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Valid Inequalities for the Telecommunications Network Design Problem

In: Optimization Essentials

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  • Yogesh K. Agarwal

    (Jaipuria Institute of Management)

Abstract

This chapter addresses the problem of designing a backbone telecommunications network using transmission facilities (e.g., optical fibers) of a fixed capacity. Given a set of nodes, traffic demands among the nodes, and the costs of installing the facilities between the nodes, we need to design a minimum-cost network that can carry all the traffic demands. The problem can be modeled as a mixed integer program using a multicommodity network flow formulation. The chapter briefly introduces the concept of valid inequalities and reviews integer rounding and Chvátal-Gomory methods generating valid inequalities. It then identified the p-partition-based substructures for p = 2, 3, and 4, from which valid inequalities can be generated by applying the Chvatál-Gomory method. Several families of such inequalities are derived, and the effect of adding these inequalities is demonstrated through simple examples. A simple but effective shrinking heuristic is developed to find the p-partitions which are likely to result in violated valid inequalities. Some computational results are presented to demonstrate the effectiveness of the proposed approach.

Suggested Citation

  • Yogesh K. Agarwal, 2024. "Valid Inequalities for the Telecommunications Network Design Problem," International Series in Operations Research & Management Science, in: Faiz Hamid (ed.), Optimization Essentials, chapter 0, pages 175-194, Springer.
  • Handle: RePEc:spr:isochp:978-981-99-5491-9_5
    DOI: 10.1007/978-981-99-5491-9_5
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