双变异遗传算法在投资组合中的应用

Application of Genetic Algorithm Based on Dual Mutation in the Optimal Portfolio Selection

针对马柯维茨均值-方差模型的特点和简单遗传算法在求解该模型中所存在的缺点和不足,本文提出了一种改进的遗传算法—双变异遗传算法。该算法在交叉算子中引入了变异算子,即在种群中出现大量的近亲个体,产生近亲繁殖,此时,交叉算子停止交叉,进行均匀变异;而变异算子按照梯度方向变异,以加快算法的收敛速度。数值试验表明,双变异遗传算法对马柯维茨均值一方差模型的求解具有全局收敛、求解速度快、避免早熟等优点。

Aiming at features of the Markowitz mean - variance model and the weakness and shortage of simple Genetic Algorithm （GA） in the model, a kind of improved GA, namely dual mutation GA, is put forward. This algorithm introduces the mutant operator in the crossover operator, that is, a great quantity of close relation individuals appear in population, inbreeding is produced, crossover is stopped to mutate uniformly; In the meantime, the mutation operator is brought in the gradient direction to accelerate the algorithm convergence speed. The numerical experiment demonstrates that dual mutation algorithm presents features of global convergence, fast speed and avoiding of prematurity in solving the Markowitz mean - variance model.