Atomic Column Generation for Consensus Between Algorithms: Application to Path Computation

• Published in: Networks Vol. 85; no. 4; pp. 396 - 411
• Main Authors: Martin, Sebastien, Bauguion, Pierre, Magnouche, Youcef, Leguay, Jérémie
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.06.2025; Wiley Subscription Services, Inc
• Subjects: Algorithms; black‐box optimization; column generation; Combinatorial analysis; combinatorial optimization; Computation; Constraints; Convergence; Dantzig-Wolfe decomposition; Optimization; path computation; Shortest-path problems
• ISSN: 0028-3045; 1097-0037
• DOI: 10.1002/net.22269

ABSTRACT In real‐life applications, most optimization problems are variants of well‐known combinatorial optimization problems, including additional constraints to fit with a particular use case. Usually, efficient algorithms to handle a restricted subset of these additional constraints already exist or can be easily derived, but combining them together is difficult. The goal of our paper is to provide a framework that allows merging several so‐called atomic algorithms to solve an optimization problem, including all associated additional constraints together. The core proposal, referred to as Atomic Column Generation (ACG) and derived from Dantzig–Wolfe decomposition, allows converging to an optimal global solution with any kind of atomic algorithms. We show that this decomposition improves the continuous relaxation and describe the associated Branch‐and‐Price algorithm. We consider a specific use case in telecommunication networks where several Path Computation Elements (PCE) are combined as atomic algorithms to route traffic. We demonstrate the efficiency of ACG on the resource‐constrained shortest path problem associated with each PCE and show that it remains competitive with benchmark algorithms.