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

To write a simulated annealing code and a genetic algorithm code in MATLAB for optimizing a function with nine variables, you can follow these steps:

Simulated Annealing:

Define the objective function that you want to optimize.
Initialize the parameters such as initial solution, temperature, cooling rate, and stopping criterion.
Start with an initial solution.
Loop until the stopping criterion is met:
- Generate a new solution by applying a perturbation to the current solution.
- Check if the new solution is better or worse than the current solution based on the objective function.
- If the new solution is better, accept it as the new current solution.
- If the new solution is worse, calculate the acceptance probability based on the temperature and accept it probabilistically.
- Reduce the temperature using the cooling rate.
Return the best solution found.

Here is a sample code for the simulated annealing:


main.m
% Objective function to optimize
objective = @(x) x(1)^2 + x(2)^2 + x(3)^2 + x(4)^2 + x(5)^2 + x(6)^2 + x(7)^2 + x(8)^2 + x(9)^2;

% Parameters
initialSolution = rand(9, 1); % Initial solution
temperature = 100; % Initial temperature
coolingRate = 0.95; % Cooling rate
stoppingCriterion = 0.01; % Stopping criterion

% Simulated Annealing
currentSolution = initialSolution;
bestSolution = currentSolution;
while temperature > stoppingCriterion
    % Generate new solution
    newSolution = currentSolution + randn(9, 1);
    
    % Calculate objective values
    currentObjective = objective(currentSolution);
    newObjective = objective(newSolution);
    
    % Accept or reject the new solution based on acceptance probability
    if newObjective < currentObjective
        currentSolution = newSolution;
    else
        acceptanceProbability = exp((currentObjective - newObjective) / temperature);
        if rand() < acceptanceProbability
            currentSolution = newSolution;
        end
    end
    
    % Update best solution
    if objective(currentSolution) < objective(bestSolution)
        bestSolution = currentSolution;
    end
    
    % Reduce temperature
    temperature = temperature * coolingRate;
end

% Display best solution and its objective value
disp("Best Solution:");
disp(bestSolution);
disp("Objective Value:");
disp(objective(bestSolution));
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Genetic Algorithm:

Define the objective function that you want to optimize.
Initialize the parameters such as population size, number of generations, crossover rate, mutation rate, and selection method.
Generate an initial population of solutions.
Loop for the specified number of generations:
- Evaluate the objective value for each individual in the population.
- Select individuals for reproduction based on their fitness.
- Apply crossover and mutation operators to create new offspring.
- Replace the worst individuals in the population with the new offspring.
Return the best solution found.

Here is a sample code for the genetic algorithm:


main.m
% Objective function to optimize
objective = @(x) x(1)^2 + x(2)^2 + x(3)^2 + x(4)^2 + x(5)^2 + x(6)^2 + x(7)^2 + x(8)^2 + x(9)^2;

% Parameters
populationSize = 100; % Population size
numGenerations = 50; % Number of generations
crossoverRate = 0.8; % Crossover rate
mutationRate = 0.03; % Mutation rate

% Genetic Algorithm
population = rand(9, populationSize); % Initial population
bestSolution = population(:, 1);
for generation = 1:numGenerations
    % Evaluate objective values
    objectiveValues = objective(population);
    
    % Select parents for reproduction
    fitness = 1 ./ objectiveValues;
    selectionProbability = fitness / sum(fitness);
    selectedIndices = randsample(1:populationSize, 2, true, selectionProbability);
    
    % Apply crossover to create new offspring
    if rand() < crossoverRate
        crossoverPoint = randi([1, 8]);
        offspring = [population(:, selectedIndices(1):crossoverPoint), population(:, selectedIndices(2):(crossoverPoint+1))];
    else
        offspring = population(:, selectedIndices);
    end
    
    % Apply mutation to the offspring
    for i = 1:numel(offspring)
        if rand() < mutationRate
            offspring(i) = offspring(i) + randn();
        end
    end
    
    % Replace worst individuals with the new offspring
    [~, worstIndex] = max(objectiveValues);
    population(:, worstIndex) = offspring;
    
    % Update best solution
    if objective(bestSolution) > objective(population(:, worstIndex))
        bestSolution = population(:, worstIndex);
    end
end

% Display best solution and its objective value
disp("Best Solution:");
disp(bestSolution);
disp("Objective Value:");
disp(objective(bestSolution));
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You can compare the performance of simulated annealing and genetic algorithm based on factors like convergence speed, final objective value obtained, and robustness to different initial conditions.

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