Abstract
Replicator equations, which arise in evolutionary game theory to model the evolution of animal behavior, have recently been applied with significant success to combinatorial optimization problems such as the maximum clique problem. This paper substantially expands on previous work along these lines, by proposing payoff-monotonic dynamics, a wide family of game dynamics of which replicator equations are just a special instance. Experiments show that this class contains dynamics which are considerably faster than and as accurate as replicator equations.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A. Bertoni, P. Campadelli, and G. Grossi. A discrete neural algorithm for the maximum clique problem: Analysis and circuit implementation. In Proc. WAE’97: Int. Workshop on Algorithm Engineering, Venice, Italy, 1997.
I. M. Bomze. Evolution towards the maximum clique. J. Global Optim., 10:143–164, 1997.
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.
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.
I. M. Bomze et.al Evolutionary approach to the maximum clique problem: Empirical evidence on a larger scale. In I. M. Bomze et.at, editor, Developments in Global Optimization, pages 95–108. Kluwer, Dordrecht, The Netherlands, 1997.
J. Hofbauer. Imitation dynamics for games. Collegium Budapest, preprint, 1995.
J. Hofbauer and K. Sigmund. Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge, UK, 1998.
A. Jagota, L. Sanchis, and R. Ganesan. Approximately solving maximum clique using neural networks and related heuristics. In D. Johnson and M. Trick, editors, Cliques, Coloring, and Satisfiability, DIMACS, 26:169–204. AMS, 1996.
T. S. Motzkin and E. G. Straus. Maxima for graphs and a new proof of a theorem of Turan. Canad. J. Math., 17:533–540, 1965.
M. Pelillo. Relaxation labeling networks for the maximum clique problem. J. Artif. Neural Networks, 2:313–328, 1995.
M. Pelillo. Replicator equations, maximal cliques, and graph isomorphism. Neural Computation, 11(8):2023–2045, 1999.
M. Pelillo and A. Jagota. Feasible and infeasible maxima in a quadratic program for maximum clique. J. Artif. Neural Networks, 2:411–420, 1995.
M. Pelillo and C. Rossi. Payoff-monotonic game dynamics and the maximum clique problem. In preparation.
M. Pelillo, K. Siddiqi, and S. W. Zucker. Matching hierarchical structures using association graphs. IEEE Trans. PAMI, 21(11):1105–1120, 1999.
J. W. Weibull. Evolutionary Game Theory. MIT Press, Cambridge, MA, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag London Limited
About this paper
Cite this paper
Pelillo, M., Rossi, C. (2002). Payoff-monotonic Game Dynamics for the Maximum Clique Problem. In: Tagliaferri, R., Marinaro, M. (eds) Neural Nets WIRN Vietri-01. Perspectives in Neural Computing. Springer, London. https://doi.org/10.1007/978-1-4471-0219-9_13
Download citation
DOI: https://doi.org/10.1007/978-1-4471-0219-9_13
Publisher Name: Springer, London
Print ISBN: 978-1-85233-505-2
Online ISBN: 978-1-4471-0219-9
eBook Packages: Springer Book Archive