融合黄金正弦和反向学习的粒子群算法matlab

粒子群算法（Particle Swarm Optimization, PSO）是一种基于群体智能的优化算法，其基本思想是模拟鸟群觅食时的群体行为，通过模拟每只鸟在搜索过程中的个体行为和群体协调行为，以期最终找到最优解。黄金正弦和反向学习是两种优化算法，可以用来优化PSO算法的搜索性能。

下面是将黄金正弦和反向学习融合到PSO算法中的MATLAB代码：

function [x,fval]=PSO_golden_sin_reverse(fitnessfun,nvars,lb,ub,options)
% PSO algorithm with golden ratio, sine and reverse learning strategies

% parameters setting
popsize = options.PopulationSize;     % population size
maxgen = options.MaxGenerations;      % maximum generation
wmax = 0.9;                           % maximum inertia weight
wmin = 0.4;                           % minimum inertia weight
c1 = 2;                               % cognitive parameter
c2 = 2;                               % social parameter
% initialization
pop = repmat(lb,popsize,1) + rand(popsize,nvars).*(repmat(ub,popsize,1)-repmat(lb,popsize,1)); % initial population
vel = zeros(popsize,nvars);           % initial velocity
pbest = pop;                          % initial pbest
gbest = pbest(1,:);                   % initial gbest
fit = feval(fitnessfun,pop);          % fitness evaluation
pbestfit = fit;                       % initial pbestfit
gbestfit = min(fit);                  % initial gbestfit
% main loop
for i = 1:maxgen
    % update inertia weight
    w = wmax-(wmax-wmin)*i/maxgen;
    % update velocity
    vel = w*vel + c1*rand(popsize,nvars).*(pbest-pop) + c2*rand(popsize,nvars).*(repmat(gbest,popsize,1)-pop);
    % update position
    pop = pop + vel;
    % impose upper and lower bounds
    pop(pop<repmat(lb,popsize,1)) = repmat(lb,sum(pop<repmat(lb,popsize,1)),1);
    pop(pop>repmat(ub,popsize,1)) = repmat(ub,sum(pop>repmat(ub,popsize,1)),1);
    % fitness evaluation
    fit = feval(fitnessfun,pop);
    % update pbest and gbest
    for j = 1:popsize
        % golden ratio learning
        if fit(j) < pbestfit(j)
            pbest(j,:) = pop(j,:);
            pbestfit(j) = fit(j);
            alpha = (sqrt(5)-1)/2;
            if rand < alpha
                % sine learning
                s = 1 + randn(1,nvars);
                pop(j,:) = pbest(j,:) + s.*(gbest-pbest(j,:));
            else
                % reverse learning
                r = randn(1,nvars);
                pop(j,:) = 2*gbest - pbest(j,:) + r.*(gbest-pbest(j,:));
            end
        end
    end
    % update gbest
    [tempgbestfit,idx] = min(pbestfit);
    if tempgbestfit < gbestfit
        gbest = pbest(idx,:);
        gbestfit = tempgbestfit;
    end
end
x = gbest;
fval = gbestfit;
end

其中，黄金正弦和反向学习分别在更新pbest时进行，具体实现如下：

% golden ratio learning
if fit(j) < pbestfit(j)
    pbest(j,:) = pop(j,:);
    pbestfit(j) = fit(j);
    alpha = (sqrt(5)-1)/2;
    if rand < alpha
        % sine learning
        s = 1 + randn(1,nvars);
        pop(j,:) = pbest(j,:) + s.*(gbest-pbest(j,:));
    else
        % reverse learning
        r = randn(1,nvars);
        pop(j,:) = 2*gbest - pbest(j,:) + r.*(gbest-pbest(j,:));
    end
end

其中，alpha为黄金比例，s为正弦学习的增益因子，r为反向学习的扰动因子。

使用该函数可以调用黄金正弦和反向学习融合的PSO算法来求解目标函数的最小值，例如：

fitnessfun = @(x) sum(x.^2);  % objective function
nvars = 10;                    % number of variables
lb = -10*ones(1,nvars);        % lower bound
ub = 10*ones(1,nvars);         % upper bound
options.PopulationSize = 50;   % population size
options.MaxGenerations = 100;  % maximum generation
[x,fval] = PSO_golden_sin_reverse(fitnessfun,nvars,lb,ub,options);  % PSO algorithm with golden ratio, sine and reverse learning

其中，目标函数为多元二次函数，nvars为变量个数，lb和ub分别为变量的上下限，options为函数参数结构体。函数返回求解得到的最优解x和最小目标函数值fval。