A Study of Some Implications of the No Free Lunch Theorem

We introduce the concept of "minimal" search algorithm for a set of functions to optimize. We investigate the structure of closed under permutation (c.u.p.) sets and we calculate the performance of an algorithm applied to them. We prove that each set of functions based on the distance to a given optimal solution, among which trap functions, onemax or the recently introduced onemix functions, and the NK-landscapes are not c.u.p. and thus the thesis of the sharpened No Free Lunch Theorem does not hold for them. Thus, it makes sense to look for a specific algorithm for those sets. Finally, we propose a method to build a "good" (although not necessarily minimal) search algorithm for a specific given set of problems. The algorithms produced with this technique show better average performance than a genetic algorithm executed on the same set of problems, which was expected given that those algorithms are problem-specific. Nevertheless, in general they cannot be applied fo...

• Type: Conference
• Year: 2008
• Where: EVOW
• Authors: Andrea Valsecchi, Leonardo Vanneschi
• Keywords: Algorithms, Artificial Intelligence, EVOW 2008, No Free Lunch Theorem, Search Algorithm