On the connection between the no free lunch theorem and the trivial property for recursively enumerable languages

We return to the no free lunch theorem, which is one of the most important theorems from the evolutionary computation foundations. We show that the no free lunch theorem can be interpreted as a trivial property of recursively enumerable languages. We demonstrate that if we consider not all problems and cost functions, i.e., a nontrivial property, the problem of finding the best evolutionary algorithm becomes Turing machine undecidable. We also demonstrate, that in spite of this negative result, the task of search for the best evolutionary computation operator is not so futile. In fact, evolutionary computation itself, being nonalgorithmic, may allow to find the best evolutionary operator in infinity, and to increase indefinitely its quality in the finite time.