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Counterexample-Driven Genetic Programming for Symbolic Regression with Formal Constraints


[ 1 ] Instytut Informatyki, Wydział Informatyki i Telekomunikacji, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.3] Information and communication technology

Year of publication


Published in

IEEE Transactions on Evolutionary Computation

Journal year: 2023 | Journal volume: vol. 27 | Journal number: no. 5

Article type

scientific article

Publication language


  • Symbolic regression
  • Constraints
  • Satisfiability Modulo Theories
  • Genetic Programming

EN In symbolic regression with formal constraints, the conventional formulation of regression problem is extended with desired properties of the target model, like symmetry, monotonicity, or convexity. We present a genetic programming algorithm that solves such problems using a Satisfiability Modulo Theories solver to formally verify the candidate solutions. The essence of the method consists in collecting the counterexamples resulting from model verification and using them to improve search guidance. The method is exact: upon successful termination, the produced model is guaranteed to meet the specified constraints. We compare the effectiveness of the proposed method with standard constraint-agnostic machine learning regression algorithms on a range of benchmarks, and demonstrate that it outperforms them on several performance indicators.

Date of online publication


Pages (from - to)

1327 - 1339




License type

CC BY (attribution alone)

Open Access Mode

czasopismo hybrydowe

Open Access Text Version

final author's version

Date of Open Access to the publication

in press

Ministry points / journal


Impact Factor

14,3 [List 2022]

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