充足可能性問題のラグランジュの方法による解法への発見的手法に関する研究(一般講演)

抄録

The satisfiability problem (SAT) is one of important problems in the field of the information science. However, no general deterministic polynomial time algorithms are known yet. The Hopfield type neural networks for solving difficult combinatorial optimization problems have used the gradient descent algorithms to solve constrained optimization problems via penalty functions. However, it is well known that the convergence to local minima is inevitable in these approaches. We proposed dynamical differential equations called LPPH for the SAT. The LPPH is based on the Lagrangian method and it is proved that every equilibrium point of the dynamics is a solution of the SAT and vice versa. Hence it is never trapped by any point which is not the solution of the SAT. From experiments it is known that the LPPH outperforms already proposed combinatorial algorithms even if it is executed by numerical simulations on conventional computers. In this paper we propose a method which combines heuristics to the LPPH dynamics.