how to write simulated annealing code and compare it with genetic algorithm code in matlab

main.m
% Define the objective function
objective = @(x) x.^2;

% Define the initial solution and the corresponding objective value
x0 = 5;
obj0 = objective(x0);

% Define the cooling schedule parameters
initialTemperature = 100;
coolingRate = 0.9;

% Simulated Annealing algorithm
x = x0;
obj = obj0;
temperature = initialTemperature;
while temperature > 1e-6
    % Generate a new solution using a random neighborhood operator
    xNew = x + randn()*temperature;
    objNew = objective(xNew);
    
    % Accept the new solution with a certain probability
    if objNew < obj || rand() < exp((obj - objNew)/temperature)
        x = xNew;
        obj = objNew;
    end
    
    % Cool down the temperature
    temperature = temperature * coolingRate;
end

% Print the final solution and objective value
disp("Simulated Annealing Algorithm:");
disp("Solution: " + x);
disp("Objective Value: " + obj);
891 chars
35 lines

main.m
% Define the objective function
objective = @(x) x.^2;

% Define the genetic algorithm parameters
populationSize = 100;
numberOfVariables = 1;
tournamentSize = 2;
mutationRate = 0.1;
generations = 100;

% Create the initial population
population = rand(populationSize, numberOfVariables);

% Genetic Algorithm
for generation = 1:generations
    % Evaluate the fitness for each individual in the population
    fitness = objective(population);
    
    % Select the parents for reproduction using tournament selection
    parents = zeros(populationSize, numberOfVariables);
    for i = 1:populationSize
        tournamentIndices = randperm(populationSize, tournamentSize);
        tournamentFitness = fitness(tournamentIndices);
        [~, index] = min(tournamentFitness);
        parents(i,:) = population(tournamentIndices(index),:);
    end
    
    % Apply crossover to generate the offspring
    offspring = zeros(populationSize, numberOfVariables);
    for i = 1:2:populationSize
        crossoverPoint = randi(numberOfVariables);
        offspring(i,:) = [parents(i,1:crossoverPoint), parents(i+1,crossoverPoint+1:end)];
        offspring(i+1,:) = [parents(i+1,1:crossoverPoint), parents(i,crossoverPoint+1:end)];
    end
    
    % Apply mutation to the offspring
    for i = 1:populationSize
        if rand() < mutationRate
            mutationPoint = randi(numberOfVariables);
            offspring(i,mutationPoint) = offspring(i,mutationPoint) + randn();
        end
    end
    
    % Replace the old population with the new offspring
    population = offspring;
end

% Evaluate the fitness for the final population
fitness = objective(population);

% Find the best solution from the final population
[~, index] = min(fitness);
bestSolution = population(index,:);

% Print the final solution and objective value
disp("Genetic Algorithm:");
disp("Solution: " + bestSolution);
disp("Objective Value: " + objective(bestSolution));
1941 chars
59 lines