Exact solution of the full RMSA problem in elastic optical networks
Fabio David, José F. de Rezende, Valmir C. Barbosa
TL;DR
The paper tackles exact optimization for the RMSA problem in Elastic Optical Networks under CC constraints, introducing RMSA-BP, the first ILP formulation that simultaneously targets maximum admitted demands, minimal regenerators, and minimal FS usage with CC enforced. It first presents a full formulation with CC via indices $z_d^e$ and related variables, then revisits the model with a preprocessing-based decomposition and big-$M$ techniques to significantly improve solvability. The authors validate their approach on the NSFNET topology using Gurobi in hierarchical multi-objective mode, demonstrating substantial solvability improvements and obtaining insight into topology-induced resource usage. The work provides a practical pathway to exact optimization for EONs and offers tools for topology analysis and deployment planning, with future work aimed at generalizing objectives and scaling further. All mathematical notation is embedded within $...$ to ensure precise, machine-readable expression of the methods and constraints.
Abstract
Exact solutions of the Routing, Modulation, and Spectrum Allocation (RMSA) problem in Elastic Optical Networks (EONs), so that the number of admitted demands is maximized while those of regenerators and frequency slots used are minimized, require a complex ILP formulation taking into account frequency-slot continuity and contiguity. We introduce the first such formulation, ending a hiatus of some years since the last ILP formulation for a much simpler RMSA variation was introduced. By exploiting a number of problem and solver specificities, we use the NSFNET topology to illustrate the practicality and importance of obtaining exact solutions.