how to write a code of genetic algorithm minimizing function and the output is optimization figure of fitness value as x-axes with number of iteration as y-axes in matlab

To write code for a genetic algorithm that minimizes a function and outputs an optimization figure of fitness value, you can follow the steps below in MATLAB:

1. Define the fitness function that you want to minimize. This function will take as input a vector of variables and return the fitness value based on how well the solution performs.

2. Set up the options for the genetic algorithm using the gaoptimset function. Specify the number of variables, population size, number of generations, and other parameters.

3. Create a plot to visualize the optimization process. Initialize an empty array to store the fitness values for each iteration.

4. Define the plot update function, which will be called after each generation. This function will update the plot with the new fitness values for the current iteration.

5. Run the genetic algorithm using the ga function. Pass in the fitness function, options, and the plot update function.

Here is an example code snippet that demonstrates how to implement these steps:

main.m
% Step 1: Define the fitness function
fitnessFcn = @(x) sum(x.^2);

% Step 2: Set up options for genetic algorithm
numberOfVariables = 10;
populationSize = 50;
numberOfGenerations = 100;
options = gaoptimset('PopulationSize', populationSize, 'Generations', numberOfGenerations);

% Step 3: Create optimization figure
figure;
fitnessValues = [];

% Step 4: Define plot update function
plotUpdateFcn = @(options, state, flag) plotUpdateFunction(options, state, flag, fitnessValues);

% Step 5: Run genetic algorithm
[x, fval] = ga(fitnessFcn, numberOfVariables, options, 'PlotFcns', plotUpdateFcn);

% Plot update function
function [state,options,optchanged] = plotUpdateFunction(options, state, flag, fitnessValues)
    if strcmp(flag, 'init')
        scatter(state.Generation, state.FunEval, 'filled', 'MarkerFaceColor', 'b');
        hold on;
        xlabel('Number of Iterations');
        ylabel('Fitness Value');
    elseif strcmp(flag, 'iter')
        fitnessValues = [fitnessValues; state.Best(end)];
        scatter(state.Generation, state.FunEval, 'filled', 'MarkerFaceColor', 'b');
    elseif strcmp(flag, 'done')
        scatter(state.Generation, state.FunEval, 'filled', 'MarkerFaceColor', 'r');
        hold off;
    end

    optchanged = false;
end
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This code creates a fitness function that minimizes the sum of squares of the input vector. It sets up the options with a population size of 50 and 100 generations. The plotUpdateFunction updates the plot after each iteration, and the genetic algorithm is run with the ga function. The optimization figure displays the fitness value on the y-axis as a function of the number of iterations on the x-axis.

Note that this is a basic example, and you might need to modify it according to your specific problem and fitness function.