Collaborative Neurodynamic Algorithms for Solving Sudoku Puzzles

In this article, Sudoku is formulated as a quadratic unconstrained binary optimization, and a variables reduction algorithm is proposed based on given elements. Collaborative neurodynamic optimization algorithms based on discrete Hopfield networks or Boltzmann machines are developed for solving the formulated optimization problem. A population of discrete Hopfield networks or Boltzmann machines operating concurrently are employed for scatter search. A particle swarm optimization rule is used to re-initialize the initial states of discrete Hopfield networks or Boltzmann machines upon their local convergence. Experimental results on five Sudoku instances are elaborated to demonstrate the efficacy of the proposed collaborative neurodynamic optimization algorithms for solving Sudoku puzzles.