With apologies, if a proponent of an algorithm cannot tell me under what circumstances the proposed algorithm would do better, the proponent is selling me snake oil. There has to be some quantitative statements about their properties, not necessarily proof of convergence to the global optimum. Otherwise it is not science, (yet). Its not an understanding of the space of an arbitrary problem that I desire, it is a measurable or mathematical characterization of the space where these algorithms work well, ideally the process of measurement should be cheaper than applying the algorithm.

EDIT: replaced 'you' with 'proponent' lest it gives the impression that I meant it personally.