Geometric Semantic Genetic Programming with Normalized and Standardized Random Programs

Illya Bakurov, José Manuel Muñoz Contreras, Mauro Castelli, Nuno Miguel Duarte Rodrigues, Sara Silva, Leonardo Trujillo, Leonardo Vanneschi

Research output: Contribution to journalArticlepeer-review


Geometric semantic genetic programming (GSGP) represents one of the most promising developments in the area of evolutionary computation (EC) in the last decade. The results achieved by incorporating semantic awareness in the evolutionary process demonstrate the impact that geometric semantic operators have brought to the field of EC. An improvement to the geometric semantic mutation (GSM) operator is proposed, inspired by the results achieved by batch normalization in deep learning. While, in one of its most used versions, GSM relies on the use of the sigmoid function to constrain the semantics of two random programs responsible for perturbing the parent’s semantics, here a different approach is followed, which allows reducing the size of the resulting programs and overcoming the issues associated with the use of the sigmoid function, as commonly done in deep learning. The idea is to consider a single random program and use it to perturb the parent’s semantics only after standardization or normalization. The experimental results demonstrate the suitability of the proposed approach: despite its simplicity, the presented GSM variants outperform standard GSGP on the studied benchmarks, with a difference in terms of performance that is statistically significant. Furthermore, the individuals generated by the new GSM variants are easier to simplify, allowing us to create accurate but significantly smaller solutions.
Original languageEnglish
Article number6
Pages (from-to)1-29
Number of pages29
JournalGenetic Programming And Evolvable Machines
Early online date8 Feb 2024
Publication statusE-pub ahead of print - 8 Feb 2024


  • Geometric semantic mutation
  • Internal covariate shift
  • Sigmoid distribution bias
  • Model simplification


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