【4-16日更新】A题所有代码.zip

% 读取数据 data = readmatrix('附件1：data_100.csv'); % 定义常数 t = data(:, 2)'; % 通过率 h = data(:, 3)'; % 坏账率 A = 200; % 系数 % "binvar"函数是MATLAB中Optimization Toolbox中的函数，需要安装Optimization Toolbox % 定义变量 x = binvar(3, 10, 'full'); % 信用评分卡-阈值组合 y = binvar(3, 1, 'full'); % 信用评分卡选择 z = binvar(10, 1, 'full'); % 阈值选择 r = intvar(1, 1, 'full'); % 收入 % 定义约束条件 Constraints = []; % 每个信用评分卡最多选择一个阈值 for i = 1:3 Constraints = [Constraints, sum(x(i, :)) <= 1]; end % 选择某个信用评分卡的同时必须选择该信用评分卡对应的一个阈值 for i = 1:3 for j = 1:10 Constraints = [Constraints, x(i, j) <= y(i)]; end end % 总共只能选择三个信用评分卡 Constraints = [Constraints, sum(y) == 3]; % 选择某个阈值的同时必须选择对应的信用评分卡 for j = 1:10 Constraints = [Constraints, sum(x(:, j)) - z(j) == 0]; end % 将等式约束转化为两个不等式约束 for j = 1:10 Constraints = [Constraints, sum(x(:, j)) <= 1 + z(j)]; Constraints = [Constraints, sum(x(:, j)) >= 1 - 2 * (1 - z(j))]; end % 计算收入 H = 0; for i = 1:3 for j = 1:10 H = H + x(i, j) * (t(j) - h(j)) * z(j); end end Constraints = [Constraints, r == A * H]; % 定义拉格朗日乘子法中的参数 lambda1 = 10; lambda2 = 10; lambda3 = 10; lambda4 = 10; % 将第一个约束条件转化为 QUBO 表达式 for i = 1:3 Constraints = [Constraints, (sum(x(i, :)) - 1)^2 - lambda1 * (sum(x(i, :)) - 1) <= 0]; end % 将第二个约束条件转化为 QUBO 表达式 for i = 1:3 Constraints = [Constraints, y(i) * (sum(x(i, :)) - 1) <= 0]; end % 将第三个约束条件转化为 QUBO 表达式 for j = 1:10 Constraints = [Constraints, (sum(x(:, j)) - z(j))^2 - lambda2 * (sum(x(:, j)) - z(j)) <= 0]; end % 将第四个约束条件转化为 QUBO 表达式 Constraints =[Constraints, (sum(y) - 3)^2 - lambda3 * (sum(y) - 3) <= 0]; % 将第五个约束条件转化为 QUBO 表达式 for j = 1:10 Constraints = [Constraints, (sum(x(:, j)) - z(j)) * (sum(x(:, j)) - z(j) - 1) <= 0]; end % 将第六个约束条件转化为 QUBO 表达式 for i = 1:3 for j = 1:10 Constraints = [Constraints, x(i, j) * (t(j) - h(j)) * z(j) * A - r <= lambda4]; end end % 定义目标函数 Objective = r; % 求解 QUBO 问题 ops = sdpsettings('solver', 'quapro'); [sol, ~, ~, ~, ~] = solvesdp(Constraints, Objective, ops); % 输出结果 disp(sol); disp(value(r));