Replica symmetry and replica symmetry breaking for the traveling salesperson problem

Hendrik Schawe, Jitesh Kumar Jha, Alexander K. Hartmann

Research output: Contribution to journalArticle

Abstract

We study the energy landscape of the traveling salesperson problem (TSP) using exact ground states and a novel linear programming approach to generate excited states with closely defined properties. We look at four different ensembles, notably the classic finite dimensional Euclidean TSP and the mean-field-like (1,2)-TSP, which has its origin directly in the mapping of the Hamiltonian circuit problem on the TSP. Our data supports previous conjectures that the Euclidean TSP does not show signatures of replica symmetry breaking neither in two nor in higher dimension. On the other hand the (1,2)-TSP exhibits some signature which does not exclude broken replica symmetry, making it a candidate for further studies in the future.

Original languageEnglish
Article number032135
JournalPhysical Review E
Volume100
Issue number3
DOIs
Publication statusPublished - 23-09-2019
Externally publishedYes

Fingerprint

Replica
replicas
Symmetry Breaking
broken symmetry
signatures
Symmetry
linear programming
symmetry
ground state
Euclidean
Signature
excitation
Energy Landscape
Hamiltonian circuit
Excited States
energy
Mean Field
Higher Dimensions
Ground State
Linear programming

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Schawe, Hendrik ; Jha, Jitesh Kumar ; Hartmann, Alexander K. / Replica symmetry and replica symmetry breaking for the traveling salesperson problem. In: Physical Review E. 2019 ; Vol. 100, No. 3.
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Replica symmetry and replica symmetry breaking for the traveling salesperson problem. / Schawe, Hendrik; Jha, Jitesh Kumar; Hartmann, Alexander K.

In: Physical Review E, Vol. 100, No. 3, 032135, 23.09.2019.

Research output: Contribution to journalArticle

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