# Spectrum Allocation Using Integer Linear Programming and Kerr Optical Frequency Combs
## 1 Introduction
This technique enables the generation of equally spaced frequency lines, stabilized by auxiliary pumping and phase locking, ensuring the spectral coherence required for high-capacity optical communication networks [1]. These systems have demonstrated transmission speeds of up to 44.2 Tb/s on a single chip, highlighting their potential for large bandwidth applications [2; 11]. Despite recent advancements, spectrum allocation in wavelength division multiplexing (WDM) systems continues to face significant challenges. The most common spectrum allocation methods include heuristic approaches, such as First Fit and Best Fit, which aim to minimize spectrum occupation by assigning carriers efficiently. Additionally, optimization techniques like Mixed-Integer Linear Programming (MILP) and genetic algorithms are employed to enhance spectral efficiency, reduce processing times, and improve overall network performance [12; 13]. These algorithms often struggle to adapt to the point-to-multipoint structure and variable distances characteristic of PONs, which increases the computational burden [13]. One of the most common and promising methods to address the challenges of spectrum allocation in optical networks is the Routing, Modulation Level, and Spectrum Assignment (RMLSA) algorithm. This algorithm dynamically optimizes routing, modulation levels, and spectrum allocation based on transmission parameters such as distance and bandwidth requirements [14; 15; 16; 17; 18]. RMLSA is particularly effective in access networks like PONs, where the ability to adjust wavelengths and modulation levels dynamically according to the distance between the central node and the users is critical. However, despite its effectiveness, the high computational cost associated with RMLSA presents a significant challenge, especially in large-scale implementations. This has led to the exploration of more efficient solutions, such as the use of hardware acceleration techniques, including GPUs and FPGAs, to reduce processing delays. Furthermore, the implementation of OFCs in optical networks faces limitations due to the uneven distribution of carrier power, which affects the optical signal-to-noise ratio (OSNR) and complicates data transmission. Ensuring optimal transmission often requires additional optical processing, which increases both technical and economic costs. Heuristic techniques used in RMLSA also require further refinement,particularly in the context of optical MRRs. For instance, many existing methods fail to account for the \(\mathrm{sech}^{2}\) profile of frequency combs, reducing their efficiency in spectrum allocation. An alternative approach proposed by [19] introduces a photonic design that integrates MRRs, considering constraints such as comb shape, request distance, and multilevel modulation. Although this approach improves spectrum allocation, the proposed heuristic algorithm does not fully optimize spectrum usage or the number of requests served, highlighting the need for more advanced optimization techniques to achieve more robust and efficient allocation. This article proposes a methodology that employs a constrained optimization approach to enhance bandwidth allocation in frequency comb systems generated by MRRs. The objective is to maximize assigned bandwidth and increase the number of requests served, thereby reducing the bandwidth blocking rate (BBR).