Scalable Column Generation Models and Algorithms for Optical Network Planning Problems

Column Generation Method has been proved to be a powerful tool to model and solve large scale optimization problems in various practical domains such as operation management, logistics and computer design. Such a decomposition approach has been also applied in telecommunication for several classes of classical network design and planning problems with a great success. \n \nIn this thesis, we confirm that Column Generation Methodology is also a powerful tool in solving several contemporary network design problems that come from a rising worldwide demand of heavy traffic (100Gbps, 400Gbps, and 1Tbps) with emphasis on cost-effective and resilient networks. Such problems are very challenging in terms of complexity as well as solution quality. Research in this thesis attacks four challenging design problems in optical networks: design of p-cycles subject to wavelength continuity, design of dependent and independent p-cycles against multiple failures, design of survivable virtual topologies against multiple failures, design of a multirate optical network architecture. For each design problem, we develop a new mathematical models based on Column Generation Decomposition scheme. \n \nNumerical results show that Column Generation methodology is the right choice to deal with hard network design problems since it allows us to efficiently solve large scale network instances which have been puzzles for the current state of art. Additionally, the thesis reveals the great flexibility of Column Generation in formulating design problems that have quite different natures as well as requirements. \n \nObtained results in this thesis show that, firstly, the design of p-cycles should be under a wavelength continuity assumption in order to save the converter cost since the difference between the capacity requirement under wavelength conversion vs. under wavelength continuity is insignificant. Secondly, such results which come from our new general design model for failure dependent p-cycles prove the fact that failure dependent p-cycles save significantly spare capacity than failure independent p-cycles. Thirdly, large instances can be quasi-optimally solved in case of survivable topology designs thanks to our new path-formulation model with online generation of augmenting paths. Lastly, the importance of high capacity devices such as 100Gbps transceiver and the impact of the restriction on number of regeneration sites to the provisioning cost of multirate WDM networks are revealed through our new hierarchical Column Generation model.