how to write simulated annealing code of 9 variables in matlab

main.m
% Define the objective function to be optimized
% This function should take a vector of size 9 and return a scalar value
% representing the cost or fitness
objective_func = @(x) sum(x.^2);

% Define the initial solution
initial_solution = rand(9, 1);

% Define the bounds for the variables
% Adjust these according to your problem's requirements
lb = zeros(9, 1);
ub = ones(9, 1);

% Define the maximum number of iterations
max_iter = 1000;

% Define the initial temperature, cooling rate, and minimum temperature
initial_temp = 100;
cooling_rate = 0.95;
min_temp = 0.01;

% Initialize the current solution and its cost
current_solution = initial_solution;
current_cost = objective_func(current_solution);

% Iterate until reaching the maximum number of iterations or minimum temperature
for iter = 1:max_iter
    % Generate a new candidate solution by perturbing the current solution
    new_solution = current_solution + randn(9, 1) * 0.1;
    
    % Apply bounds to the new solution
    new_solution = max(new_solution, lb);
    new_solution = min(new_solution, ub);
    
    % Evaluate the cost of the new solution
    new_cost = objective_func(new_solution);
    
    % Calculate the acceptance probability
    delta_cost = new_cost - current_cost;
    acceptance_prob = exp(-delta_cost / initial_temp);
    
    % Update the current solution if the new solution is accepted
    if delta_cost < 0 || rand() < acceptance_prob
        current_solution = new_solution;
        current_cost = new_cost;
    end
    
    % Update the temperature
    initial_temp = initial_temp * cooling_rate;
    
    % Check if the temperature has reached the minimum
    if initial_temp < min_temp
        break;
    end
end

% Display the final solution and its cost
disp('Final Solution:');
disp(current_solution);
disp('Final Cost:');
disp(current_cost);
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