Evolution and Optimum Seeking

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Index 429 DFP-Stewart strategy, 78{81, 177, 178, 184, 189, 195, 200, 201, 209, 210, 219, 228{231, 337, 341, 343, 363, 364 Diblock search, 33 Dichotomous search, 27, 29, 33, 39 Dickinson, A.W., 93, 98, 174 Dieter, U., 116 Di erential calculus, 2, 11 Digital computers, 6, 10{12, 14, 15, 32, 33, 92, 99, 110, 173, 236 Dijkhuis, B., 37 Dinkelbach, W., 17 Diploidy, 106, 148 Direct optimization, 13{15, 20 Direct search strategies, 40{65, 68, 90 Directed random search, 98 Discontinuity, 13, 23, 25, 42, 88, 91, 116, 176, 211, 214, 231, 236, 341, 349 Discovery, 2 Discrete distribution, 110, 243 Discrete optimization, 11, 18, 32, 39, 44, 64, 88, 91, 108, 152, 160, 243, 247 Discrete recombination, 148, 153, 156 Discretization, see parameterization Divergence, 35, 76, 169 Dixon, L.C.W., 15, 23, 29, 34, 35, 58, 71, 76, 78, 81{83 Dobzhansky, T., 101 Dominance and recessiveness, 101, 106, 148 Dowell, M., 35 Draper, N.R., 7, 65, 69 Drenick, R.F., 48 Drepper, F.R., 103, 246 Drucker, H., 61 DSC strategy, 54{57, 74, 89, 177, 183, 188, 194, 200{202, 209, 228{230, 362, 363 Dubovitskii, A.Ya., 11 Dueck, G., 98, 164 Du n, R.J., 14 Dunham, B., 102 Dvoretzky, A.,20 Dynamic optimization, 7, 9, 10, 48, 64, 89{91, 94, 99, 102, 245, 248 Dynamic programming, 11, 12, 18, 149 Ebeling, W., 102, 163 Edelbaum, T.N., 13 Edelman, G.B., 103 E ectivity of a method, see robustness E ciency of a method, see rate of convergence Eigen, M., 101 Eigenvalue problems, 5 Eigenvalues of a matrix, 76, 83, 326 Eisenberg, M.A., 239 Eldredge, N., 148 Elimination methods, see interval division methods Elitist strategy, 157 Elkin, R.M., 44, 66, 67 Elliott, D.F., 83 Ellipsoid method, 166 Emad, F.P., 98 Emery, F.E., 48, 87 Engelhardt, M., 20 Engeli, M., 43 Enumeration methods, see grid method Epigenetic apparatus, 153, 154 Equation, di erential, 15, 65, 68, 93, 246, 345, 346 Equations, system of, 5, 13, 14, 23, 39, 65, 66, 75, 83, 93, 172, 235, 336 Equidistant search, see grid method Erlicki, M.S., 48 Ermakov, S., 19 Ermoliev, Yu., 19, 90 Errors, computational, 47, 174, 205, 209, 210, 212, 219, 228, 229, 236 Euclid of Alexandria, 32 Euclidean norm, 167, 335 Euclidean space, 10, 24, 49, 97 Euler, L., 2, 15 Even block search, 27 Evolution, cultural, 244 Evolution, organic, 1, 3, 100, 102, 105, 106, 109, 142, 153, 237, 238
430 Index Evolution strategy, 3, 6, 7, 16, 105{151, 168, 173, 175, 177, 179, 200, 203, 210, 213, 219, 228{230, 232{235, 248, 333, 337, 350, 354, 355, 359, 361, 364, 365, 367, 413, see also two membered and multimembered evolution strategies Evolution strategy, asynchronous parallel, 248 Evolution strategy, parallel, 248 Evolution strategy, 1=5 success rule, 110, 112, 114, 116, 118, 142, 200, 213{ 215, 237, 349, 361 Evolution strategy (1+1), 105{119, 125, 163, 177, 185, 191, 200, 203, 212, 213, 216, 217, 228, 231{233, 328, 349, 363 Evolution strategy (1+ ), 123, 134, 145 Evolution strategy (1 , ), 145 Evolution strategy (10 , 100), 177, 186, 191, 200, 203, 211{215, 217, 228, 231{233 Evolution strategy ( +1), 119 Evolution strategy ( + ), 119 Evolution strategy ( , ), 119, 145, 148, 238, 244, 248 Evolution strategy ( ), 247 Evolution, synthetic theory, 106 Evolutionary algorithms, 151, 152, 161 Evolutionary computation, 152 Evolutionary operation, see EVOP method Evolutionary principles, 3, 100, 106, 118, 146, 244 Evolutionary programming, 151 Evolutionism, 244 EVOP method, 6, 7, 9, 64, 68, 69, 89, 101 Experimental optimization, 6{9, 36, 44, 68, 89, 91, 92, 95, 110, 113, 245, 247, see also design and analysis of experiments Expert system, 248 Extreme value controller, see optimizer Extremum, see minimum Faber, M.M., 18 Fabian, V., 20, 90 Factorial design, 38, 58, 65, 68, 246 Faddejew, D.K. and Faddejewa, W.N., 27, 67, 240 Fagiuoli, E., 96 Falkenhausen, K. von, 246 Favreau, R.F., 95, 96, 98, 100 Feasible region, 8, 9, 12, 16, 17, 25, 101 Feasible region, not connected, 217, 239, 360 Feasible starting point, search for, 62, 91, 115 Feistel, R., 102, 163 Feldbaum, A.A., 6, 9, 88{90, 99 Fend, F.A., 48 Fiacco, A.V., 16, 76, 81, 115, see also SUMT method Fibonacci division, 29{32, 38, 177, 178, 181, 187, 192, 200, 202 Fielding, K., 83 Finiteness of a sequence of iterations, 68, 166, 172 Finkelstein, J.J., 18 Fisher, R.A., 7 Fletcher, R., 24, 38, 68{71, 74, 77, 80{84, 97, 170, 171, 204, 205, 335, 349 Fletcher-Powell strategy, see DFP strategy Fletcher-Reeves strategy, 69, 70, 78, 170{ 172, 204, 233, see also conjugate gradients Flood, M.M., 68, 89 Floudas, C.A., 91 Fogarty, L.E., 68 Fogel, D.B., 151 Fogel, L.J., 102, 105, 151 Forrest, S., 152 Forsythe, G.E., 34, 66, 67 Fox, R.L., 23, 34, 205 Frankhauser, P., 246 Frankovic, B., 9 Franks, R., 95, 96, 98, 100 Fraser, A.S., 152
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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
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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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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
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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: 428 Index Coordinate strategy, 41{4
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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