基于MATLAB的免疫遗传算法函数优化问题实例

以下是一个基于MATLAB的免疫遗传算法函数优化问题实例：

假设我们要优化一个简单的函数 f(x) = x^2，其中 x 是一个实数。我们将使用免疫遗传算法来寻找该函数的最小值。

首先，我们需要定义一个适应度函数，它将计算每个个体的适应度。在这种情况下，我们可以使用函数值作为适应度：

function fitness = fitness_function(x)
fitness = x^2;
end

接下来，我们需要定义一个生成初始种群的函数。在此示例中，我们将生成一个包含 10 个个体的种群，每个个体的值在 -5 到 5 之间随机选择：

function population = generate_population(pop_size, gene_length)
population = -5 + (5+5)*rand(pop_size, gene_length);
end

现在，我们可以组合这些函数来实现免疫遗传算法。以下是完整的 MATLAB 代码：

function [best_fitness, best_solution] = immune_genetic_algorithm()

% Define parameters
pop_size = 10; % size of population
gene_length = 1; % length of each gene
num_generations = 50; % number of generations
mutation_rate = 0.1; % mutation rate
crossover_rate = 0.8; % crossover rate

% Generate initial population
population = generate_population(pop_size, gene_length);

% Evaluate fitness of initial population
fitness = zeros(pop_size, 1);
for i = 1:pop_size
fitness(i) = fitness_function(population(i));
end

% Find best solution
[best_fitness, idx] = min(fitness);
best_solution = population(idx);

% Main loop
for generation = 1:num_generations

% Select parents
parents = tournament_selection(population, fitness, 2);

% Crossover
offspring = crossover(parents, crossover_rate);

% Mutation
offspring = mutation(offspring, mutation_rate);

% Evaluate fitness of offspring
offspring_fitness = zeros(size(offspring, 1), 1);
for i = 1:size(offspring, 1)
offspring_fitness(i) = fitness_function(offspring(i));
end

% Replace worst individuals in population
[~, idx] = max(fitness);
population(idx,:) = offspring(end,:);
fitness(idx) = offspring_fitness(end);

[~, idx] = max(fitness);
population(idx,:) = offspring(end-1,:);
fitness(idx) = offspring_fitness(end-1);

% Update best solution
[current_best_fitness, idx] = min(fitness);
if current_best_fitness < best_fitness
best_fitness = current_best_fitness;
best_solution = population(idx);
end

end

end

function population = generate_population(pop_size, gene_length)
population = -5 + (5+5)*rand(pop_size, gene_length);
end

function parents = tournament_selection(population, fitness, k)
% Tournament selection
n = size(population, 1);
idx = randperm(n, k);
[~, idx2] = min(fitness(idx));
parents = population(idx(idx2),:);
end

function offspring = crossover(parents, crossover_rate)
% Single point crossover
if rand < crossover_rate
crossover_point = randi(size(parents, 2)-1);
offspring = [parents(1,1:crossover_point) parents(2,crossover_point+1:end);
parents(2,1:crossover_point) parents(1,crossover_point+1:end)];
else
offspring = parents;
end
end

function offspring = mutation(offspring, mutation_rate)
% Mutation
for i = 1:size(offspring, 1)
if rand < mutation_rate
offspring(i) = offspring(i) + randn;
end
end
end

function fitness = fitness_function(x)
fitness = x^2;
end

调用该函数的方法是：

[best_fitness, best_solution] = immune_genetic_algorithm()

该函数将返回最佳适应度和最佳解决方案。在此示例中，我们期望最佳适应度为 0，最佳解决方案为 0。