反向学习差分进化算法matlab

反向学习差分进化算法（BLDE）是一种基于差分进化算法（DE）的优化算法，用于求解非线性优化问题。它在DE的基础上，引入了反向学习的思想，通过学习历史最优解的信息来指导搜索过程，提高了优化的效率和准确性。

以下是一个使用MATLAB实现BLDE算法的示例代码：

function [x,fval] = BLDE(fun,lb,ub,options)
% BLDE: Backward Learning Differential Evolution Algorithm
% fun: Fitness function
% lb: Lower bound of variables
% ub: Upper bound of variables
% options: Algorithmic options

% Initialize parameters
N = options.PopulationSize; % Population size
D = length(lb); % Dimension of problem
F = options.Factor; % Scaling factor
CR = options.CR; % Crossover probability
maxGen = options.MaxGenerations; % Maximum number of generations
tolFun = options.FunctionTolerance; % Function tolerance
tolX = options.StepTolerance; % Step tolerance
tolStall = options.StallGenerations; % Number of generations to check stall
stallGen = 0; % Number of generations with no improvement
bestX = []; % Best solution
bestF = inf; % Best fitness

% Initialize population
X = repmat(lb,N,1) + rand(N,D).*(repmat(ub-lb,N,1));
FV = feval(fun,X);

% Evolution loop
for i = 1:maxGen
    % Mutation
    V = X(randperm(N,3),:) + F*(X(randperm(N,3),:) - X(randperm(N,3),:));
    V = max(min(V,ub),lb);
    j = randi(D,N,1);
    for k = 1:N
        V(k,j(k)) = X(k,j(k));
    end
    
    % Crossover
    U = X;
    j = randi(D,N,1);
    for k = 1:N
        for l = 1:D
            if rand < CR || l == j(k)
                U(k,l) = V(k,l);
            end
        end
    end
    
    % Selection
    FU = feval(fun,U);
    idx = FU < FV;
    X(idx,:) = U(idx,:);
    FV(idx) = FU(idx);
    
    % Update best solution
    [minF,idx] = min(FV);
    if minF < bestF
        bestF = minF;
        bestX = X(idx,:);
        stallGen = 0;
    else
        stallGen = stallGen + 1;
    end
    
    % Check termination criteria
    if bestF < tolFun || max(abs(bestX-X(idx,:))) < tolX || stallGen == tolStall
        break;
    end
end

% Return best solution
x = bestX;
fval = bestF;
end

在这个代码中，`fun`是需要优化的目标函数，`lb`和`ub`分别是变量的下界和上界，`options`包含算法的参数和选项。该函数返回最优解`x`和最优解对应的函数值`fval`。

如果需要使用该函数求解目标函数，可以定义一个函数句柄并传递给`BLDE`函数，例如：

fun = @(x) 100*(x(2)-x(1)^2)^2 + (1-x(1))^2;
lb = [-5,-5];
ub = [5,5];
options.PopulationSize = 20;
options.Factor = 0.8;
options.CR = 0.9;
options.MaxGenerations = 100;
options.FunctionTolerance = 1e-6;
options.StepTolerance = 1e-6;
options.StallGenerations = 20;
[x,fval] = BLDE(fun,lb,ub,options);