Optimal regenerator placement in translucent optical networks

Regenerator location problem: Polyhedral study and effective branch-and-cut algorithms

“…Given a fractional solution x at each node of the enumeration tree, we here discuss a min-cut based method for solving the separation problem exactly. Note that the separation of DSN inequalities using maximum flows follows from the Max-flow Min-Cut Theorem ( Ford & Fulkerson, 1974 ), reported in Rahman (2012) ; Rahman et al (2015) , which is also used in Chen et al (2015) , Fügenschuh and Fügenschuh (2008) , Fischetti et al (2014) , andÁlvarez-Miranda et al (2013) . If the identified valid cut is not an FDI, we further lift it to a stronger inequality, or a set of stronger inequalities.…”

“…• B&C _ CLR: the B&C approach for the RLP, proposed by Chen et al (2010) . We did not include method of Rahman (2012) , Rahman et al (2015) in our comparison study, because as mentioned earlier, this method is a preliminary implementation of the B&C algorithm, and its performance is not demonstrated by comparing it with best exact algorithms in the literature. Chen et al (2010) used CPLEX 10.0 as a framework to implement their B&C algorithm on a Pentium D 3.0 gigahertz PC with 2 gigabyte RAM.…”

“…Based on this observation, the following set covering formulation was given in Rahman (2012) and also published in Rahman et al (2015) .…”

“…The computational results in Chen et al (2010) show that their B&C method could optimally solve instances with up to 100 nodes and a few 20 0-and 30 0-node instances with small network density. Rahman (2012) , and Rahman, Bandyopadhyay, and Aneja (2015) also studied a set covering formulation, which is equivalent to the "vertex" formulation discussed in Fujie (2004) . With this formulation, the authors presented a computational study using a preliminary B&C approach (no comparison was made with any other approach).…”

Optimal regenerator placement for path protection in impairment-aware WDM networks

“…In [6] a novel ILP was proposed to optimally solve the RPP for translucent networks using dynamic lightpath allocation. The formulation involves an exponential number of constraints, known only implicitly.…”