Taboo Search: An Approach to the Multiple-Minima Problem for Continuous Functions

  • Djurdje Cvijović
  • Jacek Klinowski
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 62)

Abstract

We decribe an approach, based on Taboo (or “Tabu”) Search for discrete functions, for solving the multiple-minima problem of continuous functions. As demonstrated by model calculations, the algorithm avoids entrapment in local minima and continues the search to give a near-optimal final solution. The procedure is generally applicable, derivative-free, easy to implement, conceptually simpler than Simulated Annealing and open to further improvement.

Keywords

Simulated Annealing Global Minimum Current Solution Taboo List Iterative Step 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderssen, R.S. (1972). Global optimization. In Anderssen, R.S., Jennings, L.S., and Ryan, D.M., editors, Optimization, pages 27–34. University of Queensland Press, St. Lucia, Australia.Google Scholar
  2. Berry, R.S. (1993). Potential surfaces and dynamics: what clusters tell us. Chemical Reviews, 93: 2379–2394.CrossRefGoogle Scholar
  3. Choi, S.H., Hong, S.D, and Jhon, M.S. (1999). Taboo-based Monte Carlo search as a method to improve sampling efficiency. Molecular Simulation, 23: 151–168.CrossRefGoogle Scholar
  4. Committee On the Next Decade in Operations Research (CONDOR) (1988). Operations research: the next decade. Operations Research, 36 (4): 619–637.Google Scholar
  5. Cvijovié, D. and Klinowski, J. (1995). Taboo search: an approach to the multiple minima problem. Science, 267: 664–666.MathSciNetCrossRefGoogle Scholar
  6. Dekkers, A. and Aarts, E. (1991). Global optimization and simulated annealing. Mathematical Programming, 50: 367–393.MathSciNetMATHCrossRefGoogle Scholar
  7. Dixon, L.C.W. and Szegö, G.P., editors (1975). Towards Global Optimization, volume 1. North-Holland, New York, New York.Google Scholar
  8. Dixon, L.C.W. and Szegö, G.P., editors (1978). Towards Global Optimization. volume 2. North-Holland, New York, New York.Google Scholar
  9. Donnelly, R.A. (1987). Geometry optimization by simulated annealing. Chemical Physics Letters, 136: 274–278.CrossRefGoogle Scholar
  10. Doye, J.P.K. and Wales, D.J. (1997). Surveying a potential energy surface by eigenvector-following. applications to global optimisation and the structural transformations of clusters. Zeitschrift für Physik D-Atoms, Molecules, and Clusters, 40: 194–197.CrossRefGoogle Scholar
  11. Doye, J.P.K., Wales, D.J., and Berry, R.S. (1995). The effect of the range of the potential on the structures of clusters. The Journal of Chemical Physics, 103: 4234–4249.CrossRefGoogle Scholar
  12. Dutta, P., Majumdar, D., and Bhattacharyya, S.P. (1991). Global optimization of molecular geometry: a new avenue involving the use of Metropolis simulated annealing. Chemical Physics Letters, 181: 293–297.CrossRefGoogle Scholar
  13. Fletcher, R. (1980). Practical Methods of Optimization, volume 1. Wiley, New York, New York.MATHGoogle Scholar
  14. Fletcher, R. (1981). Practical Methods of Optimization, volume 2. Wiley, New York, New York.MATHGoogle Scholar
  15. Floudas, C. and Pardalos, P.M., editors (1991). Recent Advances in Global Optimization. Princeton University Press.Google Scholar
  16. Friden, C., Hertz, A., and de Werra, D. (1989). Stabulus–a technique for finding stable sets in large graphs with Tabu Search. Computing, 42: 35–44.MATHCrossRefGoogle Scholar
  17. Glover, F. (1989). Tabu Search–part I. ORSA Journal on Computing, 1: 190–206.MathSciNetMATHCrossRefGoogle Scholar
  18. Glover, F. (1990). Artificial intelligence, heuristic frameworks and Tabu Search. Managerial and Decision Economics, 11: 365–375.CrossRefGoogle Scholar
  19. Glover, F. (1990). Tabu Search–part II. ORSA Journal on Computing, 2: 4–32.MATHCrossRefGoogle Scholar
  20. Glover, F. (1990c). Tabu Search: a tutorial. Interfaces, 20: 74–94.CrossRefGoogle Scholar
  21. Glover, F. (1994). Tabu Search for nonlinear and parametric optimization (with links to Genetic Algorithms). Discrete Applied Mathematics, 49: 231–255.MathSciNetMATHCrossRefGoogle Scholar
  22. Glover, F. (1998a). Tabu Search: wellsprings and challenges. European Journal of Operational Research, 106: 221–225.MATHCrossRefGoogle Scholar
  23. Glover, F. (1998b). A template for scatter search and path relinking. In Fonlupt, C., Hao, J.-K., Lutton, E., Ronald, E., and Schoenauer, M., editors, Artificial Evolution, pages 3–51. Springer-Verlag, Berlin, Germany.Google Scholar
  24. Glover, F., Kelly, J.P., and Laguna, M. (1995). Genetic algorithms and Tabu Search: hybrids for optimization. Computers é4 Operations Research, 22: 111–134.MATHCrossRefGoogle Scholar
  25. Glover, F., Kochenberger, G.A., and Alidaee, B. (1998). Adaptive memory tabu search for binary quadratic programs. Management Science, 44: 336–345.MATHCrossRefGoogle Scholar
  26. Glover, F. and Laguna, M. (1991). Target analysis to improve a Tabu Search method for machine scheduling. Arabian Journal For Science and Engineering, 16: 239–253.Google Scholar
  27. Glover, F., Taillard, E., and de Werra, D. (1993). A user’s guide to tabu search. Annals of Operations Research, 41: 3–28.MATHCrossRefGoogle Scholar
  28. Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison Wesley, Reading, Massachusetts.Google Scholar
  29. Head, J.D. and Zerner, M.C. (1989). Newton-based optimization methods for obtaining molecular conformation. Advances in Quantum Chemistry, 20: 239–290.CrossRefGoogle Scholar
  30. Hertz, A. and de Werra, D. (1987). Using Tabu Search techniques for graph coloring. Computing, 39: 345–351.MathSciNetMATHCrossRefGoogle Scholar
  31. Hohl, D., Jones, R.O., Car, R., and Parrinello, M. (1987). The structure of selenium clusters: Se3 to Se8. Chemical Physics Letters, 139: 540–545.CrossRefGoogle Scholar
  32. Holland, J. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, Michigan.Google Scholar
  33. Hong, S.D. (2000). Evaluation of the excess free energy for two-center Lennard-Jones liquids using the bent effective acceptance ratio. Bulletin of the Korean Chemical Society, 21: 697–700.Google Scholar
  34. Hong, S.D. and Jhon, M.S. (1997). Evaluation of the excess free energy for two-center Lennard-Jones liquids using the bent effective acceptance ratio. Chemical Physics Letters, 267: 422–426.CrossRefGoogle Scholar
  35. Judson, R.S. (1992). Teaching polymers to fold. Journal of Physical Chemistry., 96: 10102–10104.CrossRefGoogle Scholar
  36. Judson, R.S., Jaeger, E.P., Treasurywala, A.M., and Peterson, M.L. (1993). Conformational searching methods for small molecules. 2. Genetic Algorithm approach. Journal of Computational Chemistry, 14: 1407–1414.CrossRefGoogle Scholar
  37. Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P. (1983). Optimization by simulated annealing. Science, 220: 671–680.MathSciNetMATHCrossRefGoogle Scholar
  38. Linert, W., IVlargl, P., and Lukovits, I. (1992). Numerical minimization procedures in molecular mechanics: structural modeling of the solvation of ß-cyclodextrin. Computers Chemistry, 16: 61–69.CrossRefGoogle Scholar
  39. Macready, W.G., Siapas, A.G., and Kauffman, S.A. (1996). Criticality and parallelism in combinatorial optimization. Science, 271: 56–59.CrossRefGoogle Scholar
  40. Morales, L.B., Garduno-Juarez, R., Aguilar-Alvarado, J.M., and RiverosCastro, F.J. (2000). A parallel tabu search for conformational energy optimization of oligopeptides. Journal of Computational Chemistry, 21: 147–156.CrossRefGoogle Scholar
  41. Pardalos, P.M., Liu, X., and Xue, G.L. (1997). A parallel tabu search for conformational energy optimization of oligopeptides. Journal of Global Optimization, 11: 55–68.MathSciNetMATHCrossRefGoogle Scholar
  42. Pardalos, P.M. and Rosen, J.B. (1987). Constrained Global Optimization: Algorithms and Applications. Springer-Verlag, Berlin, Germany.Google Scholar
  43. Phillips, A.T. and Rosen, J.B. (1994). Computational comparison of two methods for constrained global optimization. Journal of Global Optimization, 5: 325–332.MathSciNetMATHCrossRefGoogle Scholar
  44. Piela, L., Kostrowicki, J., and Scheraga, H.A. (1989). The multiple minima problem in the conformational analysis of molecules: deformation of the potential energy hypersurface by the diffusion equation method. Journal of Physical Chemistry., 93: 3339–3346.CrossRefGoogle Scholar
  45. Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (1992). Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, Cambridge, U.K.Google Scholar
  46. Rechenberg, I. (1973). Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog, Stuttgart, Germany.Google Scholar
  47. Schwefel, H.P. (1981). Numerical Optimisation of Computer Models. John Wiley, New York, New York.Google Scholar
  48. Snow, M.E. (1992). Powerful simulated annealing algorithm locates global minimum of protein folding potentials from multiple starting conformations. Journal of Computational Chemistry, 13: 579–584.CrossRefGoogle Scholar
  49. Törn, A. and Zilinskas, A. (1989). Global Optimization. Springer-Verlag, Berlin, Germany.Google Scholar
  50. Unger, R. and Moult, J. (1993). Genetic algorithms for protein folding simulations. Journal of Molecular Biology, 231: 75–81.CrossRefGoogle Scholar
  51. Laarhoven, P.J.M. and Aarts, E.H.L. (1987). Simulated Annealing. Theory and Applications. Kluwer Academic Publishers, Dordrecht, The Netherlands.Google Scholar
  52. Wales, D.J. and Doye, J.P.K. (1997). Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. Journal of Physical Chemistry, A101: 5111–5116.CrossRefGoogle Scholar
  53. Wales, D.J. and Scheraga, H.A. (1999). Review: chemistry–global optimization of clusters, crystals, and biomolecules. Science, 285: 1368–1372.CrossRefGoogle Scholar
  54. Westhead, D.R., Clark, D.E., and Murray, C.W. (1997). A comparison of heuristic search algorithms for molecular docking. Journal of Computer-Aided Molecular Design, 11: 209–228.CrossRefGoogle Scholar
  55. Wille, L.T. (1987). Minimum energy configurations of atomic clusters: new results obtained by simulated annealing. Chemical Physics Letters, 133: 405–410.CrossRefGoogle Scholar
  56. Xiao, Y.L. and Williams, D.E. (1993). Minimum energy configurations of atomic clusters: new results obtained by simulated annealing. Chemical Physics Letters, 215: 17–24.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Djurdje Cvijović
    • 1
  • Jacek Klinowski
    • 1
  1. 1.Department of ChemistryUniversity of CambridgeCambridgeUK

Personalised recommendations