A replacement scheme based on dynamic penalization for controlling the diversity of the population in Genetic Programming

Algorithms relating the amount of population's diversity to the elapsed period of execution have yielded important improvements. Particularly, schemes with a gradual shift from exploration to exploitation have excelled in several areas of Evolutionary Algorithms. A fairly recent method that applies this design principle is the Genetic Programming variant with Dynamic Management of Diversity (GP-DMD). GP-DMD applies a diversity-based replacement strategy that takes into account a user-defined function or policy that sets the amount of diversity desired in the population. Despite the improvements attained by GP-DMD, it is unable to precisely follow the user-defined policy in some cases. This calls into question its ability to perform a gradual shift from exploration to exploitation and hinders its extension to develop more complex dynamic and adaptive algorithms. This paper proposes the Genetic Programming variant with Controlled Dynamic Management of Diversity (GP-CDMD) which incorporates a novel replacement strategy that aims to improve its tracking capabilities. This is done through a probabilistic selection that takes into account the desired amount of diversity to restrict the diversity of the population. Results in the Symbolic Regression benchmark problem show a significant improvement in the tracking error, which results in features of the dynamics of the population that are more similar to the expected ones. This achievement facilitates the design of more complex diversity-based dynamic and adaptive optimizers and allows for better analyses on the implications of diversity in the GP area.