New pricing strategies and an effective exact solution framework for profit-oriented ring arborescence problems

We study novel solution methods for a class of network optimization problems that find application in strategic planning of telecommunication infrastructure. These directed network design models are used to compute centralized two-level networks under capacity constraints: Circuits on the inner level and directed trees in the periphery. We develop non-compact arc-based and set-packing formulations and integrate cuts to strengthen polyhedral descriptions of their relaxations. Theoretical results on polyhedral structure are provided that serve as the foundation of our branch-and-cut-and-price methods. For the column generation component, we introduce new relaxations of the pricing problem that are based on not necessarily elementary ring arborescences: q-d-Steiner-arb and ng-ring-Steiner-arbs. These models are related to q-arbs and ng-route relaxations known to be state-of-the-art for related network optimization models including vehicle routing. Our effective algorithmic framework incorporates iterated local search based primal heuristics and exact pricing strategies that can be applied to all considered model variants and related network design problems. The novel methods clearly outperform existing approaches from the literature regarding both solution time and solution quality. In a computational study, we show that our algorithms are capable of closing most optimality gaps for unsolved literature instances with up to 51 vertices. Furthermore, we provide results for new larger instances with up to 101 vertices.