0 2 3 8 0 0 0 0 1 1 1 1 1 1 1 1 0.04 20 0 1 3 2 0 1 0 1 1 1 1 1 1 1 1 1 1.1 78.40 563 150 7.58 321 91 0.86 119 30 0.08 32 3 6 3.1 79.00 563 150 18.70 2030.00 1.18 1.58 1.48 1.26 535 3366 136 6.68 78.20 7.08 75 150 75 150 0 1 0 1 165 151 1087 30 30 30 30 1.12 26.00 0.20 0.20 0.22 0.22 147 377 56 47 56 56 40 112 10 10 10 10 0.12 0.28 0.06 0.08 0.06 0.10 48 35 20 30 20 30 12 9 3 6 3.2 3.3 3.4 3.5 3.6 76.90 338 490 338 564 136 136 3 6 3.7 DSCP - Davies-Swann-Campey method with Palmer orthonormalization time OFC lin. search orth. case time OFC lin. search orth. case time OFC lin. search orth. case time OFC lin. search orth. case time OFC lin. search orth. case Probl. n = 95 (max) n = 75 (max) n = 30 n = 10 n = 3 9.49 448 95 6.10 338 75 0 1 1 1 1 1 - 1 1 1 1 1.16 136 30 0 1 1 1 1 1 1 1 1 0.22 56 10 0 2 3 8 0 0 0 0 1 1 1 1 1 1 1 1 0.04 20 3 6 12 9 3 6 3 6 0 1 3 2 0 1 0 1 1 1 1 1 1 1 1 1 1.1 11.90 23.20 428 713 95 190 0 0 1 1 1 1 - 1 1 1 1 14.90 14.80 563 563 150 150 3.58 6.56 321 527 91 151 932 30 30 30 30 1 3 0.58 0.72 119 147 30 40 0.08 0.12 32 48 3.1 3.2 1670.00 9.96 9.22 11.1 11.2 428 334 428 428 95 95 95 95 0 0 0 0 6.36 12.90 7.18 75 150 75 0 1 0 1 1.28 1.60 1.36 1.26 2924 136 165 136 136 28 0 0 13.70 338 490 338 564 150 0 0 25.50 0.20 0.20 0.22 0.22 383 56 47 56 56 112 10 10 10 10 0.28 0.06 0.08 0.06 0.08 35 20 31 20 30 3.3 3.4 3.5 3.6 3.7
Numerical Comparison of Strategies 223 Table 6.10 continued : POWE - Powell’s method of conjugate directions time OFC lin. search iterations case time OFC lin. search iterations case time OFC lin. search iterations case time OFC lin. search iterations case time OFC lin. search iterations case Probl. n = 135 (max) n = 100 n = 30 n = 10 n = 3 8.60 407 135 1 1 1 1 1 1 - 1 2 1 3 3.72 202 100 1 2 2 1 1 1 3 1 2 1 3 0.60 92 30 1 1 1 1 1 1 2 1 3 0.12 32 10 1 2 3 9 2 1 1 1 1 1 2 1 3 0.02 11 3 7 11 7 3 3 3 13 1 2 3 2 1 1 1 4 1 1 1 1 1 2 1 1 1.1 15.50 15.50 541 541 135 135 15.10 15.00 701 701 200 200 304 2.50 288 2.32 1963 1100.00 152 0.94 91 91 3 3 23 1 0.36 0.46 21 32 0.08 0.12 32 38 3.1 3.2 16.20 811 135 1 7.82 502 100 1 700 30 16.90 0.44 84 112 257 128 96 20 19.00 811 135 1 8.74 502 100 1 1.14 152 30 1 0.48 128 20 2 0.18 0.06 0.14 0.06 0.46 23 20 55 20 166 3.3 3.4 3.5 3.6 3.7 DFPS - Stewart’s modification of the Davidon-Fletcher-Powell method time OFC iterations case time OFC iterations case time OFC iterations case time OFC iterations case time OFC iterations case Probl. n = 180 (max) n = 100 n = 30 n = 10 n = 3 9.56 364 3.19 204 0.32 64 1 1 1 1 1 1 2 1 2 0.06 24 1 3 4 4 1 1 1 1 1 1 2 1 1 0.02 1 1 1 1 1 1 2 1 1 1.1 84.40 1274 22.00 1 5 5 1 1 1 - 1 2 1 2 1.82 4 4 45 1 0.20 0.06 3 4 2 3.1 84.20 1274 1 6 6 23.10 612 612 10.20 364 1 1 1 1 - 1 2 1 2 3.34 204 1 1.78 932.00 0.34 160 160 1640 64 0.30 3.96 0.06 48 65 61 24 0.06 0.12 0.02 0.02 0.02 0.26 10 20 25 15 10 11 10 101 1 1 11.80 364 1 3.92 204 1 0.40 7.84 64 1 0.08 1.42 24 780 15 307 1 16 1 15 3.2 3.3 3.4 3.5 3.6 3.7
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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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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
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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
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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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