Mean-field theory for optimization problems

Henri Orland

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.

Mots clés: statistical mechanics; travelling salesman problems; matching problems; partition function; mean field theory; optimization problems; order parameters; self averageness; freezing; NP completeness; replica symmetry breaking

Domaines: Articles anciens

Henri Orland. Mean-field theory for optimization problems. Journal de Physique Lettres, 1985, 46 (17), pp.763-770. ⟨10.1051/jphyslet:019850046017076300⟩. ⟨jpa-00232896⟩