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Facet-Defining Inequalities for Multi-Module Survivable Network Design Problem

Haochen Luo(hcluo***at***tamu.edu)
Kiavash Kianfar(kianfar***at***tamu.edu)

Abstract: Capacitated survivable network design (SND), i.e., designing a network that can survive edge failures with minimum flow-routing plus capacity-installation cost, is a fundamental problem in network science and its applications. In this paper, we study a highly applicable form of the SND, referred to as the multi-module SND (MM-SND), in which transmission capacities on edges can be sum of integer multiples of differently sized capacity modules. For the first time, we formulate the MM-SND as a mixed integer program (MIP) using preconfigured-cycles (p-cycles) to reroute flow on failed edges. We derive several classes of valid inequalities for this MIP, and show that the valid inequalities previously developed in the literature for the single-module SND are special cases of our inequalities. Furthermore, we show that our valid inequalities are facet-defining for the MM-SND in many cases. Our computational results, using a heuristic separation algorithm, show that these inequalities are very effective in solving the MM-SND. In particular they are more effective than compared to using single-module inequalities alone.

Keywords: multi-module survivable network design; n-step cutset inequalities; n-step MIR; telecommunication network design

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Category 2: Integer Programming (Cutting Plane Approaches )

Category 3: Applications -- Science and Engineering (Facility Planning and Design )

Citation:

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Entry Submitted: 05/08/2019
Entry Accepted: 05/08/2019
Entry Last Modified: 05/08/2019

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