Shape-constrained multi-objective genetic programming for symbolic regression

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@Article{HAIDER:2023:asoc,

• author = "C. Haider and F. O. {de Franca} and B. Burlacu and G. Kronberger",
• title = "Shape-constrained multi-objective genetic programming for symbolic regression",
• journal = "Applied Soft Computing",
• volume = "132",
• pages = "109855",
• year = "2023",
• ISSN = "1568-4946",
• DOI = "doi:10.1016/j.asoc.2022.109855",
• URL = "https://www.sciencedirect.com/science/article/pii/S1568494622009048",
• keywords = "genetic algorithms, genetic programming, Multi-objective optimization, Shape-constrained regression, Symbolic regression",
• abstract = "We describe and analyze algorithms for shape-constrained symbolic regression, which allow the inclusion of prior knowledge about the shape of the regression function. This is relevant in many areas of engineering - in particular, when data-driven models, which are based on data of measurements must exhibit certain properties (e.g. positivity, monotonicity, or convexity/concavity). To satisfy these properties, we have extended multi-objective algorithms with shape constraints. A soft-penalty approach is used to minimize both the constraint violations and the prediction error. We use the non-dominated sorting genetic algorithm (NSGA-II) as well as the multi-objective evolutionary algorithm based on decomposition (MOEA/D). The algorithms are tested on a set of models from physics textbooks and compared against previous results achieved with single objective algorithms. Further, we generated out-of-domain samples to test the extrapolation behavior using shape constraints and added a different level of noise on the training data to verify if shape constraints can still help maintain the prediction errors to a minimum and generate valid models. The results showed that the multi-objective algorithms were capable of finding mostly valid models, also when using a soft-penalty approach. Further, we investigated that NSGA-II achieved the best overall ranks on high noise instances",

}

Genetic Programming entries for Christian Haider Fabricio Olivetti de Franca Bogdan Burlacu Gabriel Kronberger

Citations