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International Conference on Principles and Practice of Constraint Programming

CP 2016: Principles and Practice of Constraint Programming pp 316–332Cite as

Constraint Programming for Strictly Convex Integer Quadratically-Constrained Problems

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9892))

Abstract

Inspired by the geometric reasoning exploited in discrete ellipsoid-based search (DEBS) from the communications literature, we develop a constraint programming (CP) approach to solve problems with strictly convex quadratic constraints. Such constraints appear in numerous applications such as modelling the ground-to-satellite distance in global positioning systems and evaluating the efficiency of a schedule with respect to quadratic objective functions. We strengthen the key aspects of the DEBS approach and implement them as combination of a global constraint and variable/value ordering heuristics in IBM ILOG CP Optimizer. Experiments on a variety of benchmark instances show significant improvement compared to the default settings and state-of-the-art performance compared to competing technologies of mixed integer programming, semi-definite programming, and mixed integer nonlinear programming.

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Notes

  1. 1.

    Depending on the data, it is sometimes not possible to transform a matrix to exactly achieve this ordering [20].

  2. 2.

    A major improvement was made in solving IQCPs in CPLEX v12.6.3 [25].

  3. 3.

    There are four versions of the SDP solver that deal with problem-specific structures. The SDP results presented are the best version for each individual problem instance, representing the “virtual best” SDP solver.

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Acknowledgement

We would like to thank Nick Sahinidis for the BARON license and Felipe Serrano and Benjamin Müller for valuable discussions. This research has been supported by the Natural Sciences and Engineering Research Council of Canada and the University of Toronto School of Graduate Studies Doctoral Completion Award.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, M5S 3G8, Canada

    Wen-Yang Ku & J. Christopher Beck

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  1. Wen-Yang Ku
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Correspondence to Wen-Yang Ku .

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Editors and Affiliations

  1. University of Nice Sophia Antipolis , Sophia Antipolis, France

    Michel Rueher

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Ku, WY., Beck, J.C. (2016). Constraint Programming for Strictly Convex Integer Quadratically-Constrained Problems . In: Rueher, M. (eds) Principles and Practice of Constraint Programming. CP 2016. Lecture Notes in Computer Science(), vol 9892. Springer, Cham. https://doi.org/10.1007/978-3-319-44953-1_21

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  • DOI: https://doi.org/10.1007/978-3-319-44953-1_21

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  • Online ISBN: 978-3-319-44953-1

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