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

TL;DR

The goal of this 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, and derived from Dantzig–Wolfe decomposition, allows converging to an optimal global solution with any kind of atomic algorithms.

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.

Figures (10)

• Figure 1: Mapping example between required constraints vs. supported features. Bold lines represent a possible selection of atomic algorithms, i.e. features from PCE1 and PCE3. This example shows that the Augmented PCE selects the most appropriate PCEs as atomic algorithms to handle the requested constraints.
• Figure 2: Framework description, where the upper block represents the branching strategy and the bottom block represents the column generation to solve the ACG model.
• Figure 3: Computation time (ms) to compare the different options of the ACG method on feasible instances from Grid topologies.
• Figure 5: Columns and branches generated by the different options of the ACG method on feasible instances from Grid topologies.
• Figure 6: Computation time (ms) for comparing the three methods, state-of-the-art compact ILP, dedicated algorithm MultiPulse method, and our generic ACG method on feasible instances from Grid topologies.

Theorems & Definitions (17)

• proposition 1
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• proposition 2
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• proposition 4
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• definition 1
• proposition 5