In this paper, a genetic model based on the operations of recombination and mutation is studied and applied to combinatorial optimization problems.

Results are:

  1. The equations of the deterministic dynamics in the thermodynamic limit (infinite populations) are derived and, for a sufficiently small mutation rate, the attractors are characterized;

  2. A general approximation algorithm for combinatorial optimization problems is designed. The algorithm is applied to the Max Ek-Sat problem, and the quality of the solution is analyzed. It is proved to be optimal for k≥3 with respect to the worst case analysis; for Max E3-Sat the average case performances are experimentally compared with other optimization techniques.

Genetic algorithms, Markov chains, dynamical systems, combinatorial optimization, approximation algorithms, Hopfield's networks.
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© 2000 Massachusetts Institute of Technology
2000
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