Configuration space analysis of travelling salesman problems

S. Kirkpatrick , G. Toulouse

The travelling salesman problem (TSP) and the Ising model of a spin glass are archetypes, respectively, of the combinatorial optimization problems of computer science and of the frustrated disordered systems studied in condensed matter physics. It has recently been proposed that these two fields have many phenomena in common. To see if, in fact, combinatorial optimization problems may be spin glasses, we define a random distance TSP as similar as possible to the idealized infinite-ranged model of spin glasses. Thermodynamic observables and internal correlations among locally stable configurations are analysed in the light of recent results for spin glasses. Evidence for freezing due to frustration and for a hierarchical, ultrametric structure of configuration space in this TSP is presented.

Mots clés: Ising model; operations research; spin glasses

Domaines: Articles anciens

S. Kirkpatrick, G. Toulouse. Configuration space analysis of travelling salesman problems. Journal de Physique, 1985, 46 (8), pp.1277-1292. ⟨10.1051/jphys:019850046080127700⟩. ⟨jpa-00210072⟩