Abstract
The proper management of diversity is essential to the success of Evolutionary Algorithms. Specifically, methods that explicitly relate the amount of diversity maintained in the population to the stopping criterion and elapsed period of execution, with the aim of attaining a gradual shift from exploration to exploitation, have been particularly successful. However, in the area of Genetic Programming, the performance of this design principle has not been studied. In this paper, a novel Genetic Programming method, Genetic Programming with Dynamic Management of Diversity (GP-DMD), is presented. GP-DMD applies this design principle through a replacement strategy that combines penalties based on distance-like functions with a multi-objective Pareto selection based on accuracy and simplicity. The proposed general method was adapted to the well-established Symbolic Regression benchmark problem using tree-based Genetic Programming. Several state-of-the-art diversity management approaches were considered for the experimental validation, and the results obtained showcase the improvements both in terms of mean square error and size. The effects of GP-DMD on the dynamics of the population are also analyzed, revealing the reasons for its superiority. As in other fields of Evolutionary Computation, this design principle contributes significantly to the area of Genetic Programming.
Highlights
Genetic Programming [30] (GP) is a successful paradigm of Evolutionary Algorithms (EAs) that has been applied to a wide variety of domains [2, 20, 25]
Since there is a clear relationship between this balance and the amount of diversity maintained in the population, several strategies to alter the amount of population’s diversity have been devised [35]
A novel design paradigm that explicitly relates the amount of diversity maintained in the population to the stopping criterion and elapsed period of execution has yielded important advances both for single-objective continuous and combinatorial optimization [9, 34]
Summary
Genetic Programming [30] (GP) is a successful paradigm of Evolutionary Algorithms (EAs) that has been applied to a wide variety of domains [2, 20, 25]. Genetic Programming with Dynamic Management of Diversity (GP-DMD) and, to some of the successful single-objective optimizers [34], it incorporates the principle discussed through a novel replacement strategy. This replacement strategy extends the ones applied in single-objective optimization domains by introducing a multi-objective selection that considers that in the GP case, both the maximization of accuracy and the minimization of tree sizes are important aspects. Most of the techniques discussed are used to validate the proposal put forth in this paper
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