Solving and Rating Sudokus using Constraint Satisfiability Approaches and Genetic Algorithms

Sudoku is a very simple and well-known puzzle that has achieved international popularity in the recent past. This project addresses the problem of encoding Sudoku puzzles into conjunctive normal form (CNF), and subsequently solving them using polynomial-time propositional satisfiability (SAT) inference techniques. We introduce two straightforward SAT encodings for Sudoku: the minimal encoding and the extended encoding. Using these encodings for large Sudoku puzzles, however, generates too many clauses, which impede the performance of state-of-the-art SAT solvers. So, we present an optimized CNF encoding in order to deal with large instances of Sudoku puzzles, wherein we use fixed cells in Sudoku to remove obvious redundancies during the encoding phase. Finally, we discuss solving and generating Sudoku puzzles with evolutionary algorithms. Another goal is to test if we can use genetic algorithm solvers as rating machines to test the difficulty levels of new puzzles.