An adaptive GP-based memetic algorithm for symbolic regression

Abstract

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.