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Consider the problem MAX-SATISFY over F2, that is, given a system of m linear equations with n variables over F2, find a solution satisfying the maximal number of equations. An improved particle swarm optimization (PSO) method is proposed for computing maximal satisfying solution of a polynomial equation system with equation number being far larger than variable number in a finite field. As far as we know, it's the first time to adopt the heuristic intelligent algorithm (PSO) to solve such discrete equations in finite field. It's obvious that there are no solutions satisfying all the equations. So our goal is to find a solution which satisfies as many equations as possible. Four randomly generated Boolean equations are solved with sizes F2 100Ã20, F2 300Ã50, F2 500Ã100 and F2 1000Ã200. Empirical results show that algorithm has a robust performance and strong exploration and exploitation abilities.
Artificial Intelligence and Computational Intelligence, 2009. AICI '09. International Conference on (Volume:2 )
Date of Conference: 7-8 Nov. 2009