MATLAB 匈牙利算法实现雷达干扰资源分配

下面是使用 MATLAB 实现匈牙利算法进行雷达干扰资源分配的示例代码：\n\nmatlab\nfunction [assignment] = hungarian_algorithm(cost_matrix)\n % 初始化变量\n rows = size(cost_matrix, 1);\n cols = size(cost_matrix, 2);\n infinity = inf(rows, cols);\n mask = zeros(rows, cols);\n row_cover = zeros(rows, 1);\n col_cover = zeros(1, cols);\n path = zeros(rows+cols, 2);\n step = 1;\n \n % 步骤1：对每一行减去该行最小值\n for i = 1:rows\n min_val = min(cost_matrix(i, :));\n cost_matrix(i, :) = cost_matrix(i, :) - min_val;\n end\n \n % 步骤2：对每一列减去该列最小值\n for i = 1:cols\n min_val = min(cost_matrix(:, i));\n cost_matrix(:, i) = cost_matrix(:, i) - min_val;\n end\n \n % 步骤3：在每一行找到一个0，并标记行和列\n for i = 1:rows\n for j = 1:cols\n if cost_matrix(i, j) == 0 && row_cover(i) == 0 && col_cover(j) == 0\n mask(i, j) = 1;\n row_cover(i) = 1;\n col_cover(j) = 1;\n break;\n end\n end\n end\n \n % 步骤4：循环直到所有行都被标记\n while sum(row_cover) < rows\n % 步骤5：找到未被标记的零元素\n zero_found = false;\n while ~zero_found\n [row, col] = find(mask == 0);\n for k = 1:length(row)\n i = row(k);\n j = col(k);\n if row_cover(i) == 0 && col_cover(j) == 0\n zero_found = true;\n break;\n end\n end\n if ~zero_found\n % 步骤6：更新标记\n min_val = min(cost_matrix(~row_cover, ~col_cover));\n cost_matrix(row_cover, col_cover) = cost_matrix(row_cover, col_cover) + min_val;\n cost_matrix(~row_cover, ~col_cover) = cost_matrix(~row_cover, ~col_cover) - min_val;\n end\n end\n \n % 步骤7：在找到的零元素所在行找到标记\n row = i;\n col = 0;\n while row ~= 0\n col = find(mask(row, :) == 1, 1);\n path(step, :) = [row, col];\n step = step + 1;\n \n % 步骤8：在找到的标记所在列找到标记\n row = find(mask(:, col) == 2, 1);\n path(step, :) = [row, col];\n step = step + 1;\n end\n \n % 步骤9：修改标记，重新开始循环\n mask(path(:, 1), path(:, 2)) = 1 - mask(path(:, 1), path(:, 2));\n row_cover = sum(mask, 2) > 0;\n col_cover = sum(mask, 1) > 0;\n step = 1;\n end\n \n % 步骤10：根据标记生成最优分配方案\n assignment = zeros(rows, cols);\n for i = 1:rows\n col = find(mask(i, :) == 1);\n if ~isempty(col)\n assignment(i, col) = 1;\n end\n end\nend\n\n\n使用示例：\n\nmatlab\ncost_matrix = [1, 2, 3; 4, 5, 6; 7, 8, 9];\nassignment = hungarian_algorithm(cost_matrix);\ndisp(assignment);\n\n\n这个示例中，cost_matrix是一个3x3的矩阵，表示雷达和干扰源之间的成本。hungarian_algorithm函数将返回一个3x3的二进制矩阵，表示每个雷达是否被分配给了一个干扰源。输出结果将显示最优的资源分配方案。