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arXiv · 2509.21355

Domain-Informed Genetic Superposition Programming: A Case Study on SFRC Beams

Mohammad Sadegh Khorshidi·Navid Yazdanjue·Hassan Gharoun·Mohammad Reza Nikoo·Fang Chen·Amir H. Gandomi
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Abstract

This study presents domain-informed genetic superposition programming (DIGSP), a symbolic regression framework tailored for engineering systems governed by separable physical mechanisms. DIGSP partitions the input space into domain-specific feature subsets and evolves independent genetic programming (GP) populations to model material-specific effects. Early evolution occurs in isolation, while ensemble fitness promotes inter-population cooperation. To enable symbolic superposition, an adaptive hierarchical symbolic abstraction mechanism (AHSAM) is triggered after stagnation across all populations. AHSAM performs analysis of variance- (ANOVA) based filtering to identify statistically significant individuals, compresses them into symbolic constructs, and injects them into all populations through a validation-guided pruning cycle. The DIGSP is benchmarked against a baseline multi-gene genetic programming (BGP) model using a dataset of steel fiber-reinforced concrete (SFRC) beams. Across 30 independent trials with 65% training, 10% validation, and 25% testing splits, DIGSP consistently outperformed BGP in training and test root mean squared error (RMSE). The Wilcoxon rank-sum test confirmed statistical significance (p < 0.01), and DIGSP showed tighter error distributions and fewer outliers. No significant difference was observed in validation RMSE due to limited sample size. These results demonstrate that domain-informed structural decomposition and symbolic abstraction improve convergence and generalization. DIGSP offers a principled and interpretable modeling strategy for systems where symbolic superposition aligns with the underlying physical structure.

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Mohammad Sadegh Khorshidi, Navid Yazdanjue, Hassan Gharoun, Mohammad Reza Nikoo, Fang Chen, Amir H. Gandomi. 2025-09-20. Domain-Informed Genetic Superposition Programming: A Case Study on SFRC Beams. https://arxiv.org/abs/2509.21355

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