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An introduction to population approaches for optimization and hierarchical objective functions: A discussion on the role of tabu search. (English) Zbl 0775.90292


MSC:

90C27 Combinatorial optimization
90-08 Computational methods for problems pertaining to operations research and mathematical programming
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[1] N. Agmon, Biochemistry 27(1988)3507–3511. · doi:10.1021/bi00409a057
[2] E. Amaldi and S. Nicolis, Stability-capacity diagram of a neural network with Ising bonds, J. Physique 50(1989)2333–2345. · doi:10.1051/jphys:0198900500170233300
[3] E. Amaldi, E. Mayoraz and D. de Werra, Discrete optimization problems in neural network design, DMA preprint, EPF-Lausanne, Switzerland (August 1990). · Zbl 0801.68148
[4] R.H. Austin et al., Biochemistry 14(1975)5355–5373. · doi:10.1021/bi00695a021
[5] M. Ball and M. Magazine, The design and analysis of heuristics, Networks 11(1981)215–219. · doi:10.1002/net.3230110210
[6] E. Baum, Intractable computations without local minima (reply), Phys. Rev. Lett. 59(1987)374. · doi:10.1103/PhysRevLett.59.374
[7] J. Beardwood, J.H. Halton and J.M. Hammersley, The shortest path through many points, Proc. Cambridge Philos. Soc. 55(1959)299–327. · Zbl 0118.35601 · doi:10.1017/S0305004100034095
[8] T.L. Blundell and L.N. Johnson,Protein Chrystallography (Academic Press, New York, 1976).
[9] H. Bohr and S. Brunak, A traveling salesman approach to protein conformation, Complex Syst. 3(1989)9–28. · Zbl 0724.92008
[10] E. Bonomi and J.L. Lutton, TheN-city traveling salesman problem and the Metropolis algorithm, SIAM Rev. 26(1984)551–568. · Zbl 0551.90095 · doi:10.1137/1026105
[11] E. Bonomi and J.L. Lutton, The asymptotic behavior of quadratic sum assignment problems: A statistical mechanics approach, Eur. J. Oper. Res. 26(1986)295–300. · Zbl 0598.90065 · doi:10.1016/0377-2217(86)90193-1
[12] S.G. Boxer et al., Nonphotochemical holeburning in a protein matrix: Chlorophyllide in apomyoglobin, J. Chem Phys. 86(1987)2439–2441. · doi:10.1063/1.452092
[13] B. Braschi, Solving the traveling salesman problem with simulated annealing techniques on a concurrent supercomputer, Report RR 752-I, TIM3-INPG Grenoble, France (November, 1988).
[14] B.F. Campbell, M.R. Chance and J.M. Friedman, Science 238(1987)373–376. · doi:10.1126/science.3659921
[15] J.E. Cohen, Threshold phenomena in random structures, Discr. Appl. Math. 19(1988)113–128. · Zbl 0633.05065 · doi:10.1016/0166-218X(88)90008-X
[16] J.P. Cohoon et al., Punctuated equilibria: A parallel genetic algorithm, in:Proc. 2nd Int. Conf. on Genetic Algorithms and their Applications, ed. J.J. Grefenstette (Lawrence Erlbaum Associates, Hillsdale, NJ, 1987) pp. 148–154.
[17] W. Conover,Practical Nonparametric Statistics (Wiley, New York, 1980).
[18] B. Derrida and H. Flyvbjerg, Multivalley structure in Kauffman’s model: Analogy with spin glasses, J. Phys. A Math. Gen. 19(1986)L1003.
[19] B. Derrida, Valleys and overlaps in Kauffman’s model, Philos. Magazine B 56(1987)917. · doi:10.1080/13642818708215326
[20] B. Derrida and O. Golinelli, Barrier heights in the Kauffman model, J. Physique 50(1989)1587. · doi:10.1051/jphys:0198900500130158700
[21] D. de Werra and A. Hertz, Tabu search techniques: A tutorial and an application to neural networks, OR Spektrum 11(1989)131–141. · Zbl 0672.90089 · doi:10.1007/BF01720782
[22] J. Edmonds, Paths, trees and flowers, Can. J. Math. 17(1965)449–467. · Zbl 0132.20903 · doi:10.4153/CJM-1965-045-4
[23] R. Elber and M. Karplus, Multiple conformational states of proteins: A molecular dynamics analysis of myoglobin, Science 235(1987)318–321. · doi:10.1126/science.3798113
[24] R. Elber and M. Karplus, A method for determining reaction paths in large molecules, Chem. Phys. Lett. 139(1987)375. · doi:10.1016/0009-2614(87)80576-6
[25] N. Eldredge and S.J. Gould, Punctuated equilibria: An alternative to phyletic gradualism, in:Models of Paleobiology, ed. T.J.M. Schopf (Freeman, Cooper and Co., 1972) pp. 82–115.
[26] C.N. Fiechter, A parallel tabu search algorithm for large traveling salesman problems, preprint ORWP 90/1, EPF-Lausanne, Switzerland (February 1990).
[27] W. Fontana, W. Schnabl and P. Schuster, Physical aspects of evolutionary optimization and adaptation, Phys. Rev. A40(1989)3301–3321.
[28] J.F. Fontanari and R. Meir, Overlap distribution in the binary perceptron; A numerical study, Division of Chemistry preprint, CalTech, Pasadena, CA (1989).
[29] J.F. Fontanari and R. Köberle, Landscape statistics of the binary perceptron, J. Physique 51(1990)1403–1413. · doi:10.1051/jphys:0199000510130140300
[30] G.C. Fox and D. Walker, Concurrent computers in science, CalTech Concurrent Computation Program Report 646, CalTech, Pasadena, CA (1988).
[31] G.C. Fox et al.,Solving Problems on Concurrent Processors, vol. 1 (Prentice Hall, Englewood Cliffs, NJ, 1988).
[32] H. Frauenfelder, G.A. Petsko and D. Tsernoglou, Nature 280(1979)558–563. · doi:10.1038/280558a0
[33] H. Frauenfelder, in:Structure and Motion: Membranes, Nucleic Acids, and Proteins, ed. E. Clementi et al. (Adenine, Guilderland, NY, 1985) p. 205.
[34] H. Frauenfelder, F. Parak and R.D. Young, Ann. Rev. Biophys. Biophys. Chem. 17(1988)451–479. · doi:10.1146/annurev.bb.17.060188.002315
[35] H. Frauenfelder et al., Glassy behavior of a protein, Phys. Rev. Lett. 62(1989)1916–1919. · doi:10.1103/PhysRevLett.62.1916
[36] H. Frauenfelder, P.J. Steinbach and R.D. Young, Conformational relaxation in proteins, Chem. Scripta 29A(1989)145–150.
[37] H. Frauenfelder, Proteins – Paradigms of complex systems, in:Proc. 25th Anniversary Conf. on Frontiers in Physics, High Technology and Mathematics, ed. H.A. Cerdeira and S.O. Lundqvist, Miramare, Trieste, Italy (World Scientific, Singapore, 1990).
[38] H. Frauenfelder et al., Proteins and pressure, J. Phys. Chem. 94(1990)1024–1037. · doi:10.1021/j100366a002
[39] H. Frauenfelder, Function and dynamics of myoglobin, in:Perspectives in Biological Dynamics and Theoretical Medicine, reprinted from Annals of the New York Academy of Sciences, vol. 504(1990) pp. 151–167. · doi:10.1111/j.1749-6632.1987.tb48730.x
[40] T.R. Gingeras and R.J. Roberts, Science 209(1980)1322. · doi:10.1126/science.6251542
[41] F. Glover, Tabu search. Part I, ORSA J. Comput. 1(1989)190–206.
[42] F. Glover, Candidate list strategies and tabu search, CAAI Research Report, University of Colorado, Boulder, CO, (July 1989).
[43] F. Glover, Tabu search. Part II, ORSA J. Comput. 2(1990) 4–32.
[44] F. Glover, Tabu search for nonlinear and parametric optimization, paper presented at the EPFL Seminar on OR and AI Search Methods for Optimization Problems (November 1990).
[45] F. Glover, private communication (3 May, 1991).
[46] V.I. Goldanskii, Dokl. Akad. Nauk. SSSR 272(1983)978–981.
[47] D.E. Goldberg,Genetic Algorithms in Search, Optimization and Machine Learning (Addison Wesley, Reading, MA, 1989). · Zbl 0721.68056
[48] G.S. Grest et al., Monte Carlo and mean field slow cooling simulations for spin glasses: Relation to NP-completeness, in:Heidelberg Colloquium in Glassy Dynamics, Lecture Notes in Physics, Vol. 275, ed. J.L. van Hemmen and I. Morgenstern (Springer, Berlin, 1987)307–324.
[49] R. Hall and P.G. Wolynes, The aperiodic crystal picture and free energy barriers in glasses, J. Chem. Phys. 86(1987)2943. · doi:10.1063/1.452045
[50] A. Hertz and D. de Werra, Using tabu search techniques for graph coloring, Computing 29(1987)345–351. · Zbl 0626.68051 · doi:10.1007/BF02239976
[51] T. Hirata, A correlation between theb value and the fractal dimension of earthquakes, J. Geophys. Res. 94(1989)7507–7514. · doi:10.1029/JB094iB06p07507
[52] G.W. Hoffmann et al., TheN-dimensional network, in:Theoretical Immunology, Part 2, ed. A.S. Perelson (Addison-Wesley, Redwood City, CA, 1988).
[53] T. Hogg, The dynamics of complex computational systems, in:Complexity, Entropy, and the Physics of Information, ed. W.H. Zurek (Addison-Wesley, Redwood City, CA, 1990).
[54] J.H. Holland,Adaptation in Natural and Artificial Systems (University of Michigan Press, Ann Arbor, 1975). · Zbl 0317.68006
[55] B.A. Huberman and M. Kerszberg, Ultradiffusion: the relaxation of hierarchical systems, J. Phys. A18(1985)L331-L336.
[56] B.A. Huberman and T. Hogg, Complexity and adaptation, Physica 22D(1986)376–384.
[57] B.A. Huberman and T. Hogg, Phase transitions in artificial intelligence systems, Art. Int. 33(1987)155–171. · doi:10.1016/0004-3702(87)90033-6
[58] B.A. Huberman (ed.),The Ecology of Computation (North-Holland, Amsterdam, 1988). · Zbl 0800.68012
[59] B.A. Huberman, The performance of cooperative processes, Physica D42(1990)38–47.
[60] J.S. Judd,Neural Network Design and the Complexity of Learning (MIT Press, Cambridge, MA, 1990).
[61] J.O. Kephart, T. Hogg and B.A. Huberman, Dynamics of computational ecosystems, Phys. Rev. A40(1989)404–421.
[62] R.M. Karp, Probabilistic analysis of partitioning algorithms for the traveling salesman problem in the plane, Math. Oper. Res. 2(1977)209–224. · Zbl 0391.90091 · doi:10.1287/moor.2.3.209
[63] R.M. Karp, A patching algorithm for the nonsymmetric traveling-salesman problem, SIAM J. Comput. 8(1979)561–573. · Zbl 0427.90064 · doi:10.1137/0208045
[64] S.A. Kauffman and S. Levin, Towards a general theory of adaptive walks on rugged landscapes, J. Theor. Biol. 128(1987)11–45. · doi:10.1016/S0022-5193(87)80029-2
[65] S.A. Kauffman and E.D. Weinberger, The NK model of rugged fitness landscapes and its application to maturation of the immune response, J. Theor. Biol. 141(1989)211–245. · doi:10.1016/S0022-5193(89)80019-0
[66] S.A. Kauffman, Adaptation on rugged fitness landscapes, in:Lectures in the Sciences of Complexity, ed. D. Stein (Addison-Wesley, Redwood City, CA, 1989) pp. 527–618.
[67] V.I. Keilis-Borok, Introduction: Non-linear systems in the problem of earthquake prediction, Phys. Earth Planet. Interiors 61(1990)1–7. · doi:10.1016/0031-9201(90)90089-G
[68] H. Keller and P.G. Debrunner, Evidence for conformational and diffusion mean square displacements in frozen aqueous solution of oxymyoglobin, Phys. Rev. Lett. 45(1980)68–71. · doi:10.1103/PhysRevLett.45.68
[69] M. Kimura,The Neutral Theory of Molecular Evolution (Cambridge University Press, New York, 1983).
[70] S. Kirkpatrick, C.D. Gelatt and M.P. Vecchi, Optimization by simulated annealing, Science 220(1983)671–680. · Zbl 1225.90162 · doi:10.1126/science.220.4598.671
[71] S. Kirkpatrick and G. Toulouse, Configuration space analysis of traveling salesman problems, J. Physique 46(1985)1277–1292. · doi:10.1051/jphys:019850046080127700
[72] W. Koehler, J. Friedrich and H. Scheer, Conformational barriers in low-temperature proteins in glasses, Phys. Rev. A37(1988)660–662.
[73] E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys,The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization (Wiley-Interscience, Chichester, 1985). · Zbl 0562.00014
[74] S. Lin and B.W. Kernighan, An effective heuristic algorithm for the traveling salesman problem, Oper. Res. 21(1973)498–516. · Zbl 0256.90038 · doi:10.1287/opre.21.2.498
[75] B. Manderick, M. de Weger and P. Spiessens, The genetic algorithm and the structure of the fitness landscape, in:Proc. 4th Int. Conf. on Genetic Algorithms, ed. R.K. Belew and L.B. Booker, San Diego, CA (Morgan Kaufmann, San Mateo CA, 1991) pp. 143–150.
[76] E.N. Miranda and N. Parga, Ultrametricity in the Kauffman model: A numerical test, J. Phys. A: Math. Gen. 21(1988)357. · doi:10.1088/0305-4470/21/6/007
[77] S.A. Molchanov, V.P. Pisarenko and A. Ya. Reznikova, Multiscale models of failure and percolation, Phys. Earth Planet. Interiors 61(1990)36–43. · doi:10.1016/0031-9201(90)90093-D
[78] P. Moscato, On evolution, search, optimization, genetic algorithms and martial arts: Towards memetic algorithms, CalTech Concurrent Computation Program Report 826, CalTech, Pasadena, CA (1989).
[79] P. Moscato and J.F. Fontanari, Stochastic versus deterministic update in simulated annealing, Phys. Lett. A 146(1990)204–208. · doi:10.1016/0375-9601(90)90166-L
[80] P. Moscato and M.G. Norman, A ”memetic” approach for the traveling salesman problem. Implementation of a computational ecology for combinatorial optimization on message-passing systems, in preparation.
[81] F. Mosteller and R. Rourke,Sturdy Statistics (Addison-Wesley, Reading, MA, 1973).
[82] G.S. Narkunskaya and M.G. Shnirman, Hierarchical model of defect development and seismicity, Phys. Earth Planet. Interiors 61(1990)29–35. · doi:10.1016/0031-9201(90)90092-C
[83] T. Noguti and N. Go, Proteins 5(1989)97. · doi:10.1002/prot.340050203
[84] M.G. Norman and P. Moscato, A competitive-cooperative approach to complex combinatorial search, CalTech Concurrent Computation Program, Report C3P-790, Pasadena, CA (1989); selected work for theProc. 20th Joint Conf. on Informatics and Operations Research (20th JAIIO), Buenos Aires, Argentina, (August 1991) pp. 3.15–3.29.
[85] M. Padberg and G. Rinaldi, Optimization of 532-city symmetric TSP, Oper. Res. Lett. 6(1987)1–7. · Zbl 0618.90082 · doi:10.1016/0167-6377(87)90002-2
[86] R.G. Palmer et al., Models of hierarchically constrained dynamics for glassy relaxation, Phys. Rev. Lett. 53(1984)958. · doi:10.1103/PhysRevLett.53.958
[87] F. Parak et al., J. Mol. Biol. 145(1981)825–833. · doi:10.1016/0022-2836(81)90317-X
[88] N. Parga, Overlap distributions and taxonomy analysis of spin-glass states with equal weights, J. Physique 48(1987)449.
[89] G.A. Petsko and D. Ringe, Ann. Rev. Biophys. Bioeng. 13(1984)331–371. · doi:10.1146/annurev.bb.13.060184.001555
[90] R. Pfaffenberger and J. Patterson,Statistical Methods (Irwin, Homewood, IL, 1981). · Zbl 0392.90001
[91] K. Rose, E. Gurewitz and G.C. Fox, Statistical mechanics and phase transitions in clustering, Phys. Rev. Lett. 65(1990)945–948. · doi:10.1103/PhysRevLett.65.945
[92] K. Rose, E. Gurewitz and G.C. Fox, A deterministic annealing approach to clustering, Pattern Recognition Lett. 11(1990)589–594. · Zbl 0800.68817 · doi:10.1016/0167-8655(90)90010-Y
[93] D. Sankoff and J.B. Kruskal (eds.),Time Warps, String Edits and Macromolecules: The Theory and Practice of Sequence Comparison (Addison-Wesley, Reading, MA, 1983). · Zbl 0512.68048
[94] J. Skorin-Kapov, Tabu search applied to the quadratic assignment problem, ORSA J. Comput. 2(1990)33–45. · Zbl 0752.90054
[95] R.F. Smalley, Jr. et al., A fractal approach to the clustering of earthquakes: Application to the seismicity of the New Hebrides, Bull. Seismol. Soc. America 77(1987)1368–1381.
[96] S.A. Solla, G.B. Sorkin and S.R. White, Configuration space analysis for optimization problems, in:Disordered Systems and Biological Organization, ed. E. Bienenstock, NATO ASI Series Vol. F20 (1985).
[97] G.B. Sorkin, Efficient simulated annealing on fractal energy landscapes, Algorithmica 6(1991)367–418. · Zbl 0728.90073 · doi:10.1007/BF01759051
[98] G.B. Sorkin, Theory and practice of simulated annealing in fractal landscapes, Ph.D. Thesis, University of California, Berkeley, CA (1991). · Zbl 0728.90073
[99] C.M. Soukolis, K. Levin and G.S. Grest, Irreversibility and metastability in spin-glasses. I. Ising model, Phys. Rev. B28(1983)1495.
[100] V. Srajer, K.T. Schomacker and P.M. Champion, Spectral broadening in biomolecules, Phys. Rev. Lett. 57(1986)1267–1270. · doi:10.1103/PhysRevLett.57.1267
[101] G.L. Stebbins and F.J. Ayala, Is a new evolutionary synthesis necessary?, Science 213(1981)967–971. · doi:10.1126/science.213.4511.967
[102] F.H. Stillinger and T.A. Weber, Packing structures and transitions in liquids and solids, Science 225(1984)983. · doi:10.1126/science.225.4666.983
[103] G. Toulouse, Theory of the frustration effect in spin glasses: I, Commun. Phys. 2(1977)115.
[104] G. Toulouse, How ”frustration” set in, Physics Today 42(1989)97. · doi:10.1063/1.2811258
[105] M.S. Waterman, Bull. Math. Biol. 46(1984)473–500.
[106] D. Whitley, T. Starkweather and D’Ann Fuquay, Scheduling problems and traveling salesman: The genetic edge recombination operator, in:Proc. 3rd Int. Conf. on Genetic Algorithms, ed. J.D. Schaffer, Fairfax, VA (Morgan Kaufmann, San Mateo CA, 1989) pp. 133–140.
[107] K. Wuthrich, Science 234(1989)45–50; Accounts Chem. Res. 22(1989)36–44. · doi:10.1126/science.2911719
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