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Strengthening Convex Relaxations with Bound Tightening for Power Network Optimization

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Principles and Practice of Constraint Programming (CP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9255))

Abstract

Convexification is a fundamental technique in (mixed-integer) nonlinear optimization and many convex relaxations are parametrized by variable bounds, i.e., the tighter the bounds, the stronger the relaxations. This paper studies how bound tightening can improve convex relaxations for power network optimization. It adapts traditional constraint-programming concepts (e.g., minimal network and bound consistency) to a relaxation framework and shows how bound tightening can dramatically improve power network optimization. In particular, the paper shows that the Quadratic Convex relaxation of power flows, enhanced by bound tightening, almost always outperforms the state-of-the-art Semi-Definite Programming relaxation on the optimal power flow problem.

NICTA—NICTA is funded by the Australian Government through the Department of Communications and the Australian Research Council through the ICT Centre of Excellence Program.

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Author information

Authors and Affiliations

  1. NICTA - Optimisation Research Group, Canberra, Australia

    Carleton Coffrin, Hassan L. Hijazi & Pascal Van Hentenryck

  2. College of Engineering and Computer Science, Australian National University, Canberra, Australia

    Carleton Coffrin, Hassan L. Hijazi & Pascal Van Hentenryck

Authors
  1. Carleton Coffrin
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  2. Hassan L. Hijazi
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  3. Pascal Van Hentenryck
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Corresponding author

Correspondence to Carleton Coffrin .

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Editors and Affiliations

  1. École Polytechnique de Montréal, Montréal, Québec, Canada

    Gilles Pesant

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Coffrin, C., Hijazi, H.L., Van Hentenryck, P. (2015). Strengthening Convex Relaxations with Bound Tightening for Power Network Optimization. In: Pesant, G. (eds) Principles and Practice of Constraint Programming. CP 2015. Lecture Notes in Computer Science(), vol 9255. Springer, Cham. https://doi.org/10.1007/978-3-319-23219-5_4

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  • DOI: https://doi.org/10.1007/978-3-319-23219-5_4

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