- author = "Hiroshi Kera and Hitoshi Iba",
- title = "Vanishing Ideal Genetic Programming",
- booktitle = "Proceedings of 2016 IEEE Congress on Evolutionary Computation (CEC 2016)",
- year = "2016",
- editor = "Yew-Soon Ong",
- pages = "5018--5025",
- address = "Vancouver",
- month = "24-29 " # jul,
- publisher = "IEEE Press",
- keywords = "genetic algorithms, genetic programming, VIGP",
- isbn13 = "978-1-5090-0623-6",
-
DOI = "
doi:10.1109/CEC.2016.7748325",
- size = "8 pages",
- abstract = "In symbolic regression, which aims to find a function that satisfies the target values for all data points, one of the major challenges is that the solutions cannot be uniquely determined. Genetic programming (GP) provides a powerful approach to symbolic regression in that it does not require models of functions to be fixed. However, it is known that GP suffers from a phenomenon known as bloat, meaning that candidate functions attain an excessively complicated form during the search, which is undesirable in many applications. While the majority of approaches for regulating bloat introduce anti-bloat genetic operators or anti-bloat selection schemes, most of these are derived from heuristics and/or require well-tuned hyperparameters. In the present study, we propose a novel approach in which genetic trees of GP are reduced during the search using a basis of a set of polynomials (vanishing ideal) that are equivalent to zero for the data points of symbolic regression. The vanishing ideal is computed using an algebraic approach, and because it only requires data points as input, our approach does not involve the tuning of any hyper-parameters. The proposed approach regulates bloat and efficiently determines simple solutions. We compare our approach with standard GP with a penalty term for the height of trees in the fitness, and demonstrate the effectiveness of our approach to two tasks (real-valued symbolic regression and the 6-parity problem).",
-
notes = "'fitness is based only on .. [at] the data points'
'Removal of vanishing polynomials might be similar to
removal of introns'
Genetic repair? Unclear how vanishing polynomial is removed from GP tree. Buchberger-Moeller (BM) algorithm. Taylor v. Pade. Only rational polynomials. Mostly continuous eg Keijzer-15 but also looks at 6-parity (with XOR). DEAP
WCCI2016",
