Mean-field theory for optimization problems

Abstract

A mean-field theory for optimization problems of the Travelling Salesman type, or of the Matching type, is presented. It involves an infinite set of order parameters which measure the lack of self-averageness of the system and its degree of freezing. We further conjecture that NP-completeness is associated with replica symmetry breaking Theorie de champ moyen pour les problemes d'optimisation du type «Voyageur de Commerce» ou problemes d'«appariement», a l'aide d'un ensemble infini de parametres d'ordre, qui mesurent l'absence d'automoyennage du systeme et donc son degre de gel. On conjecture que la NP-complexite est associee a la brisure de symetrie des repliques