Evolution and Optimum Seeking

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272 References Gaidukov, A.I. (1966), Primeneniye sluchainovo poiska pri optimalnom projektirovanii, Prikladnye zadichi tekhnicheskoi kibernetiki (1966), 420-436 Gal, S. (1971), Sequential minimax search for a maximum when prior information is available, SIAM J. Appl. Math. 21, 590-595 Gal, S. (1972), Multidimensional minimax search for a maximum, SIAM J. Appl. Math. 23, 513-526 Galar, R. (1994), Evolutionary simulations and insights into progress, in: Sebald and Fogel (1994), pp. 344-352 Galar, H., H. Kwasnicka, W. Kwasnicki (1980), Simulation of some processes of development, in: Dekker, Savastano, and Vansteenkiste (1980), pp. 133-142 Gar nkel, R.S., G.L. Nemhauser (1972), Integer programming, Wiley, NewYork Gar nkel, R.S., G.L. Nemhauser (1973), A survey of integer programming emphasizing computation and relations among models, in: Hu and Robinson (1973), pp. 77-155 Gauss, C.F. (1809), Determinatio orbitae observationibus quotcumque quam proxime satisfacientis, Werke, Band 7 (Theoria motus corporum coelestium in sectionibus conicis solem ambientium), Liber secundus, Sectio III, pp. 236-257, Hamburgi sumtibus Frid. Perthes et I.H. Besser, 1809 reprint: Teubner, Leipzig, Germany, 1906 Gaviano, M., E. Fagiuoli (1972), Remarks on the comparison between random search methods and the gradient method, in: Szego (1972), pp. 337-349 Gelfand, I.M. M.L. Tsetlin (1961), The principle of nonlocal search in automatic optimization systems, Soviet Physics Doklady 6(3), 192-194 Geo rion, A.M. (Ed.) (1972), Perspectives on optimization, Addison-Wesley, Reading MA Gerardin, L. (1968), Natur als Vorbild|die Entdeckung der Bionik, Kindler, Munich Gersht, A.M., A.I. Kaplinskii (1971), Convergence of the continuous variant ofthe Robbins-Monro procedure, ARC 32, 71-75 Gessner, P., K. Spremann (1972), Optimierung in Funktionenraumen, Springer, Berlin Gessner, P., H. Wacker (1972), Dynamische Optimierung|Einfuhrung, Modelle, Computerprogramme, Hanser, Munich Gilbert, E.G. (1967), A selected bibliography on parameter optimization methods suitable for hybrid computation, Simulation 8, 350-352 Gilbert, P., W.J. Chandler (1972), Interference between communicating parallel processes, CACM 15, 427-437
References 273 Gill, P.E., W. Murray (1972), Quasi-Newton methods for unconstrained optimization, JIMA 9, 91-108 Ginsburg, T. (1963), The conjugate gradient method, Numer. Math. 5, 191-200 Girsanov, I.V. (1972), Lectures on mathematical theory of extremum problems, Springer, Berlin Glass, H., L. Cooper (1965), Sequential search|a method for solving constrained optimization problems, JACM 12, 71-82 Glover, F. (1986), Future paths for integer programming and links to arti cial intelligence, Comp. Oper. Res. 13, 533-549 Glover, F. (1989), Tabu search|part I, ORSA-J. on Computing 1, 190-206 Glover, F., H.-J. Greenberg (1989), New approaches for heuristic search|a bilateral linkage with arti cial intelligence, Europ. J. Oper. Res. 39, 119-130 Gnedenko, B.W. (1970), Lehrbuch der Wahrscheinlichkeitsrechnung, 6th ed., Akademie- Verlag, Berlin Goldberg, D.E. (1989), Genetic algorithms in search, optimization, and machine learning, Addison-Wesley, Reading MA Goldfarb, D. (1969), Su cient conditions for the convergence of a variable metric algorithm, in: Fletcher (1969a), pp. 273-282 Goldfarb, D. (1970), A family of variable-metric methods derived by variational means, Math. Comp. 24, 23-26 Goldfeld, S.M., R.E. Quandt, H.F. Trotter (1966), Maximization by quadratic hillclimbing, Econometrica 34, 541-551 Goldfeld, S.M., R.E. Quandt, H.F. Trotter (1968), Maximization by improved quadratic hill-climbing and other methods, Princeton University, Econometric Research Program, research memo. RM-95, Princeton NJ, April 1968 Goldstein, A.A. (1962), Cauchy's method of minimization, Numer. Math. 4, 146-150 Goldstein, A.A. (1965), On Newton's method, Numer. Math. 7, 391-393 Goldstein, A.A., J.F. Price (1967), An e ective algorithm for minimization, Numer. Math. 10, 184-189 Goldstein, A.A., J.F. Price (1971), On descent from local minima, Math. Comp. 25, 569-574 Golinski, J., Z.K. Lesniak (1966), Optimales Entwerfen von Konstruktionen mit Hilfe der Monte-Carlo-Methode, Bautechnik 43, 307-311
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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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Page 229 and 230: Numerical Comparison of Strategies
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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),
Page 279: References 271 Fogel, L.J., A.J. Ow
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 and 306: 298 References Oldenburger, R. (Ed.
Page 307 and 308: 300 References Peschel, M. (1980),
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
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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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