One of the mysteries of evolution is why it works so well both in the real world and as a software optimization method. It's obvious in both cases that it produces wonderfully efficient results in sometimes unexpected ways. As yet, though, there is no mathematic proof of why genetic algorithms seem bound for success. A new paper by Marek W. Gutowski of the Institute of Physics at the Polish Academy of Sciences in Poland offers some insights into the problem. The paper titled, Amazing Geometry of Genetic Space or Are Genetic Algorithms Convergent? (PDF format) provides this conclusion: "The chances of improvement are always higher than for lack of it, if the selection of parents is performed either in soft, or hard but adaptive, manner. This is a very general result, completely independent of the optimization problem under study. It applies equally well to discrete, continuous and mixed optimization problems." Along the way, he offers a proof that soft selection is superior to other methods.