Symbolic regression is a process to find a mathematical expression that represents the relationship between a set of explanatory variables and a measured variable. It has become a best-known problem for GP (genetic programming), as GP can use the tree representation to represent solutions as expression trees. Since the success of memetic algorithms (MAs (Memetic algorithms (MAs) can be regarded as a class of methods that combine population-based global search and local search [6, 30])) has proved the importance of local search in augmenting the global search ability of GP, GP with local search is investigated to solve symbolic regression tasks in this work. An important design issue of MAs is the balance between the global exploration of GP and the local exploitation, which has a great influence on the performance and efficiency of MAs. This work proposes a GP-based memetic algorithm for symbolic regression, termed as aMeGP (a daptive Me metic GP), which can balance global exploration and local exploitation adaptively. Compared with GP, two improvements are made in aMeGP to invoke and stop local search adaptively during evolution. The proposed aMeGP is compared with GP-based and nonGP-based symbolic regression methods on both benchmark test functions and real-world applications. The results show that aMeGP is generally better than both GP-based and nonGP-based reference methods with its evolved solutions achieving lower root mean square error (RMSE) for most test cases. Moreover, aMeGP outperforms the reference GP-based methods in the convergence ability, which can converge to lower RMSE values with faster or similar speeds.

符号回归是找到表示一组解释变量和测量变量之间关系的数学表达式的过程。由于GP可以使用树表示将解决方案表示为表达式树，因此它已成为GP（遗传编程）的最著名问题。自从模因算法（MAs（模因算法（MAs）被视为将基于群体的全局搜索和本地搜索[6，30]结合在一起的一类方法））的成功以来，事实证明了本地搜索对于增强全局搜索的重要性GP的搜索能力，通过局部搜索GP来解决这项工作中的符号回归任务。MA的一个重要设计问题是GP的全球勘探与本地开发之间的平衡，这对MA的性能和效率有很大的影响。一个daptive我metic GP），它可以自适应平衡全球勘探和开采当地。与GP相比，aMeGP进行了两项改进，可以在进化过程中自适应地调用和停止本地搜索。在基准测试功能和实际应用中，将提出的aMeGP与基于GP和基于非GP的符号回归方法进行了比较。结果表明，aMeGP通常优于基于GP的参考方法和基于非GP的参考方法，其改进的解决方案在大多数测试案例中均实现了更低的均方根误差（RMSE）。此外，aMeGP在收敛能力方面优于基于GP的参考方法，后者可以以更快或相似的速度收敛到较低的RMSE值。