用MATLAB写一个用改进的非支配排序算法求解渐进覆盖选址模型代码

好的，以下是使用MATLAB编写改进的非支配排序算法求解渐进覆盖选址模型的代码示例：

% 首先定义问题参数
numLocations = 100; % 候选位置数量
numObjectives = 2; % 目标函数数量
coverageRadius = 10; % 覆盖半径
gridSize = 100; % 区域大小

% 生成随机位置矩阵
locations = rand(numLocations, 2) * gridSize;

% 计算每个位置的覆盖率
coverage = zeros(numLocations, 1);
for i = 1:numLocations
    for j = 1:numLocations
        if i == j
            continue;
        end
        dist = norm(locations(i, :) - locations(j, :));
        if dist < coverageRadius
            coverage(i) = coverage(i) + 1;
        end
    end
end

% 定义非支配排序函数
function [fronts, ranks] = non_dominated_sort(scores)
    numSolutions = size(scores, 1);
    fronts = {};
    ranks = zeros(numSolutions, 1);
    dominatedBy = zeros(numSolutions, 1);
    dominates = cell(numSolutions, 1);
    numDominates = zeros(numSolutions, 1);

    for i = 1:numSolutions
        p = scores(i, :);
        for j = 1:numSolutions
            if i == j
                continue;
            end
            q = scores(j, :);
            if all(p <= q) && any(p < q)
                dominates{i} = [dominates{i} j];
                numDominates(j) = numDominates(j) + 1;
            elseif all(p >= q) && any(p > q)
                dominatedBy(i) = dominatedBy(i) + 1;
            end
        end
        if dominatedBy(i) == 0
            ranks(i) = 1;
            if isempty(fronts{1})
                fronts{1} = i;
            else
                fronts{1} = [fronts{1} i];
            end
        end
    end

    i = 1;
    while ~isempty(fronts{i})
        nextFront = [];
        for j = fronts{i}
            for k = dominates{j}
                numDominates(k) = numDominates(k) - 1;
                if numDominates(k) == 0
                    ranks(k) = i + 1;
                    if isempty(nextFront)
                        nextFront = k;
                    else
                        nextFront = [nextFront k];
                    end
                end
            end
        end
        i = i + 1;
        fronts{i} = nextFront;
    end
end

% 使用改进的非支配排序算法求解渐进覆盖选址模型
populationSize = 50; % 种群大小
maxGenerations = 100; % 最大进化代数

% 初始化种群
population = rand(populationSize, numLocations) > 0.5;
scores = zeros(populationSize, numObjectives);
for i = 1:populationSize
    solution = population(i, :);
    covered = any(pdist2(locations, locations(solution, :)) < coverageRadius, 2);
    scores(i, :) = [-sum(solution) sum(covered)];
end

for generation = 1:max