用Octave计算组合优化问题（蜂群算法）
 
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整个蜂群分三种蜜蜂：
采蜜蜂：在已知蜜源附近搜索更好的解
侦察蜂：在未知区域搜索新的蜜源
守卫蜂：保护已知的蜜源
守卫蜂：保护已知的蜜源
蜂群算法核心逻辑：
好的地方多搜，差的地方少搜，彻底不行就换新地方。
蜂群算法流程：
1. 初始化
随机生成 SN 个蜜源（SN = 采蜜蜂数 = 观察蜂数）
每个蜜源对应一个解\(x_i\)
计算每个蜜源的适应度（解越好，适应度越高）
2. 采蜜蜂阶段
对每个蜜源 \(x_i\)，在附近产生一个新解：
\(v_{ij} = x_{ij} + \phi_{ij}(x_{ij} - x_{kj})\)
- \(k\)：随机选另一个蜜源
- \(\phi_{ij}\)：[-1,1] 之间的随机数
新解更好就替换旧蜜源，否则保留旧的。
3. 观察蜂阶段
按概率选择蜜源：
\(P_i = \frac{\text{fit}_i}{\sum \text{fit} }\)
选中后，同样在附近产生新解，贪心保留更好的。
4. 侦察蜂阶段
如果某个蜜源连续多次（limit 次）没改进，就放弃它，随机生成一个新蜜源代替。
5. 迭代循环
重复步骤2–4，直到达到最大迭代次数，适应度最高的蜜源就是最优解。
求解\(\min f(x)=x^2,\quad x\in[-5,5]\)，代码如下：
>> % ========== 蜂群算法 ABC ==========

% 目标函数
f = @(x) x.^2;

% 参数
SN = 20;        % 蜜源数量（采蜜蜂数）
limit = 10;     % 停滞上限，超过变侦察蜂
max_iter = 100; % 最大迭代次数
dim = 1;        % 变量维数
lb = -5;        % 下界
ub = 5;         % 上界

% 1. 初始化蜜源
food = lb + (ub-lb)*rand(SN, dim);
fit = 1 ./ (1 + abs(f(food))); % 适应度
trial = zeros(SN, 1);          % 停滞次数

% 最优记录
[best_fit, best_idx] = max(fit);
best_x = food(best_idx, :);

for iter = 1:max_iter
    % === 2. 采蜜蜂阶段 ===
    for i = 1:SN
        k = randi(SN);
        while k == i
            k = randi(SN);
        end
        phi = 2*rand - 1;
        v = food(i, :) + phi*(food(i, :) - food(k, :));
        v = max(lb, min(ub, v));
        
        fv = 1/(1+abs(f(v)));
        if fv > fit(i)
            food(i, :) = v;
            fit(i) = fv;
            trial(i) = 0;
        else
            trial(i) = trial(i)+1;
        end
    end
    
    % === 3. 观察蜂阶段 ===
    prob = fit / sum(fit);
    for i = 1:SN
        if rand < prob(i)
            k = randi(SN);
            while k == i
                k = randi(SN);
            end
            phi = 2*rand - 1;
            v = food(i, :) + phi*(food(i, :) - food(k, :));
            v = max(lb, min(ub, v));
            
            fv = 1/(1+abs(f(v)));
            if fv > fit(i)
                food(i, :) = v;
                fit(i) = fv;
                trial(i) = 0;
            else
                trial(i) = trial(i)+1;
            end
        end
    end
    
    % === 4. 侦察蜂阶段 ===
    for i = 1:SN
        if trial(i) > limit
            food(i, :) = lb + (ub-lb)*rand;
            fit(i) = 1/(1+abs(f(food(i, :))));
            trial(i) = 0;
        end
    end
    
    % 更新最优
    [curr_best_fit, idx] = max(fit);
    if curr_best_fit > best_fit
        best_fit = curr_best_fit;
        best_x = food(idx, :);
    end
    
    fprintf('iter=%d, best_x=%.4f, f(x)=%.4f\n', ...
            iter, best_x, f(best_x));
end
----------
iter=1, best_x=0.2559, f(x)=0.0655
iter=2, best_x=0.0427, f(x)=0.0018
iter=3, best_x=0.0427, f(x)=0.0018
iter=4, best_x=-0.0029, f(x)=0.0000
iter=5, best_x=-0.0029, f(x)=0.0000
iter=6, best_x=-0.0029, f(x)=0.0000
iter=7, best_x=-0.0029, f(x)=0.0000
iter=8, best_x=-0.0029, f(x)=0.0000
iter=9, best_x=-0.0029, f(x)=0.0000
iter=10, best_x=-0.0029, f(x)=0.0000
iter=11, best_x=-0.0029, f(x)=0.0000
iter=12, best_x=-0.0029, f(x)=0.0000
iter=13, best_x=0.0024, f(x)=0.0000
iter=14, best_x=0.0024, f(x)=0.0000
iter=15, best_x=0.0024, f(x)=0.0000
iter=16, best_x=0.0024, f(x)=0.0000
iter=17, best_x=0.0024, f(x)=0.0000
iter=18, best_x=0.0024, f(x)=0.0000
iter=19, best_x=0.0024, f(x)=0.0000
iter=20, best_x=0.0022, f(x)=0.0000
iter=21, best_x=-0.0007, f(x)=0.0000
iter=22, best_x=-0.0007, f(x)=0.0000
iter=23, best_x=-0.0007, f(x)=0.0000
iter=24, best_x=-0.0002, f(x)=0.0000
iter=25, best_x=-0.0000, f(x)=0.0000
iter=26, best_x=-0.0000, f(x)=0.0000
iter=27, best_x=-0.0000, f(x)=0.0000
iter=28, best_x=-0.0000, f(x)=0.0000
iter=29, best_x=-0.0000, f(x)=0.0000
iter=30, best_x=-0.0000, f(x)=0.0000
iter=31, best_x=-0.0000, f(x)=0.0000
iter=32, best_x=-0.0000, f(x)=0.0000
iter=33, best_x=-0.0000, f(x)=0.0000
iter=34, best_x=-0.0000, f(x)=0.0000
iter=35, best_x=-0.0000, f(x)=0.0000
iter=36, best_x=-0.0000, f(x)=0.0000
iter=37, best_x=0.0000, f(x)=0.0000
iter=38, best_x=0.0000, f(x)=0.0000
iter=39, best_x=0.0000, f(x)=0.0000
iter=40, best_x=0.0000, f(x)=0.0000
iter=41, best_x=0.0000, f(x)=0.0000
iter=42, best_x=0.0000, f(x)=0.0000
iter=43, best_x=0.0000, f(x)=0.0000
iter=44, best_x=0.0000, f(x)=0.0000
iter=45, best_x=0.0000, f(x)=0.0000
iter=46, best_x=0.0000, f(x)=0.0000
iter=47, best_x=0.0000, f(x)=0.0000
iter=48, best_x=-0.0000, f(x)=0.0000
iter=49, best_x=-0.0000, f(x)=0.0000
iter=50, best_x=-0.0000, f(x)=0.0000
iter=51, best_x=-0.0000, f(x)=0.0000
iter=52, best_x=0.0000, f(x)=0.0000
iter=53, best_x=0.0000, f(x)=0.0000
iter=54, best_x=0.0000, f(x)=0.0000
iter=55, best_x=0.0000, f(x)=0.0000
iter=56, best_x=0.0000, f(x)=0.0000
iter=57, best_x=0.0000, f(x)=0.0000
iter=58, best_x=0.0000, f(x)=0.0000
iter=59, best_x=0.0000, f(x)=0.0000
iter=60, best_x=0.0000, f(x)=0.0000
iter=61, best_x=0.0000, f(x)=0.0000
iter=62, best_x=0.0000, f(x)=0.0000
iter=63, best_x=0.0000, f(x)=0.0000
iter=64, best_x=0.0000, f(x)=0.0000
iter=65, best_x=0.0000, f(x)=0.0000
iter=66, best_x=0.0000, f(x)=0.0000
iter=67, best_x=0.0000, f(x)=0.0000
iter=68, best_x=0.0000, f(x)=0.0000
iter=69, best_x=0.0000, f(x)=0.0000
iter=70, best_x=0.0000, f(x)=0.0000
iter=71, best_x=0.0000, f(x)=0.0000
iter=72, best_x=0.0000, f(x)=0.0000
iter=73, best_x=0.0000, f(x)=0.0000
iter=74, best_x=0.0000, f(x)=0.0000
iter=75, best_x=0.0000, f(x)=0.0000
iter=76, best_x=0.0000, f(x)=0.0000
iter=77, best_x=0.0000, f(x)=0.0000
iter=78, best_x=0.0000, f(x)=0.0000
iter=79, best_x=0.0000, f(x)=0.0000
iter=80, best_x=0.0000, f(x)=0.0000
iter=81, best_x=0.0000, f(x)=0.0000
iter=82, best_x=0.0000, f(x)=0.0000
iter=83, best_x=0.0000, f(x)=0.0000
iter=84, best_x=0.0000, f(x)=0.0000
iter=85, best_x=0.0000, f(x)=0.0000
iter=86, best_x=0.0000, f(x)=0.0000
iter=87, best_x=0.0000, f(x)=0.0000
iter=88, best_x=0.0000, f(x)=0.0000
iter=89, best_x=0.0000, f(x)=0.0000
iter=90, best_x=0.0000, f(x)=0.0000
iter=91, best_x=0.0000, f(x)=0.0000
iter=92, best_x=0.0000, f(x)=0.0000
iter=93, best_x=0.0000, f(x)=0.0000
iter=94, best_x=0.0000, f(x)=0.0000
iter=95, best_x=0.0000, f(x)=0.0000
iter=96, best_x=0.0000, f(x)=0.0000
iter=97, best_x=0.0000, f(x)=0.0000
iter=98, best_x=0.0000, f(x)=0.0000
iter=99, best_x=0.0000, f(x)=0.0000
iter=100, best_x=0.0000, f(x)=0.0000
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