simulated annealing with random starting point of 9 variables in matlab

main.m
% Define the objective function to be minimized
objectiveFunction = @(x) sum(x.^2);

% Define the number of variables and search space bounds
numVariables = 9;
lb = -10 * ones(numVariables, 1);
ub = 10 * ones(numVariables, 1);

% Define the initial temperature and cooling schedule parameters
initialTemperature = 100;
coolingRate = 0.95;

% Initialize the current state
currentState = unifrnd(lb, ub, numVariables, 1);
currentObjective = objectiveFunction(currentState);
bestState = currentState;
bestObjective = currentObjective;

% Start the simulated annealing process
while initialTemperature > 1e-3
    % Generate a random neighbor state by perturbing the current state
    neighborState = currentState + randn(numVariables, 1);
    
    % Clamp the neighbor state within the search space bounds
    neighborState = max(min(neighborState, ub), lb);
    
    % Calculate the objective function value for the neighbor state
    neighborObjective = objectiveFunction(neighborState);
    
    % Compare the neighbor objective value with the current objective value
    deltaObjective = neighborObjective - currentObjective;
    
    % If the neighbor objective value is better, move to the neighbor state
    if deltaObjective < 0
        currentState = neighborState;
        currentObjective = neighborObjective;
        
        % Update the best state and objective if necessary
        if currentObjective < bestObjective
            bestState = currentState;
            bestObjective = currentObjective;
        end
    else
        % If the neighbor objective value is worse, move to it with a certain probability
        acceptanceProbability = exp(-deltaObjective / initialTemperature);
        
        if rand() < acceptanceProbability
            currentState = neighborState;
            currentObjective = neighborObjective;
        end
    end
    
    % Decrease the temperature according to the cooling schedule
    initialTemperature = initialTemperature * coolingRate;
end

% Display the best state and objective value
disp("Best State:");
disp(bestState);
disp("Best Objective Value:");
disp(bestObjective);
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