Beyond No Free Lunch: Realistic algorithms for arbitrary problem classes

In this paper we present a simple and general new No Free Lunch-like result that applies to revisiting algorithms searching arbitrary problem sets. We begin by unifying the assumptions of closure under permutation and non-revisiting algorithms. We then propose a new approach to reasoning about search algorithm performance, treating search algorithms as stochastic processes and thereby admitting revisiting; for this approach we need only make a simple assumption that search algorithms are applied for optimisation (i.e. maximisation or minimisation), rather than considering arbitrary performance measures. As a consequence of a proof that non-revisiting enumeration has the best possible expected performance for arbitrary distributions over arbitrary problem sets, this allows us to show that better than enumeration performance by some algorithm on some problem set predicts nothing about performance on a second problem set when nothing is known about the relation between the two. Finally we...

• Type: Conference
• Year: 2010
• Where: CEC
• Authors: James A. R. Marshall, Thomas G. Hinton
• Keywords: Arbitrary Problem Sets, Artificial Intelligence, CEC 2010, Problem Set, Search Algorithms