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arXiv · 2607.24455

A Grand-Canonical Solution to a Class of Random Optimization Problems

Izat B Baybusinov·Enrico M Fenoaltea·Zhen Han·Yi-Cheng Zhang
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Abstract

We introduce a general framework to solve a class of combinatorial opti- mization 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 re- lax 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.

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Izat B Baybusinov, Enrico M Fenoaltea, Zhen Han, Yi-Cheng Zhang. 2026-07-27. A Grand-Canonical Solution to a Class of Random Optimization Problems. https://doi.org/10.1016/j.chaos.2026.118012

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