Novel Loop Structures and the Evolution of Mathematical Algorithms

摘要: In this paper, we analyze the capability of Genetic Programming (GP) to synthesize non-trivial, non-approximative, and deterministic mathematical algorithms with integer-valued results. Such usually involve loop structures. We raise question which representation for loops would be most efficient. define five tree-based program representations realize concept in different ways, including two novel methods use convergence variable values as implicit stopping criteria. Based on experiments four problems under three fitness functions (error sum, hit rate, constant 1) find that GP can statistically significantly outperform random walks. Still, evolving said seems hard success rates are not high. Furthermore, found none could consistently others, but indirect criteria utilized a much higher degree than other instructions.