Interval-valued GA-P algorithms

When genetic programming (GP) methods are applied to solve symbolic regression problems, we obtain a point estimate of a variable, but it is not easy to calculate an associated confidence interval. We designed an interval arithmetic-based model that solves this problem. Our model extends a hybrid technique, the GA-P method, that combines genetic algorithms and genetic programming. Models based on interval GA-P can devise an interval model from examples and provide the algebraic expression that best approximates the data. The method is useful for generating a confidence interval for the output of a model, and also for obtaining a robust point estimate from data which we know to contain outliers. The algorithm was applied to a real problem related to electrical energy distribution. Classical methods were applied first, and then the interval GA-P. The results of both studies are used to compare interval GA-P with GP, GA-P, classical regression methods, neural networks, and fuzzy models.

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