When Nearer is Better

Maurice Clerc (1)

1 Retraité

We define a numerical "nearer is better " truth value that can be computed or estimated for all functions on a given definition space. The set of all these functions can be then partitioned into three subsets: the ones for which this truth value is positive, the ones for which it is negative, and the ones for which is is null. We show that most of classical functions belong to the first subset, as the second one is useful to design problems that are deceptive for most of optimisation algorithms. Also for this two subsets the No Free Lunch Theorem does not hold. Therefore it may exist a best algorithm, and we suggest a way to design it.

Mots clés: optimisation; optimization; best algorithm; deceptive function; particle swarm

Domaines: Optimisation et contrôle [math.OC]

Maurice Clerc. When Nearer is Better. 2007. ⟨hal-00137320v1⟩