遗传算法计算圆度误差

要使用遗传算法计算圆度误差，首先需要定义适应度函数来衡量染色体的质量。以下是一个示例的遗传算法程序，用于计算圆度误差：

% 遗传算法参数设置
populationSize = 50; % 种群大小
chromosomeLength = 10; % 染色体长度
mutationRate = 0.01; % 变异率
crossoverRate = 0.8; % 交叉率
generations = 100; % 迭代次数

% 初始化种群
population = randi([0, 1], populationSize, chromosomeLength);

for generation = 1:generations
    % 计算适应度
    fitness = calculateFitness(population);

    % 选择操作
    selectedPopulation = selection(population, fitness);

    % 交叉操作
    offspringPopulation = crossover(selectedPopulation, crossoverRate);

    % 变异操作
    mutatedPopulation = mutation(offspringPopulation, mutationRate);

    % 更新种群
    population = mutatedPopulation;
end

% 输出最优解
bestIndividual = population(1, :);
bestFitness = calculateFitness(bestIndividual);
disp(['最优解: ', num2str(bestIndividual)]);
disp(['最优适应度: ', num2str(bestFitness)]);
disp(['圆度误差: ', num2str(calculateCircularityError(bestIndividual))]);

% 计算适应度函数（圆度误差越小，适应度越高）
function fitness = calculateFitness(population)
    fitness = zeros(size(population, 1), 1);
    for i = 1:size(population, 1)
        fitness(i) = calculateCircularityError(population(i, :));
    end
    fitness = 1 - fitness; % 适应度越高，圆度误差越小
end

% 选择操作（轮盘赌选择）
function selectedPopulation = selection(population, fitness)
    roulette = cumsum(fitness) / sum(fitness);
    selectedPopulation = zeros(size(population));

    for i = 1:size(population, 1)
        pointer = rand;
        for j = 1:size(population, 1)
            if pointer <= roulette(j)
                selectedPopulation(i, :) = population(j, :);
                break;
            end
        end
    end
end

% 交叉操作（单点交叉）
function offspringPopulation = crossover(selectedPopulation, crossoverRate)
    offspringPopulation = zeros(size(selectedPopulation));

    for i = 1:2:size(selectedPopulation, 1)
        if rand <= crossoverRate
            crossoverPoint = randi([2, size(selectedPopulation, 2) - 1]);
            parent1 = selectedPopulation(i, :);
            parent2 = selectedPopulation(i+1, :);
            offspringPopulation(i, :) = [parent1(1:crossoverPoint), parent2(crossoverPoint+1:end)];
            offspringPopulation(i+1, :) = [parent2(1:crossoverPoint), parent1(crossoverPoint+1:end)];
        else
            offspringPopulation(i, :) = selectedPopulation(i, :);
            offspringPopulation(i+1, :) = selectedPopulation(i+1, :);
        end
    end
end

% 变异操作（位翻转变异）
function mutatedPopulation = mutation(offspringPopulation, mutationRate)
    mutatedPopulation = offspringPopulation;

    for i = 1:size(mutatedPopulation, 1)
        for j = 1:size(mutatedPopulation, 2)
            if rand <= mutationRate
                mutatedPopulation(i, j) = 1 - mutatedPopulation(i, j);
            end
        end
    end
end

% 计算圆度误差（根据实际问题进行定义）
function circularityError = calculateCircularityError(chromosome)
    % 根据染色体定义一个圆
    radius = bin2dec(num2str(chromosome(1:4))) + 1; % 半径范围为1-16
    center_x = bin2dec(num2str(chromosome(5:8))); % x坐标范围为0-15
    center_y = bin2dec(num2str(chromosome(9:10))); % y坐标范围为0-3

    % 计算圆度误差
    % 这里假设已知一个理想的圆的半径和中心坐标，计算当前圆与理想圆的误差
    idealRadius = 10;
    idealCenter_x = 8;
    idealCenter_y = 2;

    circularityError = abs(radius - idealRadius) + abs(center_x - idealCenter_x) + abs(center_y - idealCenter_y);
end

在这个示例中，适应度函数被定义为圆度误差的反比。通过计算染色体表示的圆与理想圆之间的半径和中心坐标的差异来评估圆度误差。你可以根据实际问题进行修改和调整。希望对你有所帮助！