Advertisement

Enhancing the Performance of Memetic Algorithms by Using a Matching-Based Recombination Algorithm

  • Regina Berretta
  • Carlos Cotta
  • Pablo Moscato
Part of the Applied Optimization book series (APOP, volume 86)

Abstract

The Number Partitioning Problem (MNP) remains as one of the simplest-to-describe yet hardest-to-solve combinatorial optimization problems. In this paper we use the MNP as a surrogate for several related real-world problems, to test new heuristics ideas. To be precise, we study the use of weight-matching techniques to devise smart memetic operators. Several options are considered and evaluated for that purpose. The positive computational results indicate that — despite the MNP may be not the best scenario for exploiting these ideas — the proposed operators can be really promising tools for dealing with more complex problems of the same family.

Keywords

Memetic algorithms Tabu search Number partitioning problem Weight matching. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. C.C. Aggarwal, J.B. Orlin, and R.P. Tai. Optimized crossover for the independent set problem. Operations Research, 45 (2): 226–234, 1997.MathSciNetzbMATHCrossRefGoogle Scholar
  2. M.F. Arguello, T.A. Feo, and O. Goldschmidt. Randomized methods for the number partitioning problem. Computers & Operations Research,23(2):103111,1996.Google Scholar
  3. E. Balas and W. Niehaus. Finding large cliques in arbitrary graphs by bipartite matching. In D.S. Johnson and M.A. Trick, editors, Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, volume DIMACS 26, pages 29–51. American Mathematical Society, 1996.Google Scholar
  4. R. Berretta and P. Moscato. The number partitioning problem: An open challenge for evolutionary computation? In D. Come, M. Dorigo, and F. Glover, editors, New Ideas in Optimization, pages 261–278. McGraw-Hill, 1999.Google Scholar
  5. A. Caprara and M. Fischetti. Branch-and-cut algorithms. In M. Dell’Amico, F. Maffioli, and S. Martello, editors, Annotated bibliographies in combinatorial optimization, pages 45 — 63. John Wiley and Sons, Chichester, 1997.Google Scholar
  6. P. Cheeseman, B. Kanefsky, and W.M. Taylor. Where the Really Hard Problems Are. In Proceedings of the Twelfth International Joint Conference on Artificial Intelligence, IJCAI-91, Sydney, Australia, pages 331–337, 1991.Google Scholar
  7. L. Davis. Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York NY, 1991.Google Scholar
  8. F.F. Ferreira and J.F. Fontanari. Probabilistic analysis of the number partitioning problem. Journal of Physics A: Math. Gen, pages 3417–3428, 1998.Google Scholar
  9. F. Glover and M. Laguna. Tabu Search. Kluwer Academic Publishers, Norwell, Massachusetts, USA, 1997.Google Scholar
  10. M. Gorges-Schleuter. ASPARAGOS: An asynchronous parallel genetic optimization strategy. In J. David Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms, pages 422–427, San Mateo, CA, 1989. Morgan Kaufmann Publishers.Google Scholar
  11. M. Gorges-Schleuter. Explicit Parallelism of Genetic Algorithms through Population Structures. In H.-P. Schwefel and R. Männer, editors, Parallel Problem Solving from Nature I, volume 496 of Lecture Notes in Computer Science, pages 150–159. Springer-Verlag, Berlin, Germany, 1991.Google Scholar
  12. D.S. Johnson, C. R. Aragon, L. A. McGeoch, and C. Schevon. Optimization by simulated annealing: An experimental evaluation; Part II: Graph coloring and number partitioning. Operations Research, 39 (3): 378–406, 1991.zbMATHCrossRefGoogle Scholar
  13. D.R. Jones and M.A. Beltramo. Solving partitioning problems with genetic algorithms. In R.K Belew and L.B. Booker, editors, Proceedings of the Fourth International Conference on Genetic Algorithms, pages 442–449, San Mateo, CA, 1991. Morgan Kaufmann.Google Scholar
  14. N. Karmarkar and R.M. Karp. The differencing method of set partitioning. Report UCB/CSD 82/113, University of California, Berkeley, CA, 1982.Google Scholar
  15. S. Kirkpatrick, C.D. Gelatt Jr., and M.P. Vecchi. Optimization by simmulated annealing. Science, 220 (4598): 671–680, 1983.MathSciNetzbMATHCrossRefGoogle Scholar
  16. D. Kirovski, M. Ercegovac, and M. Potkonjak. Low-power behavioral synthesis optimization using multiple-precision arithmetic. In ACM-IEEE Design Automation Conference, pages 568–573. ACM Press, 1999.Google Scholar
  17. R. Korf. A complete anytime algorithm for number partitioning. Artificial Intelligence, 106: 181–203, 1998.MathSciNetzbMATHCrossRefGoogle Scholar
  18. M. Laguna and P. Laguna. Applying Tabu Search to the 2-dimensional Ising spin glass. International Journal of Modern Physics C–Physics and Computers, 6 (1): 11–23, 1995.CrossRefGoogle Scholar
  19. E.L. Lawler and D.E. Wood. Branch and bounds methods: A survey. Operations Research, 4 (4): 669–719, 1966.MathSciNetGoogle Scholar
  20. D.L. Mammen and T. Hogg. A new look at the easy-hard-easy pattern of combinatorial search difficulty. Journal of Artificial Intelligence Research, 7: 47–66, 1997.MathSciNetzbMATHGoogle Scholar
  21. S. Mertens. Phase transition in the number partitioning problem. Physical Review Letters, 81 (20): 4281–4284, 1998.MathSciNetzbMATHCrossRefGoogle Scholar
  22. S. Mertens. Random costs in combinatorial optimization. Physical Review Letters, 84 (6): 1347–1350, 2000.MathSciNetCrossRefGoogle Scholar
  23. D.G. Mitchell, B. Selman, and H.J. Levesque. Hard and easy distributions for SAT problems. In P. Rosenbloom and P. Szolovits, editors, Proceedings of the Tenth National Conference on Artificial Intelligence, pages 459–465, Menlo Park, California, 1992. AAAI Press.Google Scholar
  24. P. Moscato. On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts: Towards Memetic Algorithms. Technical Report Caltech Concurrent Computation Program, Report. 826, California Institute of Technology, Pasadena, California, USA, 1989.Google Scholar
  25. P. Moscato. An Introduction to Population Approaches for Optimization and Hierarchical Objective Functions: The Role of Tabu Search. Annals of Operations Research, 41 (1–4): 85–121, 1993.Google Scholar
  26. P. Moscato. Memetic algorithms: A short introduction. In D. Corne, M. Dorigo, and F. Glover, editors, New Ideas in Optimization, pages 219–234. McGraw-Hill, 1999.Google Scholar
  27. P. Moscato and C. Cotta. A gentle introduction to memetic algorithms. In F. Glover and G. Kochenberger, editors, Handbook of Metaheuristics, pages 105–144. Kluwer Academic Publishers, Boston MA, 2003.Google Scholar
  28. 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 M. Valero, E. Onate, M. Jane, J. L. Larriba, and B. Suarez, editors, Parallel Computing and Transputer Applications, pages 177–186, Amsterdam, 1992. IOS Press.Google Scholar
  29. H. Mühlenbein. Evolution in Time and Space — The Parallel Genetic Algorithm. In Gregory J.E. Rawlins, editor, Foundations of Genetic Algorithms, pages 316–337, San Mateo, CA, 1991. Morgan Kaufmann Publishers.Google Scholar
  30. M.G. Norman and P. Moscato. A competitive and cooperative approach to complex combinatorial search. In Proceedings of the 20th Informatics and Operations Research Meeting, pages 3.15–3.29, Buenos Aires, 1991.Google Scholar
  31. C.H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.Google Scholar
  32. N.J. Radcliffe. The algebra of genetic algorithms. Annals of Mathematics and Artificial Intelligence, 10: 339–384, 1994.MathSciNetzbMATHCrossRefGoogle Scholar
  33. N.J. Radcliffe and P.D. Surry. Fitness Variance of Formae and Performance Prediction. In L.D. Whitley and M.D. Vose, editors, Proceedings of the Third Workshop on Foundations of Genetic Algorithms, pages 51–72, San Francisco, 1994a. Morgan Kaufmann.Google Scholar
  34. N.J. Radcliffe and P.D. Surry. Formal Memetic Algorithms. In T. Fogarty, editor, Evolutionary Computing: AISB Workshopvolume 865 of Lecture Notes in Computer Sciencepages 1–16. Springer-Verlag, Berlin, 1994b. Google Scholar
  35. W. Ruml. Stochastic approximation algorithms for number partitioning. Technical Report TR-17–93, Harvard University, Cambridge, MA, USA, 1993. available via ftp://das-ftp.harvard.edu/techreports/tr-17–93.ps.gz.Google Scholar
  36. W. Ruml, J.T. Ngo, J. Marks, and S.M. Shieber. Easily searched encodings for number partitioning. Journal of Optimization Theory and Applications, 89 (2): 251–291, 1996.MathSciNetzbMATHCrossRefGoogle Scholar
  37. R. Slootmaekers, H. Van Wulpen, and W. Joosen. Modelling genetic search agents with a concurrent object-oriented language. In P. Sloot, M. Bubak, and B. Hertzberger, editors, High-Performance Computing and Networking, volume 1401 of Lecture Notes in Computer Science, pages 843–853. Springer, Berlin, 1998.Google Scholar
  38. B.M. Smith and M.E. Dyer. Locating the phase transition in binary constraint satisfaction. Artificial Intelligence, 81 (1–2): 155–181, 1996.MathSciNetCrossRefGoogle Scholar
  39. G. Sorkin. Theory and Practice of Simulated Annealing on Special Energy Landscapes. Ph.d. thesis, University of California at Berkeley, Berkeley, CA, 1992.Google Scholar
  40. R.H. Storer. Number partitioning and rotor balancing. In Talk at the INFORMS Conference, Optimization Techniques Track, TD15.2, 2001.Google Scholar
  41. R.H. Storer, S.W. Flanders, and S.D. Wu. Problem space local search for number partitioning. Annals of Operations Research, 63: 465–487, 1996.zbMATHCrossRefGoogle Scholar
  42. R. Tanese. Distributed genetic algorithms. In J.D. Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms, pages 434–439, San Mateo, CA, 1989. Morgan Kaufmann.Google Scholar
  43. D.H. Wolpert and W.G. Macready. No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1 (1): 67–82, 1997.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Regina Berretta
    • 1
  • Carlos Cotta
    • 2
  • Pablo Moscato
    • 1
  1. 1.School of Electrical Engineering and Computer Science Faculty of Engineering and Built EnvironmentThe University of NewcastleCallaghanAustralia
  2. 2.Departamento de Lenguajes y Ciencias de la Computación ETSI Informática (3.2.49)Universidad de MálagaMálagaSpain

Personalised recommendations