Evolutionary Game Dynamics in Combinatorial Optimization: An Overview

  • Marcello Pelillo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2037)


Replicator equations are a class of dynamical systems developed and studied in the context of evolutionary game theory, a discipline pioneered by J. Maynard Smith which aims to model the evolution of animal behavior using the principles and tools of noncooperative game theory. Because of their dynamical properties, they have been recently applied with significant success to a number of combinatorial optimization problems. It is the purpose of this article to provide a summary and an up-to-date bibliography of these applications.


Maximum Clique Evolutionary Game Replicator Dynamic Evolutionary Game Theory Isomorphism Problem 
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.
    J. Hofbauer and K. Sigmund. Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge, UK, 1998.CrossRefzbMATHGoogle Scholar
  2. 2.
    J.W. Weibull. Evolutionary Game Theory. MIT Press, Cambridge, MA, 1995.zbMATHGoogle Scholar
  3. 3.
    J.F. Crow and M. Kimura. An Introduction to Population Genetics Theory. Harper & Row, New York, 1970.zbMATHGoogle Scholar
  4. 4.
    R.A. Fisher. The Genetical Theory of Natural Selection. Oxford University Press, London, UK, 1930.CrossRefzbMATHGoogle Scholar
  5. 5.
    I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P.M. Pardalos, editors, Handbook of Combinatorial Optimization (Suppl. Vol. A), pages 1–74. Kluwer, Boston, MA, 1999.Google Scholar
  6. 6.
    T.S. Motzkin and E.G. Straus. Maxima for graphs and a new proof of a theorem of Turán. Canad. J. Math., 17:533–540, 1965.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    L.E. Gibbons, D.W. Hearn, P.M. Pardalos, and M.V. Ramana. Continuous characterizations of the maximum clique problem. Math. Oper. Res., 22:754–768, 1997.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    M. Pelillo and A. Jagota. Feasible and infeasible maxima in a quadratic program for maximum clique. J. Artif. Neural Networks, 2:411–420, 1995.Google Scholar
  9. 9.
    M. Pelillo. Relaxation labeling networks for the maximum clique problem. J. Artif. Neural Networks, 2:313–328, 1995.Google Scholar
  10. 10.
    M. Pelillo and I.M. Bomze. Parallelizable evolutionary dynamics principles for solving the maximum clique problem. In H.-M. Voigt, W. Ebeling, I. Rechenberg, and H.-P. Schwefel, editors, Parallel Problem Solving from Nature-PPSN IV, pages 676–685. Springer-Verlag, Berlin, 1996.CrossRefGoogle Scholar
  11. 11.
    I.M. Bomze. Evolution towards the maximum clique. J. Glob. Optim., 10:143–164, 1997.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    I.M. Bomze, M. Pelillo, and R. Giacomini. Evolutionary approach to the maximum clique problem: Empirical evidence on a larger scale. In I.M. Bomze, T. Csendes, R. Horst, and P.M. Pardalos, editors, Developments in Global Optimization, pages 95–108. Kluwer, Dordrecht, The Netherlands, 1997.CrossRefGoogle Scholar
  13. 13.
    I.M. Bomze and F. Rendl. Replicator dynamics for evolution towards the maximum clique: Variations and experiments. In R. De Leone, A. Murlí, P.M. Pardalos, and G. Toraldo, editors, High Performance Algorithms and Software in Nonlinear Optimization, pages 53–67. Kluwer, Dordrecht, The Netherlands, 1998.CrossRefGoogle Scholar
  14. 14.
    I.M. Bomze. Global escape strategies for maximizing quadratic forms over a simplex. J. Glob. Optim., 11:325–338, 1997.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    I.M. Bomze, M. Budinich, M. Pelillo, and C. Rossi. A new “annealed” heuristic for the maximum clique problem. In P.M. Pardalos, editor, Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems, pages 78–95. Kluwer, Dordrecht, The Netherlands, 2000.CrossRefGoogle Scholar
  16. 16.
    I.M. Bomze and V. Stix. Genetic engineering via negative fitness: Evolutionary dynamics for global optimization. Ann. Oper. Res., 89:279–318, 1999.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    I.M. Bomze, M. Pelillo, and V. Stix. Approximating the maximum weight clique using replicator dynamics. IEEE Trans. Neural Networks, 11(6):1228–1241, 2000.CrossRefGoogle Scholar
  18. 18.
    M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H.Freeman, San Francisco, CA, 1979.zbMATHGoogle Scholar
  19. 19.
    D.S. Johnson. The NP-completeness column: An ongoing guide. J. Algorithms, 9:426–444, 1988.MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    M. Pelillo. Replicator equations, maximal cliques, and graph isomorphism. Neural Computation, 11(8):2023–2045, 1999.CrossRefGoogle Scholar
  21. 21.
    M. Pelillo, K. Siddiqi, and S.W. Zucker. Matching hierarchical structures using association graphs. IEEE Trans. Pattern Anal. Machince Intell., 21(11):1105–1120, 1999.CrossRefGoogle Scholar
  22. 22.
    H. Mühlenbein, M. Gorges-Schleuter, and O. Krämer. Evolution algorithms in combinatorial optimization. Parallel Computing, 7:65–85, 1988.CrossRefzbMATHGoogle Scholar
  23. 23.
    M. Pelillo. Relaxation labeling processes for the traveling salesman problem. In Proc. Int. J. Conf. Neural Networks, pages 2429–2432, Nagoya, Japan, 1993.Google Scholar
  24. 24.
    A. Menon, K. Mehrotra, C.K. Mohan, and S. Ranka. Optimization using replicators. In Proc. 6th. Int. Conf. Genetic Algorithms, pages 209–216. Morgan Kaufmann, 1995.Google Scholar
  25. 25.
    C. Rossi. A replicator equations based evolutionary algorithm for the maximum clique problem. In Congress on Evolutionary Computation, pages 1565–1570, 2000.Google Scholar
  26. 26.
    A. Menon, K. Mehrotra, C.K. Mohan, and S. Ranka. Replicators, majorization and genetic algorithms: New models and analytical tools. In Proc. FOGA’96-Found. of Genetic Algorithms, Aug. 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Marcello Pelillo
    • 1
  1. 1.Dipartimento di InformaticaUniversità Ca’ Foscari di VeneziaVenezia MestreItaly

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