The Need To Visualize Sudoku
preprintposted on 12.05.2021, 02:58 by Navin Ipe, Raghavendra V. Kulkarni
Sudoku puzzles are easily solved using backtracking algorithms. Yet, literature is scattered with various shy and often opaque attempts at using evolutionary algorithms and hybridizing them with known strategies of solving the puzzle. Evolutionary methods are serendipitous in nature, and this paper demonstrates the behaviour of such serendipity under constraints, using visuals that depict the sheer magnitude of the problem space and the nature in which intertwined constraints affect the scope for locating a solution, with the hope that it could inspire a new way of looking at the problem. We propose a method of visualizing the sudoku fitness landscape, the vastness and complexity of even partially brute forcing the puzzle, and a unique method of mutating puzzle states using circular swaps. These insights could potentially serve as a link to comprehend the problem space when designing solutions for vast, multidimensional problems. Additionally, finding the optimal solution for some puzzles was notably harder, compared to puzzles in the same category of given clues. A short investigation was conducted into this phenomenon, which revealed hints that compel us to propose that the direction of research that should be taken, is in discovering more about puzzle states and definitive mathematical properties of the puzzle, rather than merely designing brute-force, stochastic or hybrid approaches of finding solutions.