simulated annealing with random starting point of 9 in matlab

main.m
% Define the objective function
fun = @(x) (x-4)^2;

% Define the initial temperature
T0 = 100;

% Define the cooling rate
alpha = 0.95;

% Define the number of iterations at each temperature
numIter = 100;

% Define the number of times to restart the algorithm
numRestarts = 10;

% Define the search range
xRange = [-10, 10];

% Loop for numRestarts times
for restart = 1:numRestarts
    % Generate a random starting point within the search range
    x = xRange(1) + (xRange(2)-xRange(1)).*rand();
    
    % Initialize the current best solution
    xBest = x;
    fBest = fun(xBest);
    
    % Initialize the current temperature
    T = T0;
    
    % Loop for numIter iterations at each temperature
    for iter = 1:numIter
        % Generate a random neighbor within the search range
        xNew = x + (2*rand() - 1);
        
        % Clamp the neighbor to the search range
        xNew = max(xRange(1), min(xRange(2), xNew));
        
        % Evaluate the objective function at the neighbor
        fNew = fun(xNew);
        
        % Calculate the acceptance probability
        deltaE = fNew - fBest;
        P = exp(-deltaE / T);
        
        % Update the current solution with probability P
        if deltaE < 0 || rand() < P
            x = xNew;
            fBest = fNew;
        end
        
        % Update the current best solution
        if fBest < fun(xBest)
            xBest = x;
        end
        
        % Cool down the temperature
        T = alpha * T;
    end
    
    % Print the current best solution
    fprintf('Restart %d: Best solution found: x = %.4f, f(x) = %.4f\n', restart, xBest, fun(xBest));
end
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