3. (50 marks) Design a Genetic Algorithm for a variant of the SUDOKU puzzle of v

Question

3. (50 marks) Design a Genetic Algorithm for a variant of the SUDOKU puzzle of variable size N x N. Initial conditions of the puzzle should be a distribution of numbers that respect the rule that in one sub-rectangle each integer 1, N 2 appears only once. Permutations could be random. A) (15 marks) Determine a representation and B) (15 marks) fitness function for searching for a correct solution by a GA. C) (10 marks) Design mutation and D) (10 marks) crossover operators that attempt to permute the numbers such that starting from the initial configuration the puzzle can be solved.

Explanation / Answer

function drawSudoku(B) % Function for drawing the Sudoku board % Copyright 2014 The MathWorks, Inc. figure;hold on;axis off;axis equal % prepare to draw rectangle('Position',[0 0 9 9],'LineWidth',3,'Clipping','off') % outside border rectangle('Position',[3,0,3,9],'LineWidth',2) % heavy vertical lines rectangle('Position',[0,3,9,3],'LineWidth',2) % heavy horizontal lines rectangle('Position',[0,1,9,1],'LineWidth',1) % minor horizontal lines rectangle('Position',[0,4,9,1],'LineWidth',1) rectangle('Position',[0,7,9,1],'LineWidth',1) rectangle('Position',[1,0,1,9],'LineWidth',1) % minor vertical lines rectangle('Position',[4,0,1,9],'LineWidth',1) rectangle('Position',[7,0,1,9],'LineWidth',1) % Fill in the clues % % The rows of B are of the form (i,j,k) where i is the row counting from % the top, j is the column, and k is the clue. To place the entries in the % boxes, j is the horizontal distance, 10-i is the vertical distance, and % we subtract 0.5 to center the clue in the box. % % If B is a 9-by-9 matrix, convert it to 3 columns first if size(B,2) == 9 % 9 columns [SM,SN] = meshgrid(1:9); % make i,j entries B = [SN(:),SM(:),B(:)]; % i,j,k rows end for ii = 1:size(B,1) text(B(ii,2)-0.5,9.5-B(ii,1),num2str(B(ii,3))) end hold off end

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