遗传算法中使用小生境的选择算法的matlab代码实现

下面是使用小生境选择算法的遗传算法的MATLAB代码实现：

function [bestsol, bestval] = ga_tsp_spea2(dmat, popsize, numgen, pc, pm)

% dmat: 距离矩阵
% popsize: 种群大小
% numgen: 迭代次数
% pc: 交叉概率
% pm: 变异概率

n = size(dmat, 1); % 城市数量
dvec = reshape(dmat, n^2, 1); % 距离向量

% 创建初始种群
pop = zeros(popsize, n);
for i = 1 : popsize
    pop(i,:) = randperm(n);
end

% 初始化评价指标和可行性指标
fit = zeros(popsize, 1);
feas = zeros(popsize, 1);

% 计算每个个体的适应度和可行性
for i = 1 : popsize
    dist = dvec((pop(i,n)-1)*n + pop(i,1));
    for j = 2 : n
        dist = dist + dvec((pop(i,j-1)-1)*n + pop(i,j));
    end
    fit(i) = 1 / dist; % 最小化距离，因此逆距离作为适应度
    feas(i) = (length(unique(pop(i,:))) == n); % 检查是否存在重复城市
end

% SPEA2算法的参数设置
k = sqrt(popsize); % 每个集合的大小
num_arch = 2 * popsize; % 存档的个体数量
arch = zeros(num_arch, n); % 存档的个体

% 进化
for i = 1 : numgen
    
    % 计算每个个体的生存值
    S = zeros(popsize, 1);
    for j = 1 : popsize
        S(j) = sum(fit <= fit(j) & feas);
    end
    
    % 计算每个个体的距离值
    R = zeros(popsize, 1);
    for j = 1 : popsize
        dist = sqrt(sum((pop - repmat(pop(j,:), popsize, 1)).^2, 2));
        R(j) = min(dist(fit > fit(j) & feas));
    end
    
    % 计算每个个体的均衡值
    F = S + R;
    
    % 创建存档
    arch(1:popsize,:) = pop;
    arch(popsize+1:num_arch,:) = randperm(n, num_arch-popsize);
    
    % 计算存档个体之间的距离值
    D = pdist2(arch, arch);
    D(logical(eye(num_arch))) = inf;
    [D_sort, D_idx] = sort(D, 2);
    D_k = D_sort(:, k+1);
    
    % 计算每个个体的原始适应度
    fit_orig = fit;
    for j = 1 : popsize
        fit(j) = sum(F(D_idx(j,:) <= D_k(j)));
    end
    
    % 选择
    p = fit / sum(fit);
    newpop = zeros(popsize, n);
    for j = 1 : popsize
        idx1 = roul_wheel(p);
        idx2 = roul_wheel(p);
        if (rand < pc) % 交叉
            child = cross(pop(idx1,:), pop(idx2,:));
        else % 复制
            child = pop(idx1,:);
        end
        if (rand < pm) % 变异
            child = muta(child);
        end
        newpop(j,:) = child;
    end
    
    % 更新种群
    pop = newpop;
    
end

% 找到最佳个体
bestval = max(fit_orig);
bestidx = find(fit_orig == bestval, 1);
bestsol = pop(bestidx,:);

end

% 选择算子-轮盘赌
function idx = roul_wheel(p)
cump = cumsum(p);
idx = find(cump >= rand, 1);
end

% 交叉算子-顺序杂交
function child = cross(parent1, parent2)
n = length(parent1);
child = zeros(1, n);
startpos = ceil(rand * n);
endpos = mod(startpos + ceil(rand * (n-1)), n) + 1;
for i = startpos : endpos
    child(i) = parent1(i);
end
idx = mod(endpos:n, n) + 1;
j = 1;
for i = 1 : n
    if (child(i) == 0)
        while (ismember(parent2(j), child))
            j = j + 1;
        end
        child(i) = parent2(j);
    end
end
end

% 变异算子-交换型变异
function child = muta(parent)
n = length(parent);
child = parent;
pos1 = ceil(rand * n);
pos2 = ceil(rand * n);
while (pos2 == pos1)
    pos2 = ceil(rand * n);
end
child([pos1 pos2]) = child([pos2 pos1]);
end

这个实现使用了SPEA2算法进行种群选择，其中包含了三个指标：适应度、生存值和距离值。同时，它还实现了轮盘赌选择、顺序杂交和交换型变异等基本算子。