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MIP-based heuristic approaches for the capacitated edge activation problem: the effect of non-compactness

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Abstract

The capacitated edge activation (CEA) problem consists of activating a minimum cost set of capacitated edges to ensure the routing of some traffic demands. Most of the MIP-based heuristics proposed for network design problems are based on the so-called flow formulation that includes both activation and routing variables. Indeed, there also exists a capacity formulation that includes only activation variables. This formulation is, however, non-compact. Here, we investigate the price to pay to use the non-compact capacity formulation instead of the compact flow formulation in a MIP-based rounding heuristic for the CEA problem. Both splittable and unsplittable flows are considered. The experiments show that, indeed, the capacity formulation requires more time and solves less instances than the flow formulation, due to the time spent in separating feasibility cuts, in particular for unsplittable flows.

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References

  • Addis B, Capone A, Carello G, Gianoli L, Sansó B (2014) On the energy cost of robustness and resiliency in IP networks. Comput Netw 75(Part A):239–259

    Article  Google Scholar 

  • Addis B, Carello G, Mattia S (2017) Survivable green traffic engineering with shared protection. Networks 69(1):6–22

    Article  MathSciNet  MATH  Google Scholar 

  • Agarwal Y (2006) K-partition-based facets of the network design problem. Networks 47(3):123–139

    Article  MathSciNet  MATH  Google Scholar 

  • Agarwal Y, Aneja Y (2017) Fixed charge multicommodity network design using p-partition facets. Eur J Oper Res 258:124–135

    Article  MathSciNet  MATH  Google Scholar 

  • Amaldi E, Capone A, Gianoli L (2013) Energy-aware ip traffic engineering with shortest path routing. Comput Netw 57(6):1503–1517

    Article  MATH  Google Scholar 

  • Avella P, Mattia S, Sassano A (2007) Metric inequalities and the network loading problem. Disc Opt 4:103–114

    Article  MathSciNet  MATH  Google Scholar 

  • Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4:238–252

    Article  MathSciNet  MATH  Google Scholar 

  • Bienstock D, Chopra S, Günlük O, Tsai C-Y (1998) Minimum cost capacity installation for multicommodity network flows. Math Progr B 81:177–199

    MathSciNet  MATH  Google Scholar 

  • Bienstock D, Mattia S (2007) Using mixed-integer programming to solve power grid blackout problems. Disc Opt 4:115–141

    Article  MathSciNet  MATH  Google Scholar 

  • Crainic T, Gendreau M, Hernu G (2004) A slope scaling/lagrangian perturbation heuristic with long-term memory for multicommodity capacitated fixed-charge network design. J Heur 10:525–545

    Article  MATH  Google Scholar 

  • Crainic T, Li Y, Toulouse M (2006) A first multilevel cooperative algorithm for capacitated multicommodity network design. Comput Oper Res 33:2602–22

    Article  MATH  Google Scholar 

  • Fortz B, Poss M (2009) An improved benders decomposition applied to a multi-layer network design problem. Oper Res Lett 37(5):777–795

    Article  MathSciNet  MATH  Google Scholar 

  • Ghamlouche I, Crainic T, Gendreau M (2003) Cycle-based neighbourhoods for fixed-charge capacitated multicommodity network design. Oper Res 51:655–667

    Article  MathSciNet  MATH  Google Scholar 

  • Ghamlouche I, Crainic T, Gendreau M (2004) Path relinking, cycle-based neighborhoods and capacitated multicommodity network design. Ann Oper Res 131:109–133

    Article  MathSciNet  MATH  Google Scholar 

  • Ghiani G, Laporte G, Manni E (2015) Model-based automatic neighborhood design by unsupervised learning. Comput Oper Res 54:108–116

    Article  MathSciNet  MATH  Google Scholar 

  • Holmberg K, Yuan D (2000) A lagrangian heuristic based branch-and-bound approach for the capacitated network design problem. Oper Res 48:461–481

    Article  MathSciNet  MATH  Google Scholar 

  • Iri M (1971) On an extension of the max-flow min-cut theorem to multicommodity flows. J Oper Res Soc Jpn 13:129–135

    MATH  Google Scholar 

  • Lee C, Lee K, Park S (2013) Benders decomposition approach for the robust network design problem with flow bifurcations. Networks 62(1):1–16

    Article  MathSciNet  MATH  Google Scholar 

  • Mattia S (2012) Separating tight metric inequalities by bilevel programming. Oper Res Lett 40(6):568–572

    Article  MathSciNet  MATH  Google Scholar 

  • Mattia S (2012) Solving survivable two-layer network design problems by metric inequalities. Comput Optim Appl 51(2):809–834

    Article  MathSciNet  MATH  Google Scholar 

  • Mattia S (2013) A polyhedral study of the capacity formulation of the multilayer network design problem. Networks 62(1):17–26

    Article  MathSciNet  MATH  Google Scholar 

  • Mattia S (2013) The robust network loading problem with dynamic routing. Comput Optim Appl 54(3):619–643

    Article  MathSciNet  MATH  Google Scholar 

  • Mattia S (2016) Benders decomposition for capacitated network design. In: Proceedings of ISCO 2016, vol 9849 of LNCS, pp 71–80

  • Mattia S (2017) A polyhedral study of the robust capacitated edge activation problem. In: Proceedings of ODS 2017, vol 217 of PROMS, pp 413–419

  • Mattia S (2018) The capacity formulation of the capacitated edge activation problem. Networks 71:381–402

    Article  MathSciNet  MATH  Google Scholar 

  • Mattia S, Poss M (2018) A comparison of different routing schemes for the robust network loading problem: polyhedral results and computation. Comput Optim Appl 69:753–800

    Article  MathSciNet  MATH  Google Scholar 

  • Onaga K, Kakusho O (1971) On feasibility conditions of multicommodity flows in network. IEEE Trans Circ Theory 18(4):425–429

    Article  MathSciNet  Google Scholar 

  • Rodríguez-Martin I, Salazar-González J-J (2010) A local branching heuristic for the capacitated fixed-charge network design problem. Comput Oper Res 37(3):575–581

    Article  MathSciNet  MATH  Google Scholar 

  • Stoer M, Dahl G (1994) A polyhedral approach to multicommodity survivable network design. Numer Math 68(1):149–167

    Article  MathSciNet  MATH  Google Scholar 

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Funding

The author has been partially supported by Grants MIUR PRIN 2015B5F27W and 20153TXRX9.

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Authors and Affiliations

  1. Istituto di Analisti dei Sistemi ed Informatica (IASI), Consiglio Nazionale delle Ricerche (CNR), Via dei Taurini 19, 00135, Rome, Italy

    Sara Mattia

  2. Istituto Nazionale di Alta Matematica (INdAM), Rome, Italy

    Sara Mattia

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  1. Sara Mattia
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Correspondence to Sara Mattia.

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Communicated by P. Beraldi, M. Boccia, C. Sterle.

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Mattia, S. MIP-based heuristic approaches for the capacitated edge activation problem: the effect of non-compactness. Soft Comput 23, 2911–2921 (2019). https://doi.org/10.1007/s00500-018-3443-z

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