Genetic variation operators in grammar-guided genetic programming are fundamental to guide the evolutionary process in search and optimization problems. However, they show some limitations, mainly derived from an unbalanced exploration and local-search trade-off. This paper presents an estimation of distribution algorithm for grammar-guided genetic programming to overcome this difficulty and thus increase the performance of the evolutionary algorithm. Our proposal employs an extended dynamic stochastic context-free grammar to encode and calculate the estimation of the distribution of the search space from some promising individuals in the population. Unlike traditional estimation of distribution algorithms, the proposed approach improves exploratory behavior by smoothing the estimated distribution model. Therefore, this algorithm is referred to as SEDA, smoothed estimation of distribution algorithm. Experiments have been conducted to compare overall performance using a typical genetic programming crossover operator, an incremental estimation of distribution algorithm, and the proposed approach after tuning their hyperparameters. These experiments involve challenging problems to test the local search and exploration features of the three evolutionary systems. The results show that grammar-guided genetic programming with SEDA achieves the most accurate solutions with an intermediate convergence speed.

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