www.gusucode.com > 精通MATLAB最优化计算全书代码 程序源码 > 随书源码_精通MATLAB最优化计算/第11章 整数规划/DividePlane.m

    function  [intx,intf] = DividePlane(A,c,b,baseVector)
sz = size(A);
nVia = sz(2);
n = sz(1);
xx = 1:nVia;

if length(baseVector) ~= n
    disp('基变量的个数要与约束矩阵的行数相等！');
    mx = NaN;
    mf = NaN;
    return;
end

M = 0;
sigma = -[transpose(c) zeros(1,(nVia-length(c)))];
xb = b;

while 1   
    [maxs,ind] = max(sigma);
    if maxs <= 0
        vr = find(c~=0 ,1,'last');
        for l=1:vr
            ele = find(baseVector == l,1);
            if(isempty(ele))
                mx(l) = 0;
            else
                mx(l)=xb(ele);
            end
        end
        if max(abs(round(mx) - mx))<1.0e-7
            intx = mx;
            intf = mx*c;
            return;
        else
            sz = size(A);
            sr = sz(1);
            sc = sz(2);
            [max_x, index_x] = max(abs(round(mx) - mx));
            [isB, num] = find(index_x == baseVector);
            fi = xb(num) - floor(xb(num));
            for i=1:(index_x-1)
                Atmp(1,i) = A(num,i) - floor(A(num,i));
            end
            for i=(index_x+1):sc
                Atmp(1,i) = A(num,i) - floor(A(num,i));
            end
            Atmp(1,index_x) = 0;
            A = [A zeros(sr,1);-Atmp(1,:) 1];
            xb = [xb;-fi];
            baseVector = [baseVector sc+1];
            sigma = [sigma 0];
            
            %对偶单纯性
            while 1
                if xb >= 0
                    if max(abs(round(xb) - xb))<1.0e-7
                        vr = find(c~=0 ,1,'last');
                        for l=1:vr
                            ele = find(baseVector == l,1);
                            if(isempty(ele))
                                mx_1(l) = 0;
                            else
                                mx_1(l)=xb(ele);
                            end
                        end
                        intx = mx_1;
                        intf = mx_1*c;
                        return;
                    else
                        sz = size(A);
                        sr = sz(1);
                        sc = sz(2);
                        [max_x, index_x] = max(abs(round(mx_1) - mx_1));
                        [isB, num] = find(index_x == baseVector);
                        fi = xb(num) - floor(xb(num));
                        for i=1:(index_x-1)
                            Atmp(1,i) = A(num,i) - floor(A(num,i));
                        end
                        for i=(index_x+1):sc
                            Atmp(1,i) = A(num,i) - floor(A(num,i));
                        end
                        Atmp(1,index_x) = 0;
                        A = [A zeros(sr,1);-Atmp(1,:) 1];
                        xb = [xb;-fi];
                        baseVector = [baseVector sc+1];
                        sigma = [sigma 0];
                        continue;
                    end
                else   
                    minb_1 = inf;
                    chagB_1 = inf;
                    sA = size(A);
                    [br,idb] = min(xb);
                    for j=1:sA(2)
                        if A(idb,j)<0
                            bm = sigma(j)/A(idb,j);
                            if bm<minb_1
                                minb_1 = bm;
                                chagB_1 = j;
                            end
                        end
                    end
                    sigma = sigma -A(idb,:)*minb_1;
                    xb(idb) = xb(idb)/A(idb,chagB_1);
                    A(idb,:) = A(idb,:)/A(idb,chagB_1);
                    for i =1:sA(1)
                        if i ~= idb
                            xb(i) = xb(i)-A(i,chagB_1)*xb(idb);
                            A(i,:) = A(i,:) - A(i,chagB_1)*A(idb,:);
                        end
                    end
                    baseVector(idb) = chagB_1;
                end
            end
        end
    else
        minb = inf;
        chagB = inf;
        for j=1:n
            if A(j,ind)>0
                bz = xb(j)/A(j,ind);
                if bz<minb
                    minb = bz;
                    chagB = j;
                end
            end
        end
        sigma = sigma -A(chagB,:)*maxs/A(chagB,ind);
        xb(chagB) = xb(chagB)/A(chagB,ind);
        A(chagB,:) = A(chagB,:)/A(chagB,ind);
        for i =1:n
            if i ~= chagB
                xb(i) = xb(i)-A(i,ind)*xb(chagB);
                A(i,:) = A(i,:) - A(i,ind)*A(chagB,:);
            end
        end
        baseVector(chagB) = ind;
    end
    M = M + 1;
    if (M == 1000000)
        disp('找不到最优解！');
        mx = NaN;
        minf = NaN;
        return;
    end
end