Q-Learning with Dynamic Rewards Table Applied to the SONET/SDH Ring Problem

Given a graph $G = (V, E)$, the set partitions problem consists of defining V into disjoint sets. In this work, a method is proposed to minimize the number of partitions in sets, whose partitions have capacity constraints. The proposed procedure uses the algorithm Q-Learning that differs from the traditional one by the dynamic update of the rewards table and an extra table with bonuses for good solutions. To test the validity of the method, the idea was applied to the SONET (Synchronous Optical NETwork) ring problem, referenced as SRAP (SONET Ring Assignment Problem). SRAP is an NP-hard problem and finds applications in topologies of fiber optic networks.