Analysing the significance of no free lunch theorems on the set of real-world binary problems

Abstract

No Free Lunch theorems for optimisation state that there does not exist any algorithm better than any other one when averaged performances over the whole set of possible problems are considered. However, it has been recently suggested that algorithms might show performance differences when just the set of real-world problems is under study. In this work, we first assume that binary problems appearing in the literature are representative of the set of real-world binary problems. Then, we analyse the mean performance of several algorithms on subsets of this well-defined testbed, in particular, static combinatorial unconstrained single-objective single-player optimisation problems whose solutions can be directly encoded as arrays of binary variables. Our results provide empirical evidence that no free lunch theorems unlikely hold on this set of binary real-world problems.