Evolution and Optimum Seeking

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References 299 Overholt, K.J. (1967c), Algorithm 17|Goldsec, Comp J. 9, 415 Overholt, K.J. (1973), E ciency of the Fibonacci search method, BIT 13, 92-96 Page, S.E., D.W. Richardson (1992), Walsh functions, schema variance, and deception, Complex Systems 6, 125-135 Pagurek, B., C.M. Woodside (1968), The conjugate gradient method for optimal control problems with bounded control variables, Automatica 4, 337-349 Palmer, J.R. (1969), An improved procedure for orthogonalising the search vectors in Rosenbrock's and Swann's direct search optimisation methods, Comp. J. 12, 69-71 Papageorgiou, M. (1991), Optimierung|Statische, dynamische, stochastische Verfahren fur die Anwendung, Oldenbourg, Munich Papentin, F. (1972), A Darwinian evolutionary system, Dr. rer. nat. Diss., University of Tubingen, Germany Pardalos, P.M., J.B. Rosen (1987), Constrained global optimization|algorithms and applications, vol. 268 of Lecture Notes in Computer Science, Springer, Berlin Parkinson, J.M., D. Hutchinson (1972a), A consideration of non-gradient algorithms for the unconstrained optimization of functions of high dimensionality, in: Lootsma (1972a), pp. 99-113 Parkinson, J.M., D. Hutchinson (1972b), An investigation into the e ciency of variants on the simplex method, in: Lootsma (1972a), pp. 115-135 Pask, G. (1962), Physical and linguistic evolution in self-organizing systems, Proceedings of the 1st IFAC Symposium on Optimization and Adaptive Control, Rome, April 1962, pp. 199-227 Pask, G. (1971), A cybernetic experimental method and its underlying philosophy, Int'l J. Man-Machine Stud. 3, 279-337 Patrick, M.L. (1972), A highly parallel algorithm for approximating all zeros of a polynomial with only real zeros, CACM 15, 952-955 Pattee, H.H., E.A. Edelsack, L. Fein, A.B. Callahan (Eds.) (1966), Natural automata and useful simulations, Spartan, Washington, DC Paviani, D.A., D.M. Himmelblau (1969), Constrained nonlinear optimization by heuristic programming, Oper. Res. 17, 872-882 Pearson, J.D. (1969), Variable metric methods of minimization, Comp. J. 12, 171-178 Peckham, G. (1970), A new method for minimising a sum of squares without calculating gradients, Comp. J. 13, 418-420
300 References Peschel, M. (1980), Ingenieurtechnische Entscheidungen|Modellbildung und Steuerung mit Hilfe der Polyoptimierung, Verlag Technik, Berlin Peters, E. (1989), OptimiEst|an optimizing expert system using topologies, in: Brebbia and Hernandez (1989), pp. 222-232 Peters, E. (1991), Ein Beitrag zur wissensbasierten Auswahl und Steuerung von Optimierverfahren, Dr. rer. nat. Diss., University of Dortmund, Department of Computer Science, May 1991 Pierre, D.A. (1969), Optimization theory with applications, Wiley, New York Pierson, B.L., S.G. Rajtora (1970), Computational experience with the Davidon method applied to optimal control problems, IEEE Trans. SSC-6, 240-242 Pike, M.C., I.D. Hill, F.D. James (1967), Note on algorithm 2|Fibonacci search, and on algorithm 7|Minx, and algorithm 2 modi ed|Fibonacci search, Comp. J. 9, 416-417 Pike, M.C., J. Pixner (1965), Algorithm 2|Fibonacci search, Comp. Bull. 8, 147 Pincus, M. (1970), A Monte Carlo method for the approximate solution of certain types of constrained optimization problems, Oper. Res. 18, 1225-1228 Pinkham, R.S. (1964), Random root location, SIAM J. 12, 855-864 Pinsker, I.Sh., B.M. Tseitlin (1962), A nonlinear optimization problem, ARC 23, 1510- 1518 Plane, D.R., C. McMillan, Jr. (1971), Discrete optimization|integer programming and network analysis for management decisions, Prentice-Hall, Englewood Cli s NJ Plaschko, P., K. Wagner (1973), Evolutions-Linearisierungs-Programm zur Darstellung von numerischen Daten durchbeliebigeFunktionen, report DLR-FB-73-55, DFVLR Porz-Wahn, Germany Pluznikov, L.N., V.O. Andreyev, E.S. Klimenko (1971), Use of random search method in industrial planning, Engng. Cybern. 9, 229-235 Polak, E. (1971), Computational methods in optimization|a uni ed approach, Academic Press, New York Polak, E. (1972), A survey of methods of feasible directions for the solution of optimal control problems, IEEE Trans. AC-17, 591-596 Polak, E. (1973), An historical survey of computational methods in optimal control, SIAM Review 15, 553-584 Polak, E., G. Ribiere (1969), Note sur la convergence de methodes de directions conjuguees, Rev. Franc. Inf. Rech. Oper. 3(16), 35-43
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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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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
Page 283 and 284: References 275 Graves, R.L., P. Wol
Page 285 and 286: References 277 Heckler, R., H.-P. S
Page 287 and 288: References 279 Ho meister, F., H.-P
Page 289 and 290: References 281 Idelsohn, J.M. (1964
Page 291 and 292: References 283 Karnopp, D.C. (1966)
Page 293 and 294: References 285 Kochen, M., H.M. Has
Page 295 and 296: References 287 Kunzi, H.P., H.G. Tz
Page 297 and 298: References 289 LeCam, L.M., J. Neym
Page 299 and 300: References 291 Mamen, R., D.Q. Mayn
Page 301 and 302: 294 References Miele, A., H.Y. Huan
Page 303 and 304: 296 References Murray, W. (Ed.) (19
Page 305: 298 References Oldenburger, R. (Ed.
Page 309 and 310: 302 References Powell, M.J.D. (1970
Page 311 and 312: 304 References Rechenberg, I. (1989
Page 313 and 314: 306 References Rybashov, M.V. (1969
Page 315 and 316: 308 References Schmidt, J.W., K. Ve
Page 317 and 318: 310 References Shedler, G.S. (1967)
Page 319 and 320: 312 References Steinbuch, K. (1971)
Page 321 and 322: 314 References Tabak, D. (1970), Ap
Page 323 and 324: 316 References Varela, F.J., P. Bou
Page 325 and 326: 318 References White, L.J., R.G. Da
Page 327 and 328: 320 References Youden, W.J., O. Kem
Page 329 and 330: 322 References Glossary of Abbrevia
Page 331 and 332: 324 References
Page 333 and 334: 326 Appendix A Problem 1.2 Objectiv
Page 335 and 336: 328 Appendix A Minimum: x =(3 0:5)
Page 337 and 338: 330 Appendix A Figure A.3: Graphica
Page 339 and 340: 332 Appendix A Several of the searc
Page 345 and 346: 338 Appendix A Minimum: Start: Prob
Page 347 and 348: 340 Appendix A Problem 2.20 Objecti
Page 349 and 350: 342 Appendix A Problem 2.23 Objecti
Page 351 and 352: 344 Appendix A Start: x (0) i =10 f
Page 353 and 354: 346 Appendix A on the interval 0 y
Page 355 and 356: 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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