Decomposition Methods for the Network Optimization Problem of Simultaneous Routing and Bandwidth Allocation Based on Lagrangian Relaxation

Ruksha, Ihnat; Karbowski, Andrzej

doi:10.3390/en15207634

Open AccessArticle

Decomposition Methods for the Network Optimization Problem of Simultaneous Routing and Bandwidth Allocation Based on Lagrangian Relaxation

by

Ihnat Ruksha

¹ and

Andrzej Karbowski

^2,*

¹

Faculty of Electronics and Information Technology, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland

²

Institute of Control and Computation Engineering, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland

^*

Author to whom correspondence should be addressed.

Energies 2022, 15(20), 7634; https://doi.org/10.3390/en15207634

Submission received: 23 August 2022 / Revised: 1 October 2022 / Accepted: 1 October 2022 / Published: 16 October 2022

(This article belongs to the Special Issue Mixed-Integer Linear and Nonlinear Programming Methods for Energy Aware Traffic Control in Stationary Networks and Clouds)

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Abstract

The main purpose of the work was examining various methods of decomposition of a network optimization problem of simultaneous routing and bandwidth allocation based on Lagrangian relaxation. The problem studied is an NP-hard mixed-integer nonlinear optimization problem. Multiple formulations of the optimization problem are proposed for the problem decomposition. The decomposition methods used several problem formulations and different choices of the dualized constraints. A simple gradient coordination algorithm, cutting-plane coordination algorithm, and their more sophisticated variants were used to solve dual problems. The performance of the proposed decomposition methods was compared to the commercial solver CPLEX and a heuristic algorithm.

Keywords: green networking; network optimization; multi-criteria; routing; bandwidth allocation; optimization; MINLP; MIQP; NP-hard problems; branch and bound; Lagrangian relaxation; dual problem; simple gradient algorithm; cutting-plane method; Pyomo; CPLEX

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MDPI and ACS Style

Ruksha, I.; Karbowski, A. Decomposition Methods for the Network Optimization Problem of Simultaneous Routing and Bandwidth Allocation Based on Lagrangian Relaxation. Energies 2022, 15, 7634. https://doi.org/10.3390/en15207634

AMA Style

Ruksha I, Karbowski A. Decomposition Methods for the Network Optimization Problem of Simultaneous Routing and Bandwidth Allocation Based on Lagrangian Relaxation. Energies. 2022; 15(20):7634. https://doi.org/10.3390/en15207634

Chicago/Turabian Style

Ruksha, Ihnat, and Andrzej Karbowski. 2022. "Decomposition Methods for the Network Optimization Problem of Simultaneous Routing and Bandwidth Allocation Based on Lagrangian Relaxation" Energies 15, no. 20: 7634. https://doi.org/10.3390/en15207634

APA Style

Ruksha, I., & Karbowski, A. (2022). Decomposition Methods for the Network Optimization Problem of Simultaneous Routing and Bandwidth Allocation Based on Lagrangian Relaxation. Energies, 15(20), 7634. https://doi.org/10.3390/en15207634

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Decomposition Methods for the Network Optimization Problem of Simultaneous Routing and Bandwidth Allocation Based on Lagrangian Relaxation

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