Solution of the Simultaneous Routing and Bandwidth Allocation Problem in Energy-Aware Networks Using Augmented Lagrangian-Based Algorithms and Decomposition

Anthony Chukwuemeka Nwachukwu and Andrzej Karbowski ()
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Anthony Chukwuemeka Nwachukwu: Doctoral School, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland
Andrzej Karbowski: Faculty of Electronics and Information Technology, Institute of Control and Computation Engineering, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland

Energies, 2024, vol. 17, issue 5, 1-23

Abstract: We discuss several algorithms for solving a network optimization problem of simultaneous routing and bandwidth allocation in green networks in a decomposed way, based on the augmented Lagrangian. The problem is difficult due to the nonconvexity caused by binary routing variables. The chosen algorithms, which are several versions of the Multiplier Method, including the Alternating Direction Method of Multipliers (ADMM), have been implemented in Python and tested on several networks’ data. We derive theoretical formulations for the inequality constraints of the Bertsekas, Tatjewski and SALA methods, formulated originally for problems with equality constraints. We also introduce some modifications to the Bertsekas and Tatjewski methods, without which they do not work for an MINLP problem. The final comparison of the performance of these algorithms shows a significant advantage of the augmented Lagrangian algorithms, using decomposition for big problems. In our particular case of the simultaneous routing and bandwidth allocation problem, these algorithms seem to be the best choice.

Keywords: nonconvex optimization; augmented Lagrangian; multiplier method; alternating direction method of multipliers; separable problems; network optimization; MINLP; NP-hard problems; Lagrangian relaxation (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2024
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