Lagrangian Decomposition, Metaheuristics, and Hybrid Approaches for the Design of the Last Mile in Fiber Optic Networks

Authors:
Markus Leitner;Günther R. Raidl
Affiliations:
School of Telematics / Network Engineering, Carinthia University of Applied Sciences, Klagenfurt, Austria and Institute for Computergraphics and Algorithms, Vienna University of Technology, Vienna ...;Institute for Computergraphics and Algorithms, Vienna University of Technology, Vienna, Austria
Venue:
HM '08 Proceedings of the 5th International Workshop on Hybrid Metaheuristics
Year:
2008

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Abstract

We consider a generalization of the (Price Collecting) Steiner Tree Problem on a graph with special redundancy requirements for customer nodes. The problem occurs in the design of the last mile of real-world communication networks. We formulate it as an abstract integer linear program and apply Lagrangian Decomposition to obtain relatively tight lower bounds as well as feasible solutions. Furthermore, a Variable Neighborhood Search and a GRASP approach are described, utilizing a new construction heuristic and special neighborhoods. In particular, hybrids of these methods are also studied and turn out to often perform superior. By comparison to previously published exact methods we show that our approaches are applicable to larger problem instances, while providing high quality solutions together with good lower bounds.