A New Hybrid Metaheuristic – Combining Stochastic Tunneling and Energy Landscape Paving

  • Kay Hamacher
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7919)


(Hybrid) metaheuristics such as simulated annealing, genetic algorithms, or extremal optimization play a most prominent role in global optimization. The performance of these algorithms and their respective sampling behavior during the search process are themselves interesting problems. Here, we show that a combination of two approaches – namely Energy Landscape Paving (ELP) and Stochastic Tunneling (STUN) – can overcome known problems of other Metropolis-sampling-based procedures. We show on grounds of non-equilibrium statistical mechanics and empirical evidence on the synergistic advantages of this combined approach and discuss simulations for a complex optimization problem.


Simulated Annealing Global Optimization Tabu Search Spin Glass Ising Spin 
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.


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  1. 1.
    Arito, F., Leguizamón, G.: Incorporating tabu search principles into aco algorithms. In: Blesa, et al. (eds.) [5], pp. 130–140Google Scholar
  2. 2.
    Barahona, F.: On the computational complexity of ising spin glass models. Journal of Physics A: Mathematical and General 15(10), 3241 (1982), MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bentner, J., Bauer, G., Obermair, G.M., Morgenstern, I., Schneider, J.: Optimization of the time-dependent traveling salesman problem with monte carlo methods. Phys. Rev. E 64, 036701 (2001)Google Scholar
  4. 4.
    Binder, K., Young, A.: Spin glasses: Experimental facts, theoretical concepts, and open questions. Rev. Mod. Phys. 58(4), 801–976 (1986)CrossRefGoogle Scholar
  5. 5.
    Blesa, M.J., Blum, C., Di Gaspero, L., Roli, A., Sampels, M., Schaerf, A. (eds.): HM 2009. LNCS, vol. 5818. Springer, Heidelberg (2009)zbMATHGoogle Scholar
  6. 6.
    Chaves, A.A., Lorena, L.A.N., Miralles, C.: Hybrid metaheuristic for the assembly line worker assignment and balancing problem. In: Blesa, et al. (eds.) [5], pp. 1–14Google Scholar
  7. 7.
    Chávez, E., Navarro, G., Baeza-Yates, R., Marroquín, J.L.: Searching in metric spaces. ACM Comput. Surv. 33(3), 273–321 (2001)CrossRefGoogle Scholar
  8. 8.
    Doerner, K.F., Schmid, V.: Survey: Matheuristics for rich vehicle routing problems. In: Blesa, M.J., Blum, C., Raidl, G., Roli, A., Sampels, M. (eds.) HM 2010. LNCS, vol. 6373, pp. 206–221. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Doye, J.P.K., Wales, D.J.: Thermodynamics of global optimization. Phys. Rev. Lett. 80(7), 1357–1360 (1998)CrossRefGoogle Scholar
  10. 10.
    Fernandes, S., Lourenço, H.R.: Optimised search heuristic combining valid inequalities and tabu search. In: Blesa, M.J., Blum, C., Cotta, C., Fernández, A.J., Gallardo, J.E., Roli, A., Sampels, M. (eds.) HM 2008. LNCS, vol. 5296, pp. 87–101. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. 11.
    Glover, F.: Future paths for integer programming and links to artificial intelligence. Comput. Oper. Res. 13, 533–549 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Glover, F., Laguna, M.: Tabu Search. Kluwer, Dordrecht (1997)zbMATHCrossRefGoogle Scholar
  13. 13.
    Hamacher, K.: Adaptation in stochastic tunneling global optimization of complex potential energy landscapes. Europhys. Lett. 74(6), 944–950 (2006)CrossRefGoogle Scholar
  14. 14.
    Hamacher, K.: Energy landscape paving as a perfect optimization approach under detrended fluctuation analysis. Physica A 378(2), 307–314 (2007)CrossRefGoogle Scholar
  15. 15.
    Hansmann, U., Wille, L.T.: Global Optimization by Energy Landscape Paving. Phys. Rev. Lett. 88(23), 068105 (2002)Google Scholar
  16. 16.
    Ingber, L.: Simulated annealing: Practice versus theory. Mathematical and Computer Modelling 18(11), 29–57 (1993), MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Kirkpatrick, S., Gelatt, C., Vecchi, M.: Optimization by simulated annealing. Science 220, 671–680 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Klotz, T., Schubert, S., Hoffmann, K.: The state space of short-range Ising spin glasses: the density of states. The European Physical Journal B-Condensed Matter and Complex Systems 2(3), 313–317 (1998)CrossRefGoogle Scholar
  19. 19.
    Liwo, A., Lee, J., Ripoll, D.R., Pillardy, J., Scheraga, H.A.: Protein structure prediction by global optimization of a potential energy function. PNAS 96(10), 5482–5485 (1999)CrossRefGoogle Scholar
  20. 20.
    Maringer, D., Parpas, P.: Global optimization of higher order moments in portfolio selection. J. Glob. Opt. 43, 219–230 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Mertens, S.: Random Costs in Combinatorial Optimization. Phys. Rev. Lett. 84(6), 1347–1350 (2000)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087–1092 (1953)CrossRefGoogle Scholar
  23. 23.
    Middleton, A.A.: Improved extremal optimization for the ising spin glass. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 69(5), 055701 (2004),
  24. 24.
    Munakata, T., Nakamura, Y.: Temperature control for simulated annealing. Phys. Rev. E 64(4), 046127 (2001)Google Scholar
  25. 25.
    Nayeem, A., Vila, J., Scheraga, H.A.: A comparative study of the simulated-annealing and monte carlo-with- minimization approaches to the minimum-energy structures of polypeptides: [met]-enkephalin. J. Comp. Chem. 12(5), 594–605 (1991)CrossRefGoogle Scholar
  26. 26.
    Notay, Y.: Flexible conjugate gradients. SIAM Journal on Scientific Computing 22(4), 1444–1460 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Prügel-Bennett, A., Shapiro, J.L.: Analysis of genetic algorithms using statistical mechanics. Phys. Rev. Lett. 72(9), 1305–1309 (1994)CrossRefGoogle Scholar
  28. 28.
    Schug, A., Wenzel, W., Hansmann, U.: Energy landscape paving simulations of the trp-cage protein. J. Chem. Phys. 122, 194711 (2005)CrossRefGoogle Scholar
  29. 29.
    Sexton, R.S., Dorsey, R.E., Johnson, J.D.: Toward global optimization of neural networks: A comparison of the genetic algorithm and backpropagation. Decision Support Systems 22(2), 171–185 (1998)CrossRefGoogle Scholar
  30. 30.
    Simone, C., Diehl, M., Jünger, M., Mutzel, P., Reinelt, G.: Exact ground states of ising spin glasses: New experimental results with a branch-and-cut algorithm. J. Stat. Phys. 80, 487 (1995)zbMATHCrossRefGoogle Scholar
  31. 31.
    Wales, D.J., Scheraga, H.A.: Global Optimization of Clusters, Crystals, and Biomolecules. Science 285(5432), 1368–1372 (1999)CrossRefGoogle Scholar
  32. 32.
    Walshaw, C.: Multilevel refinement for combinatorial optimisation: Boosting metaheuristic performance. In: Blum, C., Aguilera, M.J.B., Roli, A., Sampels, M. (eds.) Hybrid Metaheuristics. SCI, vol. 114, pp. 261–289. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  33. 33.
    Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 1(1), 67–82 (1997), CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Kay Hamacher
    • 1
  1. 1.Dept. of Computer Science, Dept. of Physics & Dept. of BiologyTechnical University DarmstadtDarmstadtGermany

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