Chapter

Genetic Programming

Volume 7244 of the series Lecture Notes in Computer Science pp 158-169

Matrix Analysis of Genetic Programming Mutation

  • Andrew J. ParkesAffiliated withCarnegie Mellon UniversitySchool of Computer Science, The University of Nottingham
  • , Ender ÖzcanAffiliated withCarnegie Mellon UniversitySchool of Computer Science, The University of Nottingham
  • , Matthew R. HydeAffiliated withCarnegie Mellon UniversitySchool of Computer Science, The University of Nottingham

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Abstract

Heuristic policies for combinatorial optimisation problems can be found by using Genetic programming (GP) to evolve a mathematical function over variables given by the current state of the problem, and whose value is used to determine action choices (such as preferred assignments or branches). If all variables have finite discrete domains, then the expressions can be converted to an equivalent lookup table or ‘decision matrix’. Spaces of such matrices often have natural distance metrics (after conversion to a standard form). As a case study, and to support the understanding of GP as a meta-heuristic, we extend previous bin-packing work and compare the distances between matrices from before and after a GP-driven mutation. We find that GP mutations often correspond to large moves within the space of decision matrices. This strengthens evidence that the role of mutations within GP might be somewhat different than their role within Genetic Algorithms.

Keywords

Genetic programming Genotype-phenotype mapping