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Unformatted text preview: Project IEOR 160 Problem 2: Sudoku Solver Executive Summary Background Sudoku is a logicbased number placement puzzle. The objective is to fill a 9x9 grid so that each column, each row, and each of the nine 3x3 boxes (also called blocks or regions) contains the digits from 1 to 9, only once each (that is, exclusively). The puzzle maker provides a partially completed grid. 1 Summary We created a Sudoku solver model using AMPL that allow users to insert the partially completed Sudoku puzzle in the data file. After running the files, AMPL will be able to display 1 Description taken from http://en.wikipedia.org/wiki/Sudoku the solutions for the entire grid in the Sudoku. This model is designed so that anybody with simple AMPL knowledge can use the model to solve any Sudoku puzzle. This report will include how to input the partially completed Sudoku in the data file, as well as what each parameter, variable, and constraints mean explicitly. Technical Evaluation Please refer to Appendix A for a text copy of the model and data file. Parameters: 1. ‘ROWS’ will gives us the ROWS X ROWS grid. In this case, ROWS will equal 9 for 9x9 standard Sudoku grid. 2. ‘SMALL’ gives the SMALL X SMALL in each box. Therefore, in this case, SMALL equal 3 for the nine 3x3 boxes. 3. ‘sudoku{1..ROWS, 1..ROWS}’ or sudoku[i,j] gives us the 9x9 unsolved Sudoku table. Variables: 1. ‘x{1..ROWS,1..ROWS,1..ROWS’ or x[i,j,k] are binary variables for ith row, jth column and integer k, which means there are 9 variables for each of the 81 space for 9 integers....
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 Fall '07
 HOCHBAUM
 Linear Programming, Optimization, CPLEX

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