# Theoretical results in genetic programming: the next ten years?

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## Abstract

We consider the theoretical results in GP so far and prospective areas for the future. We begin by reviewing the state of the art in genetic programming (GP) theory including: schema theories, Markov chain models, the distribution of functionality in program search spaces, the problem of bloat, the applicability of the no-free-lunch theory to GP, and how we can estimate the difficulty of problems before actually running the system. We then look at how each of these areas might develop in the next decade, considering also new possible avenues for theory, the challenges ahead and the open issues.

## Keywords

Genetic programming Theory Challenges Open problems## Notes

### Acknowledgments

The authors would like to thank Julian Miller and the referees of this paper for their extremely useful feedback. Lee Spector is also gratefully thanked.

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