Evolution and Optimum Seeking

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220 Comparison of Direct Search Strategies for Parameter Optimization 3870 7017 7013 5207 5207 4849 2501 4808 4790 3695 3695 2509 27.6 101.0 91.2 42.4 53.1 52.5 17.3 66.3 64.4 30.1 35.3 25.5 1 2 2 1 1 2 1 2 2 1 1 1 1 1 1 - 1 2 1 1 1 1 1 - 1 2 1 1 1 1 1 - 1 2 1 1 1 1 1 - 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 2 38703 35300 35303 49132 49132 47767 24001 26415 26332 35247 35247 42993 2670 4740 4580 3680 4750 6720 1620 3600 3500 2600 3240 7890 1 1 1 1 1 1 1 1 1 1 1 10562 11244 11218 15111 15111 14633 7201 8073 8046 11270 11270 7204 221 430 439 332 440 476 153 345 345 291 319 240 2 1.1 3.1 3.2 3.3 3.4 3.5 3.6 3.7 1.1 3.1 3.2 3.3 3.4 3.5 3.6 3.7 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 3 10 4 1 1 1 2 1 2 10 4 1 1 1 1 158 415 1250 630 192 85 192 183 85 198 745 321 140 82 138 87 0.10 0.34 0.84 3.96 0.12 0.08 0.14 0.18 0.04 0.16 0.56 2.08 0.10 0.06 0.12 0.06 1 1 1 2 1 2 1 1 1 1 1 2 1 2 1 1 1 5 9 9 1 1 1 1 5 9 24 1 1 1 458 1993 3543 2143 589 589 296 271 1285 2142 3178 436 437 264 0.51 3.38 5.54 136.00 0.68 1.10 0.48 0.30 2.22 3.52 199.00 0.56 0.64 0.42 1 1 1 2 1 2 1 1 1 1 1 2 1 2 1 1 1 4 6 1 1 1 1 4 6 1 1 1 1242 4441 6347 1715 1715 816 781 2816 4012 1274 1274 785 3.14 18.70 28.60 4.68 6.98 3.00 1.80 12.00 17.60 3.20 4.62 2.80 1 1 1 - 1 2 1 1 1 1 1 - 1 2 1 1 1.1 3.1 3.2 3.3 3.4 3.5 3.6 3.7 1 1 1 1 1 2 1 1 1 3 10 4 1 1 1 2 158 415 1250 630 192 85 192 183 0.13 0.38 1.04 4.26 0.14 0.08 0.18 0.18 1 1 1 2 1 2 1 1 1 5 9 18 1 1 1 456 1997 3470 4381 567 567 296 0.53 4.12 5.90 286.00 0.72 1.10 0.48 1 1 1 2 1 2 1 1 1 4 6 1 1 1 1242 4270 6472 1709 1709 816 3.07 18.90 27.50 4.68 2.92 6.92 1 1 1 - 1 2 1 1 3870 7041 7139 5193 5193 4818 26.5 93.5 94.5 40.0 53.9 52.3 1 1 1 - 1 2 1 1 1 1 1 1 1 2 10562 11244 11218 15127 15127 14634 210 434 435 334 428 478 1 1 1 - 1 2 1 1 1 1 1 1 1 2 38701 35300 35303 49255 49255 47799 2500 4590 4730 3670 4590 6770 1 2 2 1 1 2 Probl. case cycles OFC time case cycles OFC time case cycles OFC time case cycles OFC time case cycles OFC time case cycles OFC time n = 3 n = 10 n = 30 n = 100 n = 300 n = 1000 Table 6.10 continued : Coordinate strategies FIBO, GOLD, LAGR (from top to bottom)
Numerical Comparison of Strategies 221 Table 6.10 continued : HOJE - Direct search of Hooke <strong>and</strong> Jeeves time OFC cycles case time OFC cycles case time OFC cycles case time OFC cycles case time OFC cycles case time OFC cycles case Probl. n = 3 n = 10 n = 30 n = 100 n = 300 n = 1000 1460 5710 23505 42004 12 21 21 1 1 100 784 4954 18612 9 33 32 1 1 2.37 4.82 352 352 2 2 1 1 0.43 0.74 168 168 3 3 3 1 1 0.06 0.08 48 48 3 3 3 1 1 0.02 0.02 20 20 4 4 1 1 1.1 3.1 5440 42004 1 - 758 17714 1 - 4.78 352 2 1 - 168 0.74 130 7493 4210.00 3 168 0.48 1 1 0.10 48 1 1 0.02 0.12 20 19 4 3 1 1 3.2 3.3 1700 23505 12 119 4954 9 2.86 352 16.70 0.06 237 48 12 3 1 2 1 2 2 1 2 1 2 1 2 0.02 0.18 20 4 1 2 3.4 3.5 0.70 0.62 151 20 2160 2410 23505 23505 12 12 1 1 153 137 4954 4954 9 2 1 1 3.72 3.68 352 352 2 2 1 1 168 168 3 3 1 1 0.08 0.08 48 48 3 3 1 1 0.02 0.02 20 25 4 4 1 1 3.6 3.7 ROSE - Rosenbrock method with Gram-Schmidt orthogonalization time CFC OFC orth. case time CFC OFC orth. case time CFC OFC orth. case time CFC OFC orth. case Probl. (max) n = 75 n = 30 n = 10 n = 3 145 899 1 1 1 1.18 121 0 3 3 1 1 1 0.91 120 2 3 4 1 1 1 0.08 27 1 3 5 3 2 2 2 2 1 1 1 1 1 1 1 1 1.1 242 342 2352 3879 2 3 4 18.70 19.10 575 575 1.36 2.10 161 282 0.14 0.30 41 98 3.1 3.2 - 1 1690.00 3077 121 8 0 1 1 5.02 1.98 73 1 4 1 1 0.40 0.14 45 44 3.3 3.4 4660 728 29 0.12 1 3 2.02 1 0 121 1 44 0.14 1 4 279 2.06 1 0 121 1.32 1 47 83059 4830 29 0.10 1 2 152 1.10 1 0 121 1.32 1 3 1871 236 1 1 28 101 0.16 1 1 91 1128 1.60 1 1 241 7861 17.30 1 0 226 33448 85 1 1 28 28 0.10 1 6 427 309 3.46 1 1 512 215 9.76 1 2 2833 969 194 83059 7337 47 9 1.20 1.36 279 295 3.5 3.6 3.7 3.8 3.9 - 1 8 268 367 1.16 2 12 2953 9766 30.50 2 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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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),
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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
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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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