遗传算法初始，解决DEJONG 1 function

这几天上了遗传算法的课，来做个小作业，在做作业的时候，体会真的很大。这里展示下解决DEJONG1 function的代码。

clear all;
%% plot dejong function 1
% initialize x1 and x2 in the range of [-5.12, 5.12]
[x1, x2] = meshgrid(-5.12:0.1:5.12);
z = x1.^2+x2.^2;
mesh(x1, x2, z);

%% in the solution, we adapt real value representation to encode the chromosome.
population_size = 20;
selection_size = population_size - 2;
individuals = rand(population_size, 2)*5.12*2-5.12;
max_iter = 1000;
fitness_history = zeros(1, max_iter);
iter = 1;
while iter < max_iter+1
% evalute the fitness of every individual, record the best fitness and
% the index of corresponding chromosome in the population, for
% visualization the evolutionary history, the best fitness should be
% saved
fitness_result = individuals(:, 1).^2 + individuals(:, 2).^2;
[best_fitness, best_index] = min(fitness_result);
best_x1_x2 = individuals(best_index,:);
fitness_history(iter) = best_fitness;
[~, i] = sort(fitness_result);
individuals = individuals(i, :);
fitness_result = fitness_result(i);
% %section from the population using roulettle wheel, the step is:a)sum
% %all the fitness and divide by every fitness to caculate proportion of
% %every chromosome. and the rand a number between[0,1] adopted to select
% roulettle_proportion = fitness_result./sum(fitness_result);
% roulettle_proportion = sort(roulettle_proportion, 'descend');
% select_proportion = zeros(1, population_size);
% for j = 1:population_size
% select_proportion(j) = sum(roulettle_proportion(1:j));
% end
% selection_result = [];
% for j = 1:selection_size
% r = rand(1);
% for k = 1:population_size
% if r < select_proportion(k)
% selection_result = [selection_result; individuals(k, :)];
% break;
% end
% end
% end
% individuals = selection_result;
% elitism principle to do selection
individuals = individuals(1:selection_size, :);
% crossover, randomly select parents from individuals to create
% offspring
offsprings = [];
for i = 1:(population_size - selection_size)
s = randperm(selection_size);
offsprings = [offsprings; 0.5*(individuals(s(1), :)+individuals(s(2), :))];
end
% mutation

miu = 0.01;
individuals = individuals + rand(size(individuals, 1), 2)*miu*2 - miu;
individuals = [individuals; offsprings];
iter = iter + 1;
end
plot(fitness_history);
title(['best x:[', num2str(best_x1_x2(1)), ',',num2str(best_x1_x2(2)), ']', ',best_fitness:', num2str(best_fitness)]);



这里面初始化的种群数量可以改变的，里面也有按照roulette进行selection的代码，但是我给注释掉了，因为我最开始种群数量是5，但是使用roulette的时候，出来的结果不怎么好，改成elitism的话就好很多。。



PS：最开始我还以为一个chromosome中只是包含一个决策变量，实现过程中才知道，不是。。而是全部决策变量在一条chromosome中。我这里使用的real value based representation。我问过老师，老师说在numerical问题中一般都是real value的编码方法。。