如何使用Matlab实现基于柯西变异和正余弦改进的麻雀搜索算法（SCSSA）优化卷积-长短期记忆神经网络（CNN-BiLSTM）的时间序列预测模型。4-SCSSA-CNN-BiLSTM时间序列预测

4-SCSSA-CNN-BiLSTM时间序列预测
柯西变异和正余弦改进的麻雀搜索算法（SCSSA）优化卷积-长短期记忆神经网络的数据预测模型 Matlab语言
1.Matlab版本要在2020B以上。
优化的参数为：学习率，隐藏层节点数 ，正则化参数。
评价指标包括:R2、MAE、RMSE和MAPE等，图很多，出图结果如图所示，

2.SCSSA优化算法是基于麻雀优化算法改进，融合了柯西变异和正余弦。

如何使用Matlab实现基于柯西变异和正余弦改进的麻雀搜索算法（SCSSA）优化卷积-长短期记忆神经网络（CNN-BiLSTM）的时间序列预测模型。我们将从算法的实现、模型的构建、参数优化和结果评估等方面进行详细说明。

1. 环境准备

确保你安装了Matlab 2020b或更高版本，并且安装了Deep Learning Toolbox和Optimization Toolbox。

2. SCSSA优化算法

2.1 麻雀搜索算法（SSA）

麻雀搜索算法（SSA）是一种基于群体智能的优化算法，模拟麻雀群体的觅食行为。我们在此基础上进行改进，引入柯西变异和正余弦策略。

2.2 改进的SCSSA算法

function [bestPosition, bestFitness] = SCSSA(objectiveFunction, lb, ub, n, maxIter, dim)
    % 初始化种群
    positions = lb + rand(n, dim) .* (ub - lb);
    fitness = zeros(n, 1);
    
    % 计算初始适应度
    for i = 1:n
        fitness(i) = objectiveFunction(positions(i, :));
    end
    
    % 找到初始最优解
    [bestFitness, bestIndex] = min(fitness);
    bestPosition = positions(bestIndex, :);
    
    % 参数设置
    ST = 0.8; % 发现者的比例
    PD = 0.7; % 发现者的发现概率
    SD = 0.2; % 加入者的加入概率
    
    for t = 1:maxIter
        % 更新发现者位置
        for i = 1:round(n * ST)
            if rand < PD
                r1 = rand;
                r2 = rand;
                positions(i, :) = bestPosition + r1 * (bestPosition - positions(i, :)) + r2 * (positions(i, :) - mean(positions));
            else
                r3 = rand;
                positions(i, :) = bestPosition + r3 * (positions(i, :) - mean(positions));
            end
        end
        
        % 更新加入者位置
        for i = round(n * ST) + 1:n
            if rand < SD
                r4 = rand;
                positions(i, :) = bestPosition + r4 * (positions(i, :) - mean(positions));
            else
                r5 = rand;
                positions(i, :) = positions(i, :) + r5 * (positions(i, :) - mean(positions));
            end
        end
        
        % 柯西变异
        for i = 1:n
            if rand < 0.1
                positions(i, :) = positions(i, :) + 0.01 * cauchyMutation(dim);
            end
        end
        
        % 正余弦策略
        for i = 1:n
            positions(i, :) = positions(i, :) + 0.01 * sineCosineMutation(dim, t, maxIter);
        end
        
        % 边界检查
        positions = max(min(positions, ub), lb);
        
        % 计算新适应度
        for i = 1:n
            fitness(i) = objectiveFunction(positions(i, :));
        end
        
        % 更新最优解
        [currentBestFitness, currentBestIndex] = min(fitness);
        if currentBestFitness < bestFitness
            bestFitness = currentBestFitness;
            bestPosition = positions(currentBestIndex, :);
        end
        
        % 显示当前迭代结果
        disp(['Iteration: ', num2str(t), ' Best Fitness: ', num2str(bestFitness)]);
    end
end

% 柯西变异函数
function mutation = cauchyMutation(dim)
    mutation = rand(1, dim) ./ rand(1, dim);
end

% 正余弦变异函数
function mutation = sineCosineMutation(dim, t, maxIter)
    a = 2 * pi * rand(1, dim);
    r1 = rand(1, dim);
    r2 = rand(1, dim);
    mutation = a .* (r1 > 0.5) .* cos(2 * pi * r2) + a .* (r1 <= 0.5) .* sin(2 * pi * r2);
end

3. CNN-BiLSTM模型构建

3.1 数据准备

假设你已经有了时间序列数据 X_train, Y_train, X_val, Y_val, X_test, Y_test。

3.2 模型定义

function net = createCNNBiLSTMModel(inputSize, hiddenSize, outputSize)
    layers = [
        sequenceInputLayer(inputSize)
        convolution2dLayer(3, 16, 'Padding', 'same')
        reluLayer
        maxPooling2dLayer(2, 'Stride', 2)
        bilstmLayer(hiddenSize, 'OutputMode', 'last')
        fullyConnectedLayer(outputSize)
        regressionLayer];
    
    net = layerGraph(layers);
end

4. 目标函数

定义一个目标函数，用于评估模型的性能。

function fitness = objectiveFunction(params, X_train, Y_train, X_val, Y_val)
    learningRate = params(1);
    hiddenSize = round(params(2));
    regularization = params(3);
    
    options = trainingOptions('adam', ...
        'InitialLearnRate', learningRate, ...
        'MaxEpochs', 50, ...
        'MiniBatchSize', 32, ...
        'Shuffle', 'every-epoch', ...
        'Verbose', false, ...
        'Plots', 'none', ...
        'ValidationData', {X_val, Y_val}, ...
        'ValidationFrequency', 30, ...
        'ValidationPatience', 10, ...
        'L2Regularization', regularization);
    
    inputSize = size(X_train, 2);
    outputSize = size(Y_train, 2);
    
    net = createCNNBiLSTMModel(inputSize, hiddenSize, outputSize);
    
    net = trainNetwork(X_train, Y_train, net, options);
    
    Y_pred = predict(net, X_val);
    fitness = mean((Y_pred - Y_val).^2); % 使用均方误差作为适应度
end

5. 参数优化

使用SCSSA算法优化模型参数。

% 定义参数范围
lb = [0.001, 10, 0.001]; % 学习率, 隐藏层节点数, 正则化参数
ub = [0.1, 100, 0.1];

% 定义种群大小和最大迭代次数
n = 50;
maxIter = 100;

% 调用SCSSA算法
[bestParams, bestFitness] = SCSSA(@(params) objectiveFunction(params, X_train, Y_train, X_val, Y_val), lb, ub, n, maxIter, length(lb));

disp(['Best Parameters: ', num2str(bestParams)]);
disp(['Best Fitness: ', num2str(bestFitness)]);

6. 模型训练和评估

使用优化后的参数重新训练模型，并评估其性能。

learningRate = bestParams(1);
hiddenSize = round(bestParams(2));
regularization = bestParams(3);

options = trainingOptions('adam', ...
    'InitialLearnRate', learningRate, ...
    'MaxEpochs', 50, ...
    'MiniBatchSize', 32, ...
    'Shuffle', 'every-epoch', ...
    'Verbose', true, ...
    'Plots', 'training-progress', ...
    'ValidationData', {X_val, Y_val}, ...
    'ValidationFrequency', 30, ...
    'ValidationPatience', 10, ...
    'L2Regularization', regularization);

inputSize = size(X_train, 2);
outputSize = size(Y_train, 2);

net = createCNNBiLSTMModel(inputSize, hiddenSize, outputSize);
net = trainNetwork(X_train, Y_train, net, options);

% 预测
Y_pred_train = predict(net, X_train);
Y_pred_val = predict(net, X_val);
Y_pred_test = predict(net, X_test);

% 评估指标
R2_train = 1 - sum((Y_pred_train - Y_train).^2) / sum((Y_train - mean(Y_train)).^2);
R2_val = 1 - sum((Y_pred_val - Y_val).^2) / sum((Y_val - mean(Y_val)).^2);
R2_test = 1 - sum((Y_pred_test - Y_test).^2) / sum((Y_test - mean(Y_test)).^2);

MAE_train = mean(abs(Y_pred_train - Y_train));
MAE_val = mean(abs(Y_pred_val - Y_val));
MAE_test = mean(abs(Y_pred_test - Y_test));

RMSE_train = sqrt(mean((Y_pred_train - Y_train).^2));
RMSE_val = sqrt(mean((Y_pred_val - Y_val).^2));
RMSE_test = sqrt(mean((Y_pred_test - Y_test).^2));

MAPE_train = mean(abs((Y_pred_train - Y_train) ./ Y_train)) * 100;
MAPE_val = mean(abs((Y_pred_val - Y_val) ./ Y_val)) * 100;
MAPE_test = mean(abs((Y_pred_test - Y_test) ./ Y_test)) * 100;

% 输出评估指标
disp(['R2 (Train): ', num2str(R2_train)]);
disp(['R2 (Val): ', num2str(R2_val)]);
disp(['R2 (Test): ', num2str(R2_test)]);

disp(['MAE (Train): ', num2str(MAE_train)]);
disp(['MAE (Val): ', num2str(MAE_val)]);
disp(['MAE (Test): ', num2str(MAE_test)]);

disp(['RMSE (Train): ', num2str(RMSE_train)]);
disp(['RMSE (Val): ', num2str(RMSE_val)]);
disp(['RMSE (Test): ', num2str(RMSE_test)]);

disp(['MAPE (Train): ', num2str(MAPE_train)]);
disp(['MAPE (Val): ', num2str(MAPE_val)]);
disp(['MAPE (Test): ', num2str(MAPE_test)]);

% 绘制预测结果
figure;
subplot(3, 1, 1);
plot(Y_train, 'b', Y_pred_train, 'r--');
title('Training Set Prediction');
legend('True', 'Predicted');

subplot(3, 1, 2);
plot(Y_val, 'b', Y_pred_val, 'r--');
title('Validation Set Prediction');
legend('True', 'Predicted');

subplot(3, 1, 3);
plot(Y_test, 'b', Y_pred_test, 'r--');
title('Test Set Prediction');
legend('True', 'Predicted');

7. 总结

通过以上步骤，你可以使用Matlab实现基于柯西变异和正余弦改进的麻雀搜索算法（SCSSA）优化卷积-长短期记忆神经网络（CNN-BiLSTM）的时间序列预测模型。