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A grand-canonical solution to a class of random optimization problems

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  • Baybusinov, Izat B.
  • Fenoaltea, Enrico Maria
  • Han, Zhen
  • Zhang, Yi-Cheng

Abstract

We introduce a general framework to solve a class of combinatorial optimization problems, including the matching problem, the Traveling Salesman Problem, and also the minimum weight k-factor problem. By reformulating these problems as an arrangement model, we recast the optimization task into a grand-canonical ensemble, where chemical potentials are used to relax strict topological constraints. The analytical solution found can serve as a polynomial-time algorithm to compute an approximate minimum cost for arbitrary k and link-weight distributions. Our framework is complementary to existing approaches and reveals new connections between combinatorial optimization and the statistical physics of disordered systems.

Suggested Citation

  • Baybusinov, Izat B. & Fenoaltea, Enrico Maria & Han, Zhen & Zhang, Yi-Cheng, 2026. "A grand-canonical solution to a class of random optimization problems," Chaos, Solitons & Fractals, Elsevier, vol. 207(C).
    • Handle: RePEc:eee:chsofr:v:207:y:2026:i:c:s0960077926001530
    DOI: 10.1016/j.chaos.2026.118012
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