Runtime analysis of mutation-based geometric semantic genetic programming on boolean functions

  • Authors:
  • Alberto Moraglio;Andrea Mambrini;Luca Manzoni

  • Affiliations:
  • CERCIA, University of Birmingham, Birmingham, United Kingdom;CERCIA, University of Birmingham, Birmingham, United Kingdom;DISCo, University of Milano-Bicocca, Milano, Italy

  • Venue:
  • Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
  • Year:
  • 2013

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Abstract

Geometric Semantic Genetic Programming (GSGP) is a recently introduced form of Genetic Programming (GP), rooted in a geometric theory of representations, that searches directly the semantic space of functions/programs, rather than the space of their syntactic representations (e.g., trees) as in traditional GP. Remarkably, the fitness landscape seen by GSGP is always -- for any domain and for any problem -- unimodal with a linear slope by construction. This has two important consequences: (i) it makes the search for the optimum much easier than for traditional GP; (ii) it opens the way to analyse theoretically in a easy manner the optimisation time of GSGP in a general setting. The runtime analysis of GP has been very hard to tackle, and only simplified forms of GP on specific, unrealistic problems have been studied so far. We present a runtime analysis of GSGP with various types of mutations on the class of all Boolean functions.