genetic-sudoku

genetic-sudoku is a Rust program designed to solve Sudoku puzzles using a multithreaded genetic algorithm.

By default, the program will output

• The current generation the solution was found in
• The duration of time it took to find the solution
• The solution

How To Run

USAGE:
    genetic-sudoku [FLAGS] [OPTIONS] <BOARD>

FLAGS:
        --bench      runs program in benchmark mode
    -h, --help       Prints help information
    -V, --version    Prints version information

OPTIONS:
        --mutation <F>      mutation rate as fraction
        --population <N>    population per generation
        --restart <R>       number of generations to restart population
        --fraction <S>      fraction of population selected

ARGS:
    <BOARD>    board to solve

A Sudoku puzzle board file contains a textual matrix of digits, with 0 representing empty cells in the puzzle, and non-zero values representing the numbers given in the puzzle. The current source code deals only with 9×9 Sudoku puzzles; the constant BOARD_SIZE in src/main.rs can be changed for other puzzle sizes. The boards/ directory contains a variety of puzzle boards.

The --mutation, --population, --restart and --fraction arguments specify the parameters used in running the genetic algorithm described below. There are sensible defaults for all of these. Note that the "fraction" arguments expect a floating-point number between 0.0 and 1.0.

The --bench argument causes the program to loop finding solutions. When a solution is found the program will not output the solution, but will output the normal metrics, as well as

• The average generation a solution is found in
• The average duration it takes to find a solution

It will then restart with a new random population.

How It Works

The genetic algorithm is designed to work like so:

• Generate a random population of potential solutions, say 100 of them
• For each potential solution:
  • "Overlay" the potential solution on top of the base board we're looking to solve for by only replacing the base board's 0 cells
  • Evaluate the "fitness" of the potential solution by counting the number of duplicated numbers in each row and column, then summing them to produce a score. The lower the score, the better the solution with a fitness score of 0 being a valid solution to the puzzle
• With all the potential solution fitness scores calculated:
  • Sort them and apply "natural selection" to filter out only the top percentage, say 50%
  • Group the remaining candidates into pairs
  • Have each pair produce enough children to create the next generation's population of potential solutions
    • When each child is created, for each value there is a chance, say 5%, to randomly "mutate" and generate a whole new value
    • The rest of the time, there is a 50% chance to "inherit" the value from one parent, and a 50% chance to "inherit" from the other parent
• Loop this process until a valid solution is found

Acknowledgements

The Sudoku boards in boards/mantere-koljonen are from

Mantere, Timo and Janne Koljonen (2008). Solving and Analyzing Sudokus with Cultural Algorithms. In Proceedings of 2008 IEEE World Congress on Computational Intelligence (WCCI 2008), 1-6 June, Hong Kong, China, pages 4054-4061.

as made available here. Thanks much to the authors for collecting these.

The Al Escargot board is by Arto Inkala.