Augmented Lagrangean Based Algorithms for Centralized Network Design

Capacitated spanning tree problems appear frequently as fundamental problems in many communication network design problems. An integer programming formulation and a new set of valid inequalities are presented for the linear characterization of the problem. A combination of a subgradient optimization procedure and an augmented Lagrangean-based procedure is used to generate tight lower bounds. The procedure begins with an explicit representation of a subset of the constraints, and the corresponding Lagrangean problem is solved. The solution is examined in order to identify implicit constraints that are violated. Those are added to the Lagrangean problem, forming an expanded problem, and an efficient dual ascent procedure is then applied. When no further improvement is possible through this procedure, a subgradient optimization procedure is invoked in order to further tighten the lower bound value. An exchange heuristic is applied to the nonfeasible Lagrangean solution, in an attempt to generate good feasible solutions to the problem. The procedure has been tested and has generated bounds that are significantly better than ones obtained through previously published procedures.