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Detecting Semantic Groups in MIP Models

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Integration of AI and OR Techniques in Constraint Programming (CPAIOR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9676))

Abstract

Current state-of-the-art MIP technology lacks a powerful modeling language based on global constraints, a tool which has long been standard in constraint programming. In general, even basic semantic information about variables and constraints is hidden from the underlying solver. For example, in a network design model with unsplittable flows, both routing and arc capacity variables could be binary, and the solver would not be able to distinguish between the two semantically different groups of variables by looking at type alone. If available, such semantic partitioning could be used by different parts of the solver, heuristics in primis, to improve overall performance. In the present paper we will describe several heuristic procedures, all based on the concept of partition refinement, to automatically recover semantic variable (and constraint) groups from a flat MIP model. Computational experiments on a heterogeneous testbed of models, whose original higher-level partition is known a priori, show that one of the proposed methods is quite effective.

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Notes

  1. 1.

    In applications, such as graph automorphism and DFA minimization, function f is extended to dependent on a more complex domain than just S.

  2. 2.

    The same argument applies to the more common case of a general graph, but we will consider the layered case for simplicity.

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Authors and Affiliations

  1. IBM Italy, Segrate, Italy

    Domenico Salvagnin

  2. DEI, University of Padova, Padua, Italy

    Domenico Salvagnin

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  1. Domenico Salvagnin
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Correspondence to Domenico Salvagnin .

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  1. Université Laval, Quebec, Québec, Canada

    Claude-Guy Quimper

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Salvagnin, D. (2016). Detecting Semantic Groups in MIP Models. In: Quimper, CG. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2016. Lecture Notes in Computer Science(), vol 9676. Springer, Cham. https://doi.org/10.1007/978-3-319-33954-2_24

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  • DOI: https://doi.org/10.1007/978-3-319-33954-2_24

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