This paper presents a first step of our research on designing an effective and efficient GP-based method for solving the symbolic regression. We have proposed three extensions of the standard Single Node GP, namely (1) a selection strategy for choosing nodes to be mutated based on the depth of the nodes, (2) operators for placing a compact version of the best tree to the beginning and to the end of the population, and (3) a local search strategy with multiple mutations applied in each iteration. All the proposed modifications have been experimentally evaluated on three symbolic regression problems and compared with standard GP and SNGP. The achieved results are promising showing the potential of the proposed modifications to significantly improve the performance of the SNGP algorithm.
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