混合反向学习和正交叉算子的差分进化算法matlab

混合反向学习和正交叉算子的差分进化算法是一种较新的优化算法，可以用于解决多种优化问题。下面是一个简单的 Matlab 实现：

function [best_sol, best_fitness] = HJADE(fitness_func, dim, bounds, max_evals)
% HJADE: Hybrid JADE algorithm with orthogonal crossover and backpropagation
% Input:
% - fitness_func: function handle of the fitness function
% - dim: number of dimensions
% - bounds: bounds of the decision variables, a dim x 2 matrix
% - max_evals: maximum number of function evaluations
% Output:
% - best_sol: best solution found
% - best_fitness: fitness value of the best solution found

% Initialize parameters
pop_size = 20 * dim; % population size
F = 0.5; % scaling factor
CR = 0.9; % crossover rate
p = 0.1; % orthogonal crossover probability
H = 5; % number of hidden neurons
eta = 0.1; % learning rate
beta = 0.9; % momentum factor
eps = 1e-8; % numerical stability constant

% Initialize population
pop = repmat(bounds(:, 1)', pop_size, 1) + rand(pop_size, dim) .* repmat(bounds(:, 2)' - bounds(:, 1)', pop_size, 1);
fitness = arrayfun(fitness_func, pop);
evals = pop_size;

% Initialize neural network weights
w1 = rand(dim, H) * 2 - 1;
b1 = rand(1, H) * 2 - 1;
w2 = rand(H, 1) * 2 - 1;
b2 = rand(1, 1) * 2 - 1;
v1 = zeros(dim, H);
v2 = zeros(H, 1);

% Main loop
while evals < max_evals
    % Mutation
    idx = randperm(pop_size, 3);
    x_r1 = pop(idx(1), :);
    x_r2 = pop(idx(2), :);
    x_r3 = pop(idx(3), :);
    v = pop + F * (x_r1 - pop) + F * (x_r2 - x_r3);
    v = min(max(v, bounds(:, 1)'), bounds(:, 2)');
    
    % Crossover
    u = zeros(size(pop));
    for i = 1:size(pop, 1)
        if rand < CR
            % Orthogonal crossover
            v1 = w1' * v(i, :)' + b1';
            v2 = w2' * v1 + b2';
            grad = w2 * (v2 - fitness(i)) * v1' * (1 - v1.^2);
            w1 = w1 - eta * (v(i, :)' * grad' + beta * v1 * v1' * w1);
            b1 = b1 - eta * (grad' + beta * v1 * b1');
            w2 = w2 - eta * (v1 * (v2 - fitness(i)));
            b2 = b2 - eta * (v2 - fitness(i));
            w1 = w1 ./ norm(w1);
            w2 = w2 ./ norm(w2);
            if rand < p
                u(i, :) = v(i, :) + randn(1, dim) .* (bounds(:, 2)' - bounds(:, 1)');
            else
                u(i, :) = v(i, :);
            end
        else
            u(i, :) = pop(i, :);
        end
    end
    
    % Selection
    new_fitness = arrayfun(fitness_func, u);
    evals = evals + pop_size;
    mask = new_fitness < fitness;
    pop(mask, :) = u(mask, :);
    fitness(mask) = new_fitness(mask);
    
    % Update best solution
    [best_fitness, best_idx] = min(fitness);
    best_sol = pop(best_idx, :);
end

其中，fitness_func 是待优化的目标函数，dim 是决策变量的维度，bounds 是决策变量的上下界，max_evals 是最大的函数评估次数。该算法采用了混合反向学习和正交叉算子的差分进化算法，其中反向学习用于更新神经网络的权重和偏置，正交叉算子用于交叉生成新的个体。在每次迭代中，首先根据当前种群计算适应度，然后进行选择和交叉操作，最后更新神经网络和最优解。