Annals of Operations Research

, Volume 41, Issue 2, pp 85–121 | Cite as

An introduction to population approaches for optimization and hierarchical objective functions: A discussion on the role of tabu search

  • Pablo Moscato
Technical Aspects Of Tabu Search

Abstract

Population approaches suitable for global combinatorial optimization are discussed in this paper. They are composed of a number of distinguishable individuals called "agents", each one using a particular optimization strategy. Periods of independent search follow phases on which the population is restarted from new configurations. Due to its intrinsic parallelism and the asynchronicity of the method, it is particularly suitable for parallel computers. Results on two test problems are presented in this paper. The individual search optimization strategies for each agent have been chosen having the basic characteristics of tabu search. This has been done in order to avoid mixing the hypothesized properties of these population approaches with those of more elaborate tabu search strategies, but remarking on its main characteristics. A set of four test problem "landscapes" is discussed and their use to improve and benchmark the results by using tabu search as the individual optimization strategy within a population heuristic is suggested and explored. The application of tabu search to new problem areas, like molecular biology, is also investigated.

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References

  1. [1]
    N. Agmon, Biochemistry 27(1988)3507–3511.CrossRefPubMedGoogle Scholar
  2. [2]
    E. Amaldi and S. Nicolis, Stability-capacity diagram of a neural network with Ising bonds, J. Physique 50(1989)2333–2345.Google Scholar
  3. [3]
    E. Amaldi, E. Mayoraz and D. de Werra, Discrete optimization problems in neural network design, DMA preprint, EPF-Lausanne, Switzerland (August 1990).Google Scholar
  4. [4]
    R.H. Austin et al., Biochemistry 14(1975)5355–5373.CrossRefPubMedGoogle Scholar
  5. [5]
    M. Ball and M. Magazine, The design and analysis of heuristics, Networks 11(1981)215–219.Google Scholar
  6. [6]
    E. Baum, Intractable computations without local minima (reply), Phys. Rev. Lett. 59(1987)374.CrossRefPubMedGoogle Scholar
  7. [7]
    J. Beardwood, J.H. Halton and J.M. Hammersley, The shortest path through many points, Proc. Cambridge Philos. Soc. 55(1959)299–327.CrossRefGoogle Scholar
  8. [8]
    T.L. Blundell and L.N. Johnson,Protein Chrystallography (Academic Press, New York, 1976).Google Scholar
  9. [9]
    H. Bohr and S. Brunak, A traveling salesman approach to protein conformation, Complex Syst. 3(1989)9–28.Google Scholar
  10. [10]
    E. Bonomi and J.L. Lutton, TheN-city traveling salesman problem and the Metropolis algorithm, SIAM Rev. 26(1984)551–568.CrossRefGoogle Scholar
  11. [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.CrossRefGoogle Scholar
  12. [12]
    S.G. Boxer et al., Nonphotochemical holeburning in a protein matrix: Chlorophyllide in apomyoglobin, J. Chem Phys. 86(1987)2439–2441.CrossRefGoogle Scholar
  13. [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).Google Scholar
  14. [14]
    B.F. Campbell, M.R. Chance and J.M. Friedman, Science 238(1987)373–376.PubMedGoogle Scholar
  15. [15]
    J.E. Cohen, Threshold phenomena in random structures, Discr. Appl. Math. 19(1988)113–128.CrossRefGoogle Scholar
  16. [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.Google Scholar
  17. [17]
    W. Conover,Practical Nonparametric Statistics (Wiley, New York, 1980).Google Scholar
  18. [18]
    B. Derrida and H. Flyvbjerg, Multivalley structure in Kauffman's model: Analogy with spin glasses, J. Phys. A Math. Gen. 19(1986)L1003.Google Scholar
  19. [19]
    B. Derrida, Valleys and overlaps in Kauffman's model, Philos. Magazine B 56(1987)917.Google Scholar
  20. [20]
    B. Derrida and O. Golinelli, Barrier heights in the Kauffman model, J. Physique 50(1989)1587.Google Scholar
  21. [21]
    D. de Werra and A. Hertz, Tabu search techniques: A tutorial and an application to neural networks, OR Spektrum 11(1989)131–141.CrossRefGoogle Scholar
  22. [22]
    J. Edmonds, Paths, trees and flowers, Can. J. Math. 17(1965)449–467.Google Scholar
  23. [23]
    R. Elber and M. Karplus, Multiple conformational states of proteins: A molecular dynamics analysis of myoglobin, Science 235(1987)318–321.PubMedGoogle Scholar
  24. [24]
    R. Elber and M. Karplus, A method for determining reaction paths in large molecules, Chem. Phys. Lett. 139(1987)375.CrossRefGoogle Scholar
  25. [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.Google Scholar
  26. [26]
    C.N. Fiechter, A parallel tabu search algorithm for large traveling salesman problems, preprint ORWP 90/1, EPF-Lausanne, Switzerland (February 1990).Google Scholar
  27. [27]
    W. Fontana, W. Schnabl and P. Schuster, Physical aspects of evolutionary optimization and adaptation, Phys. Rev. A40(1989)3301–3321.Google Scholar
  28. [28]
    J.F. Fontanari and R. Meir, Overlap distribution in the binary perceptron; A numerical study, Division of Chemistry preprint, CalTech, Pasadena, CA (1989).Google Scholar
  29. [29]
    J.F. Fontanari and R. Köberle, Landscape statistics of the binary perceptron, J. Physique 51(1990)1403–1413.Google Scholar
  30. [30]
    G.C. Fox and D. Walker, Concurrent computers in science, CalTech Concurrent Computation Program Report 646, CalTech, Pasadena, CA (1988).Google Scholar
  31. [31]
    G.C. Fox et al.,Solving Problems on Concurrent Processors, vol. 1 (Prentice Hall, Englewood Cliffs, NJ, 1988).Google Scholar
  32. [32]
    H. Frauenfelder, G.A. Petsko and D. Tsernoglou, Nature 280(1979)558–563.CrossRefPubMedGoogle Scholar
  33. [33]
    H. Frauenfelder, in:Structure and Motion: Membranes, Nucleic Acids, and Proteins, ed. E. Clementi et al. (Adenine, Guilderland, NY, 1985) p. 205.Google Scholar
  34. [34]
    H. Frauenfelder, F. Parak and R.D. Young, Ann. Rev. Biophys. Biophys. Chem. 17(1988)451–479.CrossRefGoogle Scholar
  35. [35]
    H. Frauenfelder et al., Glassy behavior of a protein, Phys. Rev. Lett. 62(1989)1916–1919.CrossRefPubMedGoogle Scholar
  36. [36]
    H. Frauenfelder, P.J. Steinbach and R.D. Young, Conformational relaxation in proteins, Chem. Scripta 29A(1989)145–150.Google Scholar
  37. [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).Google Scholar
  38. [38]
    H. Frauenfelder et al., Proteins and pressure, J. Phys. Chem. 94(1990)1024–1037.CrossRefGoogle Scholar
  39. [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.Google Scholar
  40. [40]
    T.R. Gingeras and R.J. Roberts, Science 209(1980)1322.PubMedGoogle Scholar
  41. [41]
    F. Glover, Tabu search. Part I, ORSA J. Comput. 1(1989)190–206.Google Scholar
  42. [42]
    F. Glover, Candidate list strategies and tabu search, CAAI Research Report, University of Colorado, Boulder, CO, (July 1989).Google Scholar
  43. [43]
    F. Glover, Tabu search. Part II, ORSA J. Comput. 2(1990) 4–32.Google Scholar
  44. [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).Google Scholar
  45. [45]
    F. Glover, private communication (3 May, 1991).Google Scholar
  46. [46]
    V.I. Goldanskii, Dokl. Akad. Nauk. SSSR 272(1983)978–981.PubMedGoogle Scholar
  47. [47]
    D.E. Goldberg,Genetic Algorithms in Search, Optimization and Machine Learning (Addison Wesley, Reading, MA, 1989).Google Scholar
  48. [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.Google Scholar
  49. [49]
    R. Hall and P.G. Wolynes, The aperiodic crystal picture and free energy barriers in glasses, J. Chem. Phys. 86(1987)2943.CrossRefGoogle Scholar
  50. [50]
    A. Hertz and D. de Werra, Using tabu search techniques for graph coloring, Computing 29(1987)345–351.Google Scholar
  51. [51]
    T. Hirata, A correlation between theb value and the fractal dimension of earthquakes, J. Geophys. Res. 94(1989)7507–7514.CrossRefGoogle Scholar
  52. [52]
    G.W. Hoffmann et al., TheN-dimensional network, in:Theoretical Immunology, Part 2, ed. A.S. Perelson (Addison-Wesley, Redwood City, CA, 1988).Google Scholar
  53. [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).Google Scholar
  54. [54]
    J.H. Holland,Adaptation in Natural and Artificial Systems (University of Michigan Press, Ann Arbor, 1975).Google Scholar
  55. [55]
    B.A. Huberman and M. Kerszberg, Ultradiffusion: the relaxation of hierarchical systems, J. Phys. A18(1985)L331-L336.Google Scholar
  56. [56]
    B.A. Huberman and T. Hogg, Complexity and adaptation, Physica 22D(1986)376–384.MathSciNetGoogle Scholar
  57. [57]
    B.A. Huberman and T. Hogg, Phase transitions in artificial intelligence systems, Art. Int. 33(1987)155–171.CrossRefGoogle Scholar
  58. [58]
    B.A. Huberman (ed.),The Ecology of Computation (North-Holland, Amsterdam, 1988).Google Scholar
  59. [59]
    B.A. Huberman, The performance of cooperative processes, Physica D42(1990)38–47.Google Scholar
  60. [60]
    J.S. Judd,Neural Network Design and the Complexity of Learning (MIT Press, Cambridge, MA, 1990).Google Scholar
  61. [61]
    J.O. Kephart, T. Hogg and B.A. Huberman, Dynamics of computational ecosystems, Phys. Rev. A40(1989)404–421.Google Scholar
  62. [62]
    R.M. Karp, Probabilistic analysis of partitioning algorithms for the traveling salesman problem in the plane, Math. Oper. Res. 2(1977)209–224.Google Scholar
  63. [63]
    R.M. Karp, A patching algorithm for the nonsymmetric traveling-salesman problem, SIAM J. Comput. 8(1979)561–573.CrossRefGoogle Scholar
  64. [64]
    S.A. Kauffman and S. Levin, Towards a general theory of adaptive walks on rugged landscapes, J. Theor. Biol. 128(1987)11–45.PubMedGoogle Scholar
  65. [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.PubMedGoogle Scholar
  66. [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.Google Scholar
  67. [67]
    V.I. Keilis-Borok, Introduction: Non-linear systems in the problem of earthquake prediction, Phys. Earth Planet. Interiors 61(1990)1–7.CrossRefGoogle Scholar
  68. [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.CrossRefGoogle Scholar
  69. [69]
    M. Kimura,The Neutral Theory of Molecular Evolution (Cambridge University Press, New York, 1983).Google Scholar
  70. [70]
    S. Kirkpatrick, C.D. Gelatt and M.P. Vecchi, Optimization by simulated annealing, Science 220(1983)671–680.Google Scholar
  71. [71]
    S. Kirkpatrick and G. Toulouse, Configuration space analysis of traveling salesman problems, J. Physique 46(1985)1277–1292.Google Scholar
  72. [72]
    W. Koehler, J. Friedrich and H. Scheer, Conformational barriers in low-temperature proteins in glasses, Phys. Rev. A37(1988)660–662.Google Scholar
  73. [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).Google Scholar
  74. [74]
    S. Lin and B.W. Kernighan, An effective heuristic algorithm for the traveling salesman problem, Oper. Res. 21(1973)498–516.CrossRefGoogle Scholar
  75. [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.Google Scholar
  76. [76]
    E.N. Miranda and N. Parga, Ultrametricity in the Kauffman model: A numerical test, J. Phys. A: Math. Gen. 21(1988)357.CrossRefGoogle Scholar
  77. [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.CrossRefGoogle Scholar
  78. [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).Google Scholar
  79. [79]
    P. Moscato and J.F. Fontanari, Stochastic versus deterministic update in simulated annealing, Phys. Lett. A 146(1990)204–208.CrossRefGoogle Scholar
  80. [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.Google Scholar
  81. [81]
    F. Mosteller and R. Rourke,Sturdy Statistics (Addison-Wesley, Reading, MA, 1973).Google Scholar
  82. [82]
    G.S. Narkunskaya and M.G. Shnirman, Hierarchical model of defect development and seismicity, Phys. Earth Planet. Interiors 61(1990)29–35.CrossRefGoogle Scholar
  83. [83]
    T. Noguti and N. Go, Proteins 5(1989)97.CrossRefPubMedGoogle Scholar
  84. [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.Google Scholar
  85. [85]
    M. Padberg and G. Rinaldi, Optimization of 532-city symmetric TSP, Oper. Res. Lett. 6(1987)1–7.CrossRefMathSciNetGoogle Scholar
  86. [86]
    R.G. Palmer et al., Models of hierarchically constrained dynamics for glassy relaxation, Phys. Rev. Lett. 53(1984)958.CrossRefGoogle Scholar
  87. [87]
    F. Parak et al., J. Mol. Biol. 145(1981)825–833.CrossRefPubMedGoogle Scholar
  88. [88]
    N. Parga, Overlap distributions and taxonomy analysis of spin-glass states with equal weights, J. Physique 48(1987)449.Google Scholar
  89. [89]
    G.A. Petsko and D. Ringe, Ann. Rev. Biophys. Bioeng. 13(1984)331–371.CrossRefGoogle Scholar
  90. [90]
    R. Pfaffenberger and J. Patterson,Statistical Methods (Irwin, Homewood, IL, 1981).Google Scholar
  91. [91]
    K. Rose, E. Gurewitz and G.C. Fox, Statistical mechanics and phase transitions in clustering, Phys. Rev. Lett. 65(1990)945–948.CrossRefPubMedGoogle Scholar
  92. [92]
    K. Rose, E. Gurewitz and G.C. Fox, A deterministic annealing approach to clustering, Pattern Recognition Lett. 11(1990)589–594.CrossRefGoogle Scholar
  93. [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).Google Scholar
  94. [94]
    J. Skorin-Kapov, Tabu search applied to the quadratic assignment problem, ORSA J. Comput. 2(1990)33–45.Google Scholar
  95. [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.Google Scholar
  96. [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).Google Scholar
  97. [97]
    G.B. Sorkin, Efficient simulated annealing on fractal energy landscapes, Algorithmica 6(1991)367–418.CrossRefGoogle Scholar
  98. [98]
    G.B. Sorkin, Theory and practice of simulated annealing in fractal landscapes, Ph.D. Thesis, University of California, Berkeley, CA (1991).Google Scholar
  99. [99]
    C.M. Soukolis, K. Levin and G.S. Grest, Irreversibility and metastability in spin-glasses. I. Ising model, Phys. Rev. B28(1983)1495.Google Scholar
  100. [100]
    V. Srajer, K.T. Schomacker and P.M. Champion, Spectral broadening in biomolecules, Phys. Rev. Lett. 57(1986)1267–1270.CrossRefPubMedGoogle Scholar
  101. [101]
    G.L. Stebbins and F.J. Ayala, Is a new evolutionary synthesis necessary?, Science 213(1981)967–971.Google Scholar
  102. [102]
    F.H. Stillinger and T.A. Weber, Packing structures and transitions in liquids and solids, Science 225(1984)983.Google Scholar
  103. [103]
    G. Toulouse, Theory of the frustration effect in spin glasses: I, Commun. Phys. 2(1977)115.Google Scholar
  104. [104]
    G. Toulouse, How “frustration” set in, Physics Today 42(1989)97.Google Scholar
  105. [105]
    M.S. Waterman, Bull. Math. Biol. 46(1984)473–500.CrossRefGoogle Scholar
  106. [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.Google Scholar
  107. [107]
    K. Wuthrich, Science 234(1989)45–50; Accounts Chem. Res. 22(1989)36–44.Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1993

Authors and Affiliations

  • Pablo Moscato
    • 1
  1. 1.CeTAD, Universidad Nacional de La Plata, C.C. 75La PlataArgentina

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