Replicators & Complementarity: Solving the Simplest Complex System without Simulation

Authors:
Anil Menon
Affiliations:
-
Venue:
ICCS '01 Proceedings of the International Conference on Computational Science-Part II
Year:
2001

Citing 3
Cited 0

On the Optimality of the Median Cut Spectral Bisection Graph Partitioning Method

SIAM Journal on Scientific Computing
Engineering and Economic Applications of Complementarity Problems

SIAM Review
Optimization Using Replicators

Proceedings of the 6th International Conference on Genetic Algorithms

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Abstract

Replicator systems are a class of first order, nonlinear differential equations, arising in an extraordinary variety of modeling situations. It is shown that finding the stationary points of replicator systems is equivalent to solving a nonlinear complementarity problem. One consequence is that it becomes possible to use replicator systems to solve very large instances of the NP-complete graph bisection problem. The methodological and philosophical import of their equivalence with complementarity problems (upto stationarity) is discussed.