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

2025-01-23

AI Summary

This paper addresses combinatorial optimization problems with multiple practical constraints—exemplified by multi-PCE path computation in telecommunications networks—by proposing the Atomic Column Generation (ACG) framework. ACG extends Dantzig–Wolfe decomposition to enable consensus-based, atomic-level coordination among arbitrary heterogeneous specialized algorithms (e.g., multi-PCE routers), integrated via column generation and branch-and-price, with provable convergence guarantees. Experiments demonstrate that ACG significantly improves the quality of the linear programming relaxation bound; on resource-constrained shortest path problems, its relaxation performance surpasses conventional approaches, while overall solution efficiency matches state-of-the-art benchmark algorithms. The core contribution is a novel, scalable, verifiable decomposition paradigm that natively supports distributed, heterogeneous algorithm integration—establishing a foundation for cooperative, architecture-agnostic optimization in complex networked systems.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• Algorithm Integration
• Complex Optimization Problems
• Telecommunication Network Routing

Innovation

• Atom Column Generation (ACG)
• Dantzig-Wolfe decomposition
• resource-constrained shortest path problems