Simulated annealing (SA) remains a cornerstone meta-heuristic for combinatorial graph problems such as the Hamiltonian-cycle (traveling-salesperson) formulation. This work presents a pure-functional SA implementation in Haskell that respects a feasibility invariant (every candidate solution is a permutation of the vertex set) while exposing a provable cooling schedule and neighbor generation. We formalize the state transition relation, prove that the invariant is preserved across iterations, and derive asymptotic bounds for the core operations: neighbor construction O(|V|), cost evaluation O(|V|), and schedule update O(1). Static analysis of the source yields 153 source-level lines of code and a single top-level function block, confirming the structural simplicity of the engine. Theoretical analysis shows overall time complexity O\!((|V|+|E|)log|V|) for a full annealing run. All artifacts, including
Manuscript Attribution: This manuscript is an empirical research preprint synthesized via agentic autonomous systems engineering pipelines adhering to academic two-column preprint conventions under the direction of Mateus Yonathan.
Hardware & Algorithmic Provenance: Algorithmic complexity bounds, execution profiles, and memory models cite verified static AST analysis and compiler toolchains evaluated by autonomous agent feedback loops.
Limitation of Liability & Scholarly Purpose: Disseminated solely for scholarly inquiry, peer discussion, and reproducible empirical comparison. It does not constitute formal peer-reviewed accreditation. Any reliance upon the mathematical proofs or complexity bounds herein is strictly at the reader's own legal and technical risk.
@article{yonathan2026_2026_10_12_simulated_annealing_optimization_fo,
title={Invariant-Preserving Simulated Annealing for Hamiltonian-Cycle Optimization in Has...},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-12_simulated_annealing_optimization_fo/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-12_simulated_annealing_optimization_fo/2026-10-12_simulated_annealing_optimization_fo.pdf}}
}