Abstract
We address the physical SONET network design problem of selecting stackable, unidirectional rings connecting central office nodes (COs) and remote nodes (RNs). This problem frequently arises in designing feeder transport networks to support centralized traffic between the COs and RNs. We formulate a 0–1 programming model for this problem. A simulated annealing-based Lagrangian relaxation procedure to find optimal or near-optimal solutions is then described. Computational results are reported showing that our procedures produce solutions that are on average within 1.1% of optimality. We show that using simulated annealing to augment the pure Lagrangian approach produces superior solutions to the Lagrangian approach.
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Appendix
Appendix
We show excerpts from the code for generating all rings such that each ring contains two central offices (COs) and at least one demand node (RN). Also, total demand associated with chosen nodes can be at most 48, and there can be at most 10 nodes of any type. We do this using exhaustive search with a series of nested loops. If Total = “No”, then there is too much demand or too many nodes already, so the subsequent loops can be skipped. This is key to the success of this exhaustive enumeration approach. Even for the large network problems that we solved which have 75 nodes and 110 links, this took less than 1 CPU second and required storing only about 130 rings.
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Park, J.S., Lim, B.H. & LeBlanc, L.J. Design of reliable SONET feeder networks. Inf Technol Manage 8, 19–29 (2007). https://doi.org/10.1007/s10799-006-0003-5
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DOI: https://doi.org/10.1007/s10799-006-0003-5