(一)DE的基本原理

主要操作：變異 - 交叉 - 選擇 

(二)DE優化BPNN

%載入資料
data = csvread('D:\matlab2016a\OA\sample.csv');

%劃分資料集
rv = rand(1,size(data,1));
[value,index] = sort(rv);
x_train = data(index(1:150),1:2);y_train = data(index(1:150),end);
x_test = data(index(151:end),1:2);y_test = data(index(151:end),end);

%歸一化處理
[train_input,inputps] = mapminmax(x_train');
test_input = mapminmax('apply',x_test',inputps);
[train_output,outputps] = mapminmax(y_train');

%設定節點
inputnum = size(train_input,1);
hiddennum = 5;
outputnum = size(train_output,1);

%設定DE引數
sizepop = 20;
dim = inputnum*hiddennum+hiddennum++hiddennum*outputnum+outputnum;
lb = [-1];ub = [1];
mutation = 0.5;
crossover = 0.2;
maxgen = 50;

if size(lb,1) == 1
    lb = ones(dim,1).*lb;
    ub = ones(dim,1).*ub;
end

%個體初始化
net = newff(train_input,train_output,hiddennum);
Targetfitness = inf;
for i = 1:sizepop
    position(i,:) = lb'+(ub'-lb').*rand(1,dim);
    predict = DEoptimization(inputnum,hiddennum,outputnum,net,train_input,train_output,position(i,:));
    predict = mapminmax('reverse',predict,outputps);
    fit(i) = sqrt(sum((predict'-y_train).^2)/length(y_train));
    if fit(i) < Targetfitness
        Targetfitness = fit(i);
        Targetposition = position(i,:);
    end
end

%迭代尋優
converage = zeros(1,maxgen);
for L = 1:maxgen
    for j = 1:sizepop
        %變異操作
        ri = randperm(sizepop,3);
        while isempty(find(ri==j))==0
            ri = randperm(sizepop,3);
        end
        mpop = position(ri(1),:)+mutation*(position(ri(2),:)-position(ri(3),:));
        if isempty(find(mpop>ub'))== 0
            mpop(find(mpop>ub')) = (ub(find(mpop>ub')))';
        end
        if isempty(find(mpop<lb'))== 0
            mpop(find(mpop<lb')) = (lb(find(mpop<lb')))';
        end
        
        %交叉操作
        tmp = zeros(1,dim);
        for i = 1:dim
            if rand < crossover
                tmp(i) = mpop(i);
            else
                tmp(i) = position(j,i);
            end
        end
        
        %選擇操作
        cpredict = DEoptimization(inputnum,hiddennum,outputnum,net,train_input,train_output,tmp);
        cpredict = mapminmax('reverse',cpredict,outputps);
        cfit = sqrt(sum((cpredict'-y_train).^2)/length(y_train));
        

        %更新
        if cfit < fit(j)
            position(j,:) = tmp;
            fit(j) = cfit;
        end
        if fit(j) < Targetfitness
            Targetposition = position(j,:);
            Targetfitness = fit(j);
        end    
    end
    converage(L) = Targetfitness;
end

w1 = Targetposition(1:inputnum*hiddennum);
b1 = Targetposition(inputnum*hiddennum+1:inputnum*hiddennum+hiddennum);
w2 = Targetposition(inputnum*hiddennum+hiddennum+1:inputnum*hiddennum+hiddennum+hiddennum*outputnum);
b2 = Targetposition(inputnum*hiddennum+hiddennum+hiddennum*outputnum+1:inputnum*hiddennum+hiddennum+hiddennum*outputnum+outputnum);

net.iw{1,1} = reshape(w1,hiddennum,inputnum);
net.lw{2,1} = reshape(w2,outputnum,hiddennum);
net.b{1} = reshape(b1,hiddennum,1);
net.b{2} = b2;

net.trainParam.epochs = 100;
net.trainParam.lr = 0.01;
net.trainParam.goal = 0.001;

net = train(net,train_input,train_output);
predict = sim(net,train_input);
predict_train = mapminmax('reverse',predict,outputps);
train_rmse = sqrt(sum((predict_train'-y_train).^2)/length(y_train));
predict = sim(net,test_input);
predict_test = mapminmax('reverse',predict,outputps);
test_rmse = sqrt(sum((predict_test'-y_test).^2)/length(y_test));
disp(['Train RMSE = ',num2str(train_rmse),' Test RMSE = ',num2str(test_rmse)])

Train RMSE = 0.61411 Test RMSE = 0.61139