Focused Grammar Generative Programming for Symbolic Regression

The patent applies dynamics by making the grammar structure adaptive and evolving rather than static. The grammar is dynamically modified based on performance feedback from evaluated candidate programs, allowing the search strategy to adapt during the process. This enables the system to transition from broad exploration to focused exploitation in promising regions of the search space, resolving the contradiction between exploring broad search spaces and maintaining computational efficiency.

The patent implements feedback mechanisms where the evaluation results of candidate programs are used to modify the grammar structure. The grammar is selectively adjusted based on performance metrics, creating a closed-loop system that learns from previous evaluations. This feedback-driven approach prevents repetitive exploration of unproductive regions while maintaining the ability to discover novel solutions, thereby improving computational efficiency without sacrificing search capability.

The patent applies segmentation by dividing the search process into distinct phases: initial broad exploration using a base grammar, and subsequent focused refinement using modified grammars. The grammar itself is segmented into modular components that can be independently adjusted based on evaluation feedback. This segmentation allows the system to switch between exploration and exploitation modes, preventing trapping in local minima while maintaining solution refinement capability.

The patent implements parameter changes by modifying grammar parameters (such as production rules and probability distributions) based on evaluation results. When local optimization is sufficient, the grammar parameters are adjusted to focus on fine-tuning. When broader exploration is needed, the parameters are reset or modified to increase diversity. This dynamic parameter adjustment resolves the contradiction between solution refinement and search flexibility.