The Neighbours' Similar Fitness Property for Local Search

For most practical optimisation problems local search outperforms random sampling - despite the "No Free Lunch Theorem". This paper introduces a property of search landscapes termed Neighbours' Similar Fitness (NSF) that underlies the good performance of neighbourhood search in terms of local improvement. Though necessary, NSF is not sufficient to ensure that searching for improvement among the neighbours of a good solution is better than random search. The paper introduces an additional (natural) property which supports a general proof that, for NSF landscapes, neighbourhood search beats random search.