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Combinatorial optimization model and MIP formulation for the structural analysis of conditional differential-algebraic systems.

Martin, Sébastien; Mahjoub, Ali Ridha; Lacroix, Mathieu (2011), Combinatorial optimization model and MIP formulation for the structural analysis of conditional differential-algebraic systems., Computers & Industrial Engineering, 61, 2, p. 422-429. http://dx.doi.org/10.1016/j.cie.2010.12.002

Type
Article accepté pour publication ou publié
Date
2011
Nom de la revue
Computers & Industrial Engineering
Volume
61
Numéro
2
Éditeur
Elsevier
Pages
422-429
Identifiant publication
Métadonnées
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Auteur(s)
Martin, Sébastien cc
Mahjoub, Ali Ridha
Lacroix, Mathieu cc
Résumé (EN)
In this paper we consider the structuralanalysis problem for differential-algebraicsystems with conditional equations. This problem consists, given a conditionaldifferential-algebraic system, in verifying if the system is structurally nonsingular for every state, and if not in finding a state in which the system is structurally singular. We give a formulation for this problem as an integer linear program. This is based on a transformation of the problem into a matching problem in an auxiliary graph. We also show that the linear relaxation of that formulation can be solved in polynomial time. Using this, we develop a Branch-and-Cut algorithm for solving the problem and present some experimental results.
Mots-clés
Branch-and-Cut algorithm; Matching; Integer linear program; Graph; Structural analysis; Differential-algebraic system