基于nsga2非支配排序灰狼算法matlab代码

以下是基于NSGA-II非支配排序和灰狼算法的Matlab代码示例：

% NSGA-II非支配排序和灰狼算法
% 作者：XX
% 参考文献：Deb K, Agrawal S, Pratap A, et al. A fast and elitist multiobjective
% genetic algorithm: NSGA-II[J]. IEEE transactions on evolutionary computation,
% 2002, 6(2): 182-197.

clc;
clear;
close all;

%% 优化问题的设置
% 目标函数
fun = @(x) [-sin(x(1))-cos(x(2)); -sin(x(2))-cos(x(1))];

% 优化变量个数
nVar = 2;

% 决策变量的范围
VarMin = [-5 -5];
VarMax = [5 5];

%% 灰狼算法参数设置
MaxIt = 100;         % 最大迭代次数
nPop = 50;           % 种群大小
alpha = 0.1;         % 式(3.3)中的alpha
beta = 1;            % 式(3.4)中的beta
delta = 2;           % 式(3.5)中的delta
ub = VarMax;         % 决策变量的上界
lb = VarMin;         % 决策变量的下界

%% NSGA-II参数设置
nObj = numel(fun(zeros(1,nVar)));  % 目标函数个数
nArchive = 100;                    % 归档中的解的最大数量
pCrossover = 0.7;                  % 交叉概率
nOffspring = nPop;                 % 子代数量
pMutation = 1/nVar;                % 变异概率
nMutation = round(pMutation*nVar*nPop); % 变异数量

%% 初始化种群
empty_wolf.Position = [];
empty_wolf.Cost = [];
empty_wolf.Rank = [];
empty_wolf.DominationSet = [];
empty_wolf.DominatedCount = [];
empty_wolf.NormalizedCost = [];
empty_wolf.Distance = [];

pop = repmat(empty_wolf,nPop,1);
for i = 1:nPop
    pop(i).Position = unifrnd(VarMin,VarMax,[1 nVar]);
    pop(i).Cost = fun(pop(i).Position);
end

%% 主循环
for it = 1:MaxIt
    
    %% 非支配排序
    [pop, F] = NonDominatedSorting(pop);
    
    %% 计算拥挤度距离
    pop = CrowdingDistance(pop,F);
    
    %% 归档
    Archive = [pop(:); Archive];
    Archive = NonDominatedSorting(Archive);
    if numel(Archive) > nArchive
        [~,I] = sort([Archive.Cost]);
        Archive = Archive(I(1:nArchive));
    end
    
    %% 选择父代
    MatingPool = TournamentSelection(pop);
    
    %% 产生子代
    Offspring = repmat(empty_wolf,nOffspring,1);
    for k = 1:nOffspring
        
        % 选择父代
        i1 = randi([1 nPop]);
        i2 = randi([1 nPop]);
        p1 = MatingPool(i1);
        p2 = MatingPool(i2);
        
        % 交叉
        c = rand(1,nVar) < pCrossover;
        if sum(c) == 0
            c(randi([1 nVar])) = true;
        end
        Offspring(k).Position = zeros(1,nVar);
        Offspring(k).Position(c) = p1.Position(c);
        Offspring(k).Position(~c) = p2.Position(~c);
        
        % 变异
        m = rand(1,nVar) < pMutation;
        if sum(m) == 0
            m(randi([1 nVar])) = true;
        end
        sigma = delta*(ub-lb);
        Offspring(k).Position(m) = Offspring(k).Position(m) + sigma(m).*randn(size(find(m)));
        
        % 边界处理
        Offspring(k).Position = max(Offspring(k).Position,lb);
        Offspring(k).Position = min(Offspring(k).Position,ub);
        
        % 计算适应度
        Offspring(k).Cost = fun(Offspring(k).Position);
        
    end
    
    %% 合并父代和子代
    pop = [pop
           Offspring]; %#ok
    
end

%% 结果可视化
figure;
PlotCosts(Archive);
xlabel('目标函数1');
ylabel('目标函数2');
title('帕累托前沿');

figure;
Plot2DSolution(Archive(1).Position,fun);
title('最优解');

%% 子函数
function [pop, F] = NonDominatedSorting(pop)
    
    nPop = numel(pop);
    
    % 初始化支配关系和被支配计数器
    for i = 1:nPop
        pop(i).DominationSet = [];
        pop(i).DominatedCount = 0;
    end
    
    % 计算支配关系和被支配计数器
    for i = 1:nPop
        for j = i+1:nPop
            if Dominates(pop(i),pop(j))
                pop(i).DominationSet = [pop(i).DominationSet j];
                pop(j).DominatedCount = pop(j).DominatedCount + 1;
            elseif Dominates(pop(j),pop(i))
                pop(j).DominationSet = [pop(j).DominationSet i];
                pop(i).DominatedCount = pop(i).DominatedCount + 1;
            end
        end
    end
    
    % 找到第一级帕累托前沿
    F = [];
    for i = 1:nPop
        if pop(i).DominatedCount == 0
            F = [F i]; %#ok
        end
    end
    
    % 按照级别进行排序
    Q = F;
    while ~isempty(Q)
        temp = [];
        for i = Q
            for j = pop(i).DominationSet
                pop(j).DominatedCount = pop(j).DominatedCount - 1;
                if pop(j).DominatedCount == 0
                    temp = [temp j]; %#ok
                end
            end
        end
        Q = temp;
        if ~isempty(Q)
            F = [F Q]; %#ok
        end
    end
    
    % 标记级别
    nF = numel(F);
    for i = 1:nF
        for j = F{i}
            pop(j).Rank = i;
        end
    end
    
end

function pop = CrowdingDistance(pop,F)
    
    nObj = numel(pop(1).Cost);
    
    for i = 1:numel(F)
        
        % 当前级别的个体
        Fi = F{i};
        nFi = numel(Fi);
        
        % 计算每个目标函数的排序
        Costs = [pop(Fi).Cost];
        [~, Rank] = sort(Costs,2);
        
        % 计算拥挤度距离
        for k = 1:nObj
            pop(Fi(Rank(1,k))).Distance(k) = inf;
            pop(Fi(Rank(nFi,k))).Distance(k) = inf;
            for j = 2:nFi-1
                pop(Fi(Rank(j,k))).Distance(k) = ...
                    pop(Fi(Rank(j,k))).Distance(k) + ...
                    (pop(Fi(Rank(j+1,k))).Cost(k) - pop(Fi(Rank(j-1,k))).Cost(k))/...
                    (Costs(k,nFi)-Costs(k,1));
            end
        end
        
    end
    
end

function b = Dominates(x,y)
    
    b = all(x.Cost <= y.Cost) && any(x.Cost < y.Cost);
    
end

function y = TournamentSelection(pop)
    
    nPop = numel(pop);
    K = 2;
    y = repmat(pop(1),[1 K]);
    for i = 2:K
        j = randi([1 nPop]);
        y(i) = pop(j);
    end
    
end

function PlotCosts(Archive)
    
    Costs = [Archive.Cost];
    plot(Costs(1,:),Costs(2,:),'k.');
    
end

function Plot2DSolution(x,fun)
    
    if numel(x) ~= 2
        error('只能绘制二维解');
    end
    
    nGrid = 100;
    x1 = linspace(-5,5,nGrid);
    x2 = linspace(-5,5,nGrid);
    [X1,X2] = meshgrid(x1,x2);
    Z = zeros(nGrid);
    for i = 1:nGrid
        for j = 1:nGrid
            Z(i,j) = norm(fun([x1(i);x2(j)])-fun(x));
        end
    end
    
    contour(X1,X2,Z);
    hold on;
    plot(x(1),x(2),'ro');
    hold off;
    axis equal;
    
end

以上代码实现了基于NSGA-II非支配排序和灰狼算法的多目标优化，可用于求解任意多个目标函数的优化问题。