Abstract: In order to effectively avoid premature and escape from local optima, an improved genetic programming algorithm focusing on the effects that genetic operators（i.e., selection, crossover and mutation） have on population diversity（mainly the genotypes and phenotypes） is proposed. At first, two benchmark problems, even-5-parity and quartic problem in symbolic regression, are adopted in the experiments to compare search abilities of three operators in discrete and continuous fitness space. Then, the Spearman correlation coefficient is used to measure the correlations between the diversity and fitness. The results show that the selection and crossover operators decrease the diversity largely, while the mutation operator maintains and even increases the diversity, which indicate that changing the diversity by controlling the operators so as to find the best individual is feasible.

Key words: genetic programming, population diversity, genetic operator, even-5-parity, symbolic regression

摘要： 为了能有效地避免过早收敛并跳出局部最优，提出了一种改进的遗传规划算法来研究遗传算子（选择、交叉和变异）对种群多样性（主要是基因型和表现型）的影响。首先在基准问题（奇偶校验和符号回归中的四次多项式函数）中比较不同的遗传算子在离散和连续的适应度空间中的搜索寻优，然后使用斯皮尔曼相关系数来度量种群多样性与适应度的相关性。结果表明选择和交叉算子极大地减少了种群多样性，变异算子则能维持甚至提高种群多样性，这说明通过控制遗传算子来改变种群多样性从而找到最优个体是可行的。

关键词: 遗传规划, 种群多样性, 遗传算子, 奇偶校验, 符号回归