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Channel Ordering for Fairness in Elastic Optical Networks via a LLM-Guided Bottleneck TSP Solver

Liangshun Wu, Wen Chen, Qingqing Wu

TL;DR

This work tackles the Channel Ordering Problem (COP) in elastic optical networks by reformulating it as a Bottleneck Traveling Salesman Problem (BTSP) on a channel graph, where the objective is to minimize the maximum adjacent interference to maximize the worst-case SNR ${\widetilde{\mathrm{SNR}}}$. A two-phase BTSP solver combines probabilistic sampling with LLM-guided heuristics to efficiently find near-optimal channel orderings, using a symmetric interference metric $U(C_i,C_j)$ and a bottleneck objective. The approach is validated with GN/EGN and split-step Fourier simulations, showing robust performance gains (0.4–1.0 dB over non-LLM seeds and about 3 dB over baselines) and scalability up to at least 90 channels, with larger $F$ and higher-order modulations further enhancing benefits. The results indicate practical potential for fair and scalable channel ordering in large-scale EONs, supporting deployment in realistic optical networks.

Abstract

In flexible-grid elastic optical networks (EONs), the ordering of frequency channels plays a crucial role in managing inter-channel interference and ensuring signal quality. We address the Channel Ordering Problem (COP) by reformulating it as a Bottleneck Traveling Salesman Problem (BTSP), where interference among channels is represented as edge weights in a graph structure. To tackle this challenge efficiently, we develop a scalable approach that integrates statistical exploration with guidance from large language models (LLMs). Extensive simulations using both the Gaussian Noise (GN) model and the split-step Fourier method demonstrate that our method achieves near-optimal signal-to-noise ratio (SNR) performance and offers robust scalability across diverse network settings, making it well-suited for practical deployment in large-scale optical communication systems.

Channel Ordering for Fairness in Elastic Optical Networks via a LLM-Guided Bottleneck TSP Solver

TL;DR

This work tackles the Channel Ordering Problem (COP) in elastic optical networks by reformulating it as a Bottleneck Traveling Salesman Problem (BTSP) on a channel graph, where the objective is to minimize the maximum adjacent interference to maximize the worst-case SNR . A two-phase BTSP solver combines probabilistic sampling with LLM-guided heuristics to efficiently find near-optimal channel orderings, using a symmetric interference metric and a bottleneck objective. The approach is validated with GN/EGN and split-step Fourier simulations, showing robust performance gains (0.4–1.0 dB over non-LLM seeds and about 3 dB over baselines) and scalability up to at least 90 channels, with larger and higher-order modulations further enhancing benefits. The results indicate practical potential for fair and scalable channel ordering in large-scale EONs, supporting deployment in realistic optical networks.

Abstract

In flexible-grid elastic optical networks (EONs), the ordering of frequency channels plays a crucial role in managing inter-channel interference and ensuring signal quality. We address the Channel Ordering Problem (COP) by reformulating it as a Bottleneck Traveling Salesman Problem (BTSP), where interference among channels is represented as edge weights in a graph structure. To tackle this challenge efficiently, we develop a scalable approach that integrates statistical exploration with guidance from large language models (LLMs). Extensive simulations using both the Gaussian Noise (GN) model and the split-step Fourier method demonstrate that our method achieves near-optimal signal-to-noise ratio (SNR) performance and offers robust scalability across diverse network settings, making it well-suited for practical deployment in large-scale optical communication systems.

Paper Structure

This paper contains 18 sections, 6 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Channel Ordering as a Bottleneck TSP
  3. System Model
  4. Graph Formulation
  5. The Proposed BTSP Solver
  6. Algorithm Overview
  7. LLM-Guided Sampling
  8. Simulation
  9. Simulation Setup
  10. Results
  11. $\widetilde{\mathrm{SNR}}$ vs. Power
  12. ${\widetilde{\mathrm{SNR}}}$ vs. Number of Channels
  13. $\widetilde{\mathrm{SNR}}$ vs. Bandwidth/Spacing Ratio
  14. $\widetilde{\mathrm{SNR}}$ vs. XCI Orders
  15. Scalability
  16. ...and 3 more sections

Figures (7)

  • Figure 1: Left: Problem formulation: a fiber span chain with Erbium-Doped Fiber Amplifiers (EDFAs) introducing ASE noise; WDM channels $C_1,\dots,C_n$ with fixed grid spacing $F$ are mapped to a graph with symmetric XCI $U(C_i,C_j)$ as edge. The task is to find a Hamiltonian cycle/path that minimizes the maximum adjacent NSR (bottleneck edge highlighted). Right: The proposed BTSP solver fuses node-wise probabilistic sampling with LLM-seeded heuristics, and elite retention for statistics-guided probability refinement, obtaining final best permutation.
  • Figure 2: $\widetilde{\mathrm{SNR}}$ v.s. power (PM-QPSK modulation, $\Delta\left(C_{\pi_i}\right)=F$, $p\left(C_{\pi_i}\right) \in[\bar{p}-5 \mathrm{~dB}, \bar{p}+5 \mathrm{~dB}]$, for $\forall C_{\pi_i} \in \mathcal{C}$).
  • Figure 3: $\widetilde{\mathrm{SNR}}$ vs. number of WDM channels (PM-QPSK modulation, $p(C_{\pi_i})=\bar{p}$+5 dBm, $\Delta\left(C_{\pi_i}\right) = F$, for $\forall C_{\pi_i} \in \mathcal{C}$)
  • Figure 4: $\widetilde{\mathrm{SNR}}$ vs. channel bandwidth/spacing ratio at high vs. low launch powers(PM-QPSK modulation, $n=6$, $F=200$ GHz).
  • Figure 5: $\widetilde{\mathrm{SNR}}$ vs. XCI Orders (PM-QPSK modulation, $p(C_{\pi_i})=\bar{p}=0$ dBm), $F=\Delta\left(C_{\pi_i}\right)=100$ GHz, for $\forall C_{\pi_i} \in \mathcal{C}$ .
  • ...and 2 more figures