Advertisement

Concepts in Optimizing Simulated Annealing Schedules: An Adaptive Approach for Parallel and Vector Machines

  • K. H. Hoffmann
  • D. Würtz
  • C. de Groot
  • M. Hanf
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 367)

Abstract

Simulated Annealing (Čemy 1983, Kirkpatrick et al. 1983) is a technique which allows to find optimal or near optimal solutions to difficult optimization problems. It has been especially successful in applications to NP-complete or NP-hard problems, which occur in a variety of fields (Garey and Johnson 1979). These include mathematics with many graph problems (e.g. Brelaz 1979, Bonomi and Lutton 1987, Andresen et al. 1988), condensed matter physics, e.g. with the problem of finding the ground state of spin glasses (Ettelaie and Moore 1985), with the problem of solving the Ginzberg-Landau equations (Doria et al. 1989), engineering problems with the design of integrated circuits including the partitioning as well as the wiring problem (Vecchi and Kirkpatrick 1983, Sechen and Sangiovanni-Vincentelli 1985, Siarry et al. 1987), the design of binary sequences with low autocorrelation (Beenker et al. 1985, Bernasconi 1987, 1988), image processing (Carnevali et al. 1985), design of X-ray mirrors (Würtz and Schneider 1989), statistics with the application as a learning paradigm in neural network theory (Bernasconi 1990) and economics for instance with the travelling salesman problem (e.g. Bonomi and Lutton 1984, Kirkpatrick and Toulouse 1985, Hanf et al. 1990). Naturally, these are only some selected examples, since it is not possible here to give reference to the few hundred simulated annealing papers which appeared during the last years.

Keywords

Optimal Schedule Ensemble Member Travelling Salesman Problem Travel Salesman Problem Ensemble Size 
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. Aarts, E., and J. Korts. 1989: Simulated Annealing and Boltzmann Machines. John Wiley&Sons, Chichester.Google Scholar
  2. Andresen, B., K.H. Hoffmann, K. Mosegaard, J. Nulton, J.M. Pedersen, and P. Salamon. 1988: On Lumped Models for Thermodynamic Properties of Simulated Annealing Problems, J. Phys. Prance 49, 1485.CrossRefGoogle Scholar
  3. Beenker, G.F.M., T.A.C.M. Claasen, and P.W.C. Hermens. 1985: Binary Sequences with a Maximally Flat Amplitude Spectrum, Philips J. of Research 40, 289.Google Scholar
  4. Bernasconi, J. 1987: Low Autocorrelation Binary Sequences: Statistical Mechanics and Configuration Space Analysis, J. Physique 40, 559.Google Scholar
  5. Bernasconi, J. 1988. Optimization Problems and Statistical Mechanics. In Chaos and Complexity, Torino. World Scientific, Singapore.Google Scholar
  6. Bernasconi, J. 1990. Learning and Optimization. In Proc. IX Sitges Conf. on Neural Networks. Springer LN Physics, Vol. 368. Springer Verlag, Heidelberg.Google Scholar
  7. Bonomi, E., and J.L. Lutton. 1984: The N-City Travelling Salesman Problem: Statistical Mechanics and the Metropolis Algorithm, SI AM Review 26, 551.Google Scholar
  8. Bonomi, E., and J.L. Lutton. 1987: Simulated Annealing Algorithm for the Minimum Weighted Perfect Euclidean Matching Problem, Operations Research.Google Scholar
  9. Brelaz, D. 1979: New Methods to Color the Vertices of a Graph, ACM 22, 251.CrossRefGoogle Scholar
  10. Burke, C.J., and M. Rosenblatt. 1958: A Markovian Function of a Markov Chain, Ann. Math. Stat. 1112.Google Scholar
  11. Carnevali, P., L. Coletti, and S. Paternello. 1985: Image Processing by Simulated Annealing, IBM J. Res. Develop., 29, 569.Google Scholar
  12. Cerny, V. 1983: Thermodynamical Approach to the Traveling Salesman Problem: An Efficient Simulation Algorithm, JOTA 45, 41.CrossRefGoogle Scholar
  13. Christoph, M., and K.H. Hoffmann. 1990: Scaling Behavior of Optimal Simulated Annealing Schedules, PreprintGoogle Scholar
  14. Darema, F., S. Kirkpatrick, and V.A. Norton. 1987: Parallel Algorithms for Chip Placement by Simulated Annealing, IBM J. Res. Develop., 31, 391.CrossRefGoogle Scholar
  15. Doria, M.M., J.E. Gubernatis, and D. Rainer. 1989: On solving the Ginzberg-Landau equations by Simulated Annealing, Los Alamos Preprint LA-UR-89–2997.Google Scholar
  16. Dueck, G., and T. Scheuer. 1988: Threshold Accepting a General Purpose Optimization Algorithm Appearing Superior to Simulated Annealing, Research Report TR 88.10.011, IBM Scientific Center, Heidelberg.Google Scholar
  17. Dueck, G. 1989: New Optimization Heuristics: The Great Deluge Algorithm and the Record-to-Record Travel, Research Report TR 89.06.011, IBM Scientific Center, Heidelberg.Google Scholar
  18. Ettelaie, R., and M.A. Moore. 1985: Residual Entropy and Simulated Annealing, J. Physique Lett. 46, L-893.Google Scholar
  19. Garey, M.R., and D.S. Johnson. 1979: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, San Francisco.Google Scholar
  20. Grötschel, M. 1984: Polyedrische Kombinatorik und Schnittebenenverfahren, Preprint No. 38, Universität AugsburgGoogle Scholar
  21. Grötschel, M., and M. Padberg. 1985: Polyhedral Theory p. 251, Polyhedral Computations p. 307, In The Travelling Salesman Problem, E.L. Lawler et al. (eds.). Wiley&Sons, Chichester.Google Scholar
  22. Grotschel, M., L. Lovasz, and A. Schrijver. 1988: Geometric Algorithms and Combinatorial Optimization, Springer Verlag, Heidelberg.CrossRefGoogle Scholar
  23. Hanf, M., D. Wiirtz, K.H. Hoffmann, C. de Groot, Y. Lehareinger, and M. Anliker. 1990: Optimization with Parallel Simulated Annealing on a Transputer Farm, submitted to: Parallel ComputingGoogle Scholar
  24. Hoffmann, K.H., and P. Salamon. 1990: The Optimal Simulated Annealing Schedule for a Simple Model, J. Phys. A - Math. Gen. 23, 3511.CrossRefGoogle Scholar
  25. Hoffmann, K.H., and P. Sibani. 1988: Diffusion in Hierarchies, Phys. Rev. A 38, 4261.Google Scholar
  26. Hoffmann, K.H., P. Sibani, J.M. Pedersen, and P. Salamon. 1990: Optimal Ensemble Size for Parallel Implementations of Simulated Annealing, Appi. Math. Lett. 3, 53.CrossRefGoogle Scholar
  27. Holland, H. 1987: Schnittebenenverfahren für Travelling Salesman und verwandte Probleme, PhD Thesis, Bonn.Google Scholar
  28. Jakobsen, M.O., K. Mosegaard, and J.M. Pedersen. 1988. Global Model Optimization in Reflection Seismology by Simulated Annealing. In Model Optimization in Exploration Geophysics 2, ed. A. Vogel, 361. Bratmschweig/ Wiesbaden: Priedr. Vieweg and Son.Google Scholar
  29. Kemeny, J.G., and J.L. Snell. 1960: Finite Markov Chains. Princeton: D. Van. Nostrand Company, Inc.Google Scholar
  30. Kirkpatrick, S., C.D. Gelatt Jr., and M.P. Vecchi. 1983: Optimization by Simulated Annealing, Science 220, 671.CrossRefGoogle Scholar
  31. Kirkpatrick, S., and G. Toulouse. 1985: Configuration Space Analysis of Travelling Salesman Problems, J. de Physique 46, 1277.CrossRefGoogle Scholar
  32. Lam, J., and J. Delosme. 1987. An Adaptive Annealing Schedule. Department of Eletrical Engineering, Yale University. 8608.Google Scholar
  33. Lin, S., and B.W. Kernighan. 1973: Oper. Res. 21, 498.CrossRefGoogle Scholar
  34. Metropolis, N., A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller. 1953: Equation of State Calculations by Fast Computing Machines, J. Chem. Phys 21, 1087.Google Scholar
  35. Morgenstem, I., and D. Würtz. 1987: Simulated Annealing for Spin-Glass-Like Optimization Problems, Z. Phys. B 67, 397.CrossRefGoogle Scholar
  36. Mühlenbein, M. Gorges-Schleuter, and O. Kramer. 1988: Evolution Algorithms in Combinatorial Optimization, Parallel Computing 7, 65.CrossRefGoogle Scholar
  37. Mühlenbein, H., and J. Kindermann. 1989: The Dynamics of Evolution and Learning. In Connectionism in Perspective. Pfeiffer et al. (eds.), p. 173, North Holland Publ., Amsterdam.Google Scholar
  38. Padberg, M., and G. Rinaldi. 1987: Optimization of a 532-city Symmetric Traveling Salesman Problem by branch and cut, Oper. Res. lett. 6Google Scholar
  39. Pedersen, J.M., K. Mosegaard, M.O. Jacobsen, and P. Salamon. 1989: Optimal Degree of Parallel Implementation in Optimization, Report HC 98–14, Oerstedt Institute, University of CopenhagenGoogle Scholar
  40. Rees, S., and R.C. Ball. 1987: Criteria for an Optimum Simulated Annealing Schedule for Problems of the Travelling Salesman Type, J. Phys. A 20, 1239.CrossRefGoogle Scholar
  41. Rossier, Y., M. Troyen, and T.M. Liebling. 1986: Probabilistic Exchange Algorithms and Euclidian Travelling Salesman Problems, OR Spektrum 8, 151.CrossRefGoogle Scholar
  42. Ruppeiner, G., J.M. Pedersen, and P. Salamon. 1990: Ensemble Approach to Simulated Annealing, PreprintGoogle Scholar
  43. Salamon, P., J. Nulton, J. Robinson, J. Pedersen, G. Ruppeiner, and L. Liao. 1988: Simulated Annealing with Constant Thermodynamic Speed, Comput. Phys. Commun. 49, 423.CrossRefGoogle Scholar
  44. Sechen, C., and A. Sangiovanni-Vincentelli. 1985: The TimberWolf Placement and Routing Package, IEEE Journal of Solid State Circuits 20, 510.CrossRefGoogle Scholar
  45. Siarry, P., L. Bergouzi, and G. Dreyfus. 1987: Thermodynamic Optimization of Block Placement, IEEE Trans, on Computer-Aided Design, 6, 211.CrossRefGoogle Scholar
  46. Sibani, P., J.M. Pedersen, K.H. Hoffmann, and P. Salamon. 1990: Monte Carlo Dynamics of Optimization Problems: A Scaling Description, Phys. Rev. A 42, 7080.Google Scholar
  47. Vecchi, M.P., and S. Kirkpatrick. 1983: Global Wiring by Simulated Annealing, IEEE Trans, on Computer Aided Design 2, 215.CrossRefGoogle Scholar
  48. Würtz, D., and T. Schneider. 1989: Optimization of X-Ray Mirrors by Simulated Annealing, IPS Research Report No. 89-02.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • K. H. Hoffmann
    • 1
  • D. Würtz
    • 2
  • C. de Groot
    • 2
  • M. Hanf
    • 1
  1. 1.Institut für Theoretische PhysikUniversität HeidelbergHeidelbergFed. Rep. Germany
  2. 2.Interdisziplinäres Projektzentrum für Supercomputing, ETH-ZentrumZürichSwitzerland

Personalised recommendations