Evolution and Optimum Seeking

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Index 439 Random exchange step, 88, 166 Random number generation, 115, 150, 210, 212, 217, 237 Random sequence, 87, 93 Random step length, 95, 96, 108 Random strategies, 3, 12, 19, 87{103, 105, 240 Random walk, 247 Randomness, 87, 91, 93, 237 Rank one methods, 82, 83, 172 Raphson, J., see Newton-Raphson method Rappl, G., 118 Raster method, see grid method Rastrigin, L.A., 93, 95, 96, 98, 99 Rate of convergence, 7, 38, 39, 64, 66, 67, 69, 90, 94{98, 101, 110, 118, 120{ 141, 167{169, 179{204, 217{232, 234, 236, 239, 240, 242, see also linear and quadratic convergence Rauch, S.W., 82 Rawlins, G.J.E., 152 Rayleigh-Ritz method, 15 Razor search, 48 Rechenberg, I., 6, 7, 97, 100, 105, 107, 118{120, 130, 142, 149, 164, 168, 172, 179, 231, 238, 245, 352 Recognition processes, 102 Recombination, 3, 101, 106, 146{148, 153{ 159, 186, 191, 200, 203, 204, 211{ 213, 215{217, 228, 231, 232, 240, 335, 355, 357, 363, 365, 366, see also discrete and intermediary recombination Reeves, C.M., 38, 69, 93, 170, 204, see also Fletcher-Reeves strategy References, 249{323 Regression, 8, 19, 84, 235, 246 Regression, non-linear, 84 Regula falsi (falsorum), 27, 34, 35, 39 Reid, J.K., 66 Rein, H., 100 Reinsch, C., 14 Relative minimum, 38, 42, 43, 66, 209 Relaxation methods, 14, 20, 41, 172, see also coordinate strategy Reliability, see robustness Repair enzymes, 142, 238 Replicator algorithm, 163 Restart of a search, 61, 67, 70, 71, 88, 89, 169, 201, 202, 205, 210, 219, 228{230, 362, 364 REVOP method, 101 Reynolds, O., 238 Rhead, D.G., 74 Rheinboldt, W.C., 5, 27, 41, 42, 82, 84 Ribiere, G., 70, 82 Rice, J.R., 57 Richardson, D.W., 155 Richardson, J.A., 58, 179 Richardson, M., 239 Riding the constraints, 16 Riedl, R., 102, 153 Ritter, K., 24, 70, 82, 88, 168 Rivlin, L., 48 Robbins, H., 19 Roberts, P.D., 70 Roberts, S.M., 16 Robots,6,9,103 Robustness, 3, 13, 34, 37{39, 53, 61, 64, 70, 90, 94, 118, 178, 204{217, 236, 238 Rocko , M.L., 41 Rodlo , R.K., 246 Rogson, M., 100 Roitblat, H., 103 Rosen, J.B., 18, 24, 57, 91, 352 Rosen, R., 100 Rosenblatt, F., 102 Rosenbrock, H.H., 23, 29, 48, 50, 54, 343, 349 Rosenbrock strategy, 16, 48{54, 64, 177, 179, 184, 190, 196, 201, 202, 207, 209, 212, 213, 216, 228, 230{232, 357, 363, 365, 366 Rosenman, E.A., 11 Ross, G.J.S., 84
440 Index Rotating coordinates method, see Rosenbrock and DSC strategies Rothe, R., 25 Roughgarden, J.W., 102 Rounding error, see accuracy of computation Rozonoer, L.I., 90 Rozvany, G., 247 Ruban, A.I., 99 Rubin, A.I., 95 Rubinov, A.M., 11 Rudd, D.F., 98, 356 Rudelson, L.Ye., 102 Rudolph, G., 91, 118, 134, 151, 154, 161, 162, 241, 243, 248 Rustay, R.C., 68, 89 Rutishauser, H., 5, 41, 43, 48, 65, 75, 172, 326 Rybashov, M.V., 68 Ryshik, I.M., 136 Saaty, T.L., 20, 27, 166 Sacks, J., 20 Saddle point, 13, 14, 17, 23, 25, 35, 36, 39, 66, 76, 88, 168, 176, 209, 211, 345 Sala , S., 100 Sameh, A.H., 239 Samuel, A.L., 102 Sargent, R.W.H., 78, 82 Saridis, G.N., 90, 98 Satterthwaite, F.E., 98, 101 Saunders, M.A., 57 Savage, J.M., 119 Savage, L.J., 41 Sawaragi, Y., 48 Sayama, H., 82 Scaling of the variables, 7, 44, 54, 58, 74, 146{148, 232, 239 Scha er, J.D., 152 Schechter, R.S., 15, 23, 28, 32, 37, 41{43, 64, 65 Schee er, L., 14 Scheel, A., 118 Schema theorem, 154 Scheraga, H.A., 89 Scheuer, E.M., 241 Scheuer, T., 98, 164 Schinzinger, R., 67 Schittkowski, K., 174 Schley, C.H., Jr., 70 Schlierkamp-Voosen, D., 163 Schmalhausen, I.I., 101 Schmetterer, L., 90 Schmidt, E., see Gram-Schmidt orthogonalization Schmidt, J.W., 35, 39 Schmitt, E., 20, 90 Schmutz, M., 103 Schneider, G., 246 Schneider, M., 100 Schrack, G., 98, 240 Schumer, M.A., 89, 93, 96{99, 101, 200, 240 Schuster, P., 101 Schwarz, H.R., 5, 41, 65, 75, 172, 326 Schwefel, D., 246 Schwefel, H.-P., 7, 102, 103, 118, 134, 148, 151, 152, 155, 163, 204, 234, 239, 242, 245{248 Schwetlick, H., 39 Scott, E.L., 102 Sebald, A.V., 151 Sebastian, D.J., 82 Sebastian, H.-J., 24 Secant method, 34, 39, 84 Second order gradient strategies, see Newton strategies Sectioning algorithms, 14 Seidel, P.L., 41, see also coordinate strategy Selection, 3, 100{102, 106, 142, 153, 157 Sensitivity analysis, 17 Separable objective function, 12, 42 Sequential methods, 27 , 38 , 88, 237 Sequential unconstrained minimization technique, see SUMT method Sergiyevskiy, G.M.,69 Sexual propagation, 3, 101, 106, 146, 147
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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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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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Page 397 and 398: 390 Appendix B GLEICH (real functio
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Page 407 and 408: 400 Appendix B C C PREPARE FINAL DA
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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 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: 438 Index Parkinson, J.M., 61 Parta
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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