Lower Bounding Procedures for Multiperiod Telecommunications Network Expansion Problems

Abstract

This paper suggests an improved formulation for the multiperiod network topology and capacity expansion problem and proposes new lower bounding schemes based on it. It differs from earlier formulations and solution methods in that entirely new and different subproblems are solved and a number of lower bound tightening schemes are added within the framework of a Lagrangian relaxation. Dual ascent and multiplier adjustment procedures are suggested for the Lagrange multiplier updating procedure. Computational results are reported to demonstrate the tightness of the bounds generated by the suggested procedures. Heuristics based on converting the dual information obtained from the Lagrangian procedure into primal feasible solutions are tested. The tests show that the Lagrangian-based heuristics generate solutions superior to solutions generated by other heuristics proposed in the literature.

Optimization of Internet Protocol network design and routing

“…In addition, (15) states that the flow of a commodity can be positive on an arc only if there is any capacity available. Note that (14) follows from (12) and (13), and (15) follows from (9), (11), and (12). Thus, (14) and (15) are redundant constraints.…”

“…Note that (14) follows from (12) and (13), and (15) follows from (9), (11), and (12). Thus, (14) and (15) are redundant constraints. They can, however, be used to improve the continuous relaxation.…”

Topological expansion of multiple-ring metropolitan area networks

“…They require that the number of links connected to a shelf of type t ∈ T be at most m t . To underline the generality of the model, we have chosen not to be explicit at this point about the backbone topology constraints (10). In general terms, they must impose that the topology of the backbone network be the one specified by the user of the model.…”

“…The purpose of this first subproblem is to connect a minimum-cost backbone network whose topology is given by constraints (10).…”

“…For each iteration of the search, we determine the best move (among a total of |N C |(|T| − 1) + |N N ||T| moves) while taking into account the tabu moves as well as the aspiration criterion described in the next subsection. The chosen site is declared tabu for a number of iterations that, in this case, is randomly determined according to a uniform discrete distribution on the interval [5,10].…”