How to do a Population and crossover on matrix ?

How to generate a 20 population of matrix and then calculate fitness funtion to eaach one using sum (sum (matrix)) then perform a random selection of parents among the 10 min value of matrix then do the crossover on them ??? And after that a randomly mutation

To achieve the minimum fitness Using matlab

Answer 1

[Shishir Reddy]

Hi @Firas Al-Kharabsheh

As per my understanding, you would like to Implement a genetic algorithm in MATLAB to minimize the sum of matrix elements by evolving a population of random matrices using selection, crossover, and mutation.

Kindly refer to the following steps for the same -

1. Set Parameters and Generate Initial Population

clc;
clear;

% Parameters
pop_size = 20;                 % Total number of matrices
matrix_size = [5, 5];          % Size of each matrix
num_generations = 50;          % Number of generations to evolve
mutation_rate = 0.1;           % Probability of mutation (10%)

% Initialize population with random integers from 0 to 10
population = cell(pop_size, 1);
for i = 1:pop_size
    population{i} = randi([0, 10], matrix_size);
end

2. Evaluate Fitness for Each Matrix and Select the Top 10 Fittest Matrices

for gen = 1:num_generations
    % Compute fitness (lower is better)
    fitness = zeros(pop_size, 1);
    for i = 1:pop_size
        fitness(i) = sum(sum(population{i}));
    end
    
    % Select 10 matrices with the lowest fitness
    [~, idx] = sort(fitness);       % Sort indices by fitness
    top10 = population(idx(1:10));  % Select best 10

3. Generate New Population via Crossover and Mutation

    new_population = cell(pop_size, 1);
    for i = 1:2:pop_size
        % Randomly select two parents from top 10
        p1 = top10{randi([1, 10])};
        p2 = top10{randi([1, 10])};

        % Crossover: combine rows from both parents
        crossover_point = randi([1, matrix_size(1)-1]);
        child1 = [p1(1:crossover_point, :); p2(crossover_point+1:end, :)];
        child2 = [p2(1:crossover_point, :); p1(crossover_point+1:end, :)];

        % Mutation: randomly change one element in each child with a small chance
        if rand < mutation_rate
            row = randi([1, matrix_size(1)]);
            col = randi([1, matrix_size(2)]);
            child1(row, col) = randi([0, 10]);
        end
        if rand < mutation_rate
            row = randi([1, matrix_size(1)]);
            col = randi([1, matrix_size(2)]);
            child2(row, col) = randi([0, 10]);
        end

        % Add children to new population
        new_population{i} = child1;
        if i+1 <= pop_size
            new_population{i+1} = child2;
        end
    end

4. Update Population and Print Progress

    % Replace the old population with the new one
    population = new_population;

    % Print best fitness in this generation
    best_fit = min(cellfun(@(m) sum(sum(m)), population));
    fprintf('Generation %d - Best Fitness: %d\n', gen, best_fit);
end

Generation 1 - Best Fitness: 81
Generation 2 - Best Fitness: 83
Generation 3 - Best Fitness: 75
Generation 4 - Best Fitness: 75
Generation 5 - Best Fitness: 74
Generation 6 - Best Fitness: 75
Generation 7 - Best Fitness: 70
Generation 8 - Best Fitness: 70
Generation 9 - Best Fitness: 69
Generation 10 - Best Fitness: 69
Generation 11 - Best Fitness: 68
Generation 12 - Best Fitness: 68
Generation 13 - Best Fitness: 68
Generation 14 - Best Fitness: 65
Generation 15 - Best Fitness: 65
Generation 16 - Best Fitness: 65
Generation 17 - Best Fitness: 65
Generation 18 - Best Fitness: 65
Generation 19 - Best Fitness: 65
Generation 20 - Best Fitness: 65
Generation 21 - Best Fitness: 65
Generation 22 - Best Fitness: 65
Generation 23 - Best Fitness: 61
Generation 24 - Best Fitness: 61
Generation 25 - Best Fitness: 61
Generation 26 - Best Fitness: 63
Generation 27 - Best Fitness: 63
Generation 28 - Best Fitness: 63
Generation 29 - Best Fitness: 63
Generation 30 - Best Fitness: 61
Generation 31 - Best Fitness: 61
Generation 32 - Best Fitness: 61
Generation 33 - Best Fitness: 60
Generation 34 - Best Fitness: 61
Generation 35 - Best Fitness: 60
Generation 36 - Best Fitness: 60
Generation 37 - Best Fitness: 57
Generation 38 - Best Fitness: 59
Generation 39 - Best Fitness: 59
Generation 40 - Best Fitness: 59
Generation 41 - Best Fitness: 59
Generation 42 - Best Fitness: 58
Generation 43 - Best Fitness: 56
Generation 44 - Best Fitness: 56
Generation 45 - Best Fitness: 54
Generation 46 - Best Fitness: 54
Generation 47 - Best Fitness: 54
Generation 48 - Best Fitness: 52
Generation 49 - Best Fitness: 53
Generation 50 - Best Fitness: 52

I hope this helps.