Deep Genetic Programming Trees Are Robust

We sample the genetic programming tree search space and show it is smooth, since many mutations on many test cases have little or no fitness impact. We generate uniformly at random high-order polynomials composed of 12,500 and 750,000 additions and multiplications and follow the impact of small changes to them. From information theory, 32 bit floating point arithmetic is dissipative, and even with 1,501 test cases, deep mutations seldom have any impact on fitness. Absolute difference between parent and child evaluation can grow as well as fall further from the code change location, but the number of disrupted fitness tests falls monotonically. In many cases, deeply nested expressions are robust to crossover syntax changes, bugs, errors, run time glitches, perturbations, and so on, because their disruption falls to zero, and so it fails to propagate beyond the program.