Regression tasks aim to determine accurate and simple relationship expressions between variables, which can be regarded as bi-objective optimization problems. As GP (genetic programming) can use expression trees as representation, it is popularly-used for regression. Introducing multi-objective techniques into GP enables it to solve bi-objective tasks, and the success of memetic algorithms show the importance of local search in improving GP. However, existing memetic GP methods are mainly single-objective, in which the local search operators cannot be applied in multi-objective optimization. Moreover, the popularly-used solution evaluation mechanism (Pareto local search) in existing multi-objective memetic methods cannot assure solution dispersion. To handle these problems, a dispersion-keeping Pareto evaluation (DkPE) mechanism is proposed, based on which new crossover and mutation operators adaptive to bi-objective GP are designed. In addition, two base bi-objective GP methods (NSGP (non-dominated sorting GP) and SPGP (strength Pareto GP)) are developed. Applying the new operators in them respectively forms two bi-objective memetic GP methods (MNSGP (memetic NSGP) and MSPGP (memetic SPGP)). Results show that MNSGP and MSPGP outperform NSGP and SPGP respectively, which reflects that DkPE based crossover/mutation increase the performance of NSGP and SPGP. Moreover, solutions evolved by MNSGP outperform reference GP and non-GP based methods.

回归任务旨在确定变量之间的准确而简单的关系表达式，这可以看作是双目标优化问题。由于GP（遗传编程）可以使用表达式树作为表示形式，因此它广泛用于回归分析。在GP中引入多目标技术使其能够解决双目标任务，而模因算法的成功表明了局部搜索在改善GP中的重要性。但是，现有的模因GP方法主要是单目标的，其中局部搜索算子不能应用于多目标优化。此外，在现有的多目标模因方法中普遍使用的解决方案评估机制（帕累托局部搜索）不能确保解决方案的分散。为了解决这些问题，提出了分散保持帕累托评估（DkPE）机制，以此为基础，设计出适用于双目标GP的新交叉和变异算子。此外，还开发了两种基本的双目标GP方法（NSGP（非支配排序GP）和SPGP（强度帕累托GP））。在其中应用新运算符分别形成两种双目标模因GP方法（MNSGP（模因NSGP）和MSPGP（模因SPGP））。结果表明，MNSGP和MSPGP分别优于NSGP和SPGP，这反映了基于DkPE的交叉/突变提高了NSGP和SPGP的性能。此外，由MNSGP演进的解决方案优于参考GP和基于非GP的方法。在其中应用新运算符分别形成两种双目标模因GP方法（MNSGP（模因NSGP）和MSPGP（模因SPGP））。结果表明，MNSGP和MSPGP分别优于NSGP和SPGP，这反映了基于DkPE的交叉/突变提高了NSGP和SPGP的性能。此外，由MNSGP演进的解决方案优于参考GP和基于非GP的方法。在它们中应用新运算符分别形成两种双目标模因GP方法（MNSGP（模因NSGP）和MSPGP（模因SPGP））。结果表明，MNSGP和MSPGP分别优于NSGP和SPGP，这反映了基于DkPE的交叉/突变提高了NSGP和SPGP的性能。而且，由MNSGP开发的解决方案优于参考GP和基于非GP的方法。