how to write simulated annealing code of 9 variables in matlab

Here is an example of how to implement the simulated annealing algorithm for a problem with 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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This code assumes a simple objective function where the goal is to minimize the sum of squares of the variables. Adjust the objective function according to your specific problem.

Make sure to specify the correct bounds for your problem by modifying the lb (lower bound) and ub (upper bound) vectors.

The code also specifies the maximum number of iterations, initial temperature, cooling rate, and minimum temperature. Adjust these parameters based on the specific requirements of your problem.

Note that this implementation uses a simple Gaussian perturbation to generate new candidate solutions. You may need to modify this part for a problem with different characteristics.

Keep in mind that simulated annealing is a randomized algorithm, so you may obtain slightly different results each time you run it.

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