Abstract: Concerning the problems that the traditional Cartesian Genetic Programming (CGP) is lack of diversity of mutation operation and the evolutionary strategy used in it has limitations, an ADvanced Real-Valued Cartesian Genetic Programming algorithm based on quasi-oppositional mutation (AD-RVCGP) was proposed. Firstly, the 1+lambda evolutionary strategy was adopted in the evolution process in AD-RVCGP just like in the traditional CGP, that is lambda offsprings were generated by a parent only through mutation operation. Secondly, three mutation operators including quasi-oppositional mutation operator, terminal mutation operator and single-point mutation operator were dynamically selected in the process of evolution, and the information of oppositional individuals was used for the mutation operation. Finally, in the evolution process, different parents were selected in the algorithm to generate the next generation individuals according to the state of evolution stage. In the test of symbolic regression problem, the convergence speed of the proposed AD-RVCGP was about 30% faster than that of the traditional CGP, and the running time was about 20% less. In addition, the error between the optimal solution obtained by AD-RVCGP and the real optimal solution was smaller than the optimal solution obtained by the traditional CGP and the real optimal solution. Experimental results show that the proposed AD-RVCGP has high convergence speed and precision for solving problem.

Key words: Real-Valued Cartesian Genetic Programming (RVCGP), oppositional individual, terminal mutation, quasi-oppositional mutation, quasi-symmetric point

摘要： 针对传统笛卡尔遗传编程（CGP）算法变异操作多样性的缺乏以及其使用的进化策略本身的局限性，提出了一种基于准反向变异的实数笛卡尔遗传编程算法（AD-RVCGP）。首先，和传统CGP一样，AD-RVCGP在进化过程中采用1+λ的进化策略，即由一个父代个体只通过变异操作产生λ个子代个体；其次，该算法在进化过程中动态选择准反向变异算子、末端变异算子和单点变异算子，并且利用反向个体的信息进行变异操作；最后，算法在进化过程中根据进化阶段的状态来选择不同的父代个体用于生成下一代个体。在符号回归问题的测试上，相较于传统CGP，AD-RVCGP的收敛加快了约30%，运行时间少了约20%；另外该算法求得的最优解与真实最优解误差更小。实验结果表明，AD-RVCGP具有较高的收敛速度和问题求解精度。

关键词: 实数笛卡尔遗传编程, 反向个体, 末端变异, 准反向变异, 准对称点