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

TL;DR

This paper introduces Atomic Column Generation (ACG), a novel framework based on Dantzig-Wolfe decomposition, enabling the integration of multiple atomic algorithms to solve complex constrained optimization problems efficiently.

Contribution

The paper presents ACG, a new decomposition-based method that merges atomic algorithms for solving constrained optimization problems, with an application to telecommunication path computation.

Findings

ACG improves the continuous relaxation of the problem.

ACG remains competitive with benchmark algorithms.

Application to telecommunication networks demonstrates effectiveness.

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.