Mixed Integer NonLinear Programs featuring “On/Off” constraints: convex analysis and applications

We call “on/off” constraint an algebraic constraint that is activated if and only if a corresponding boolean variable equals 1. Our main subject of interest is to derive tight convex formulations of Mixed Integer NonLinear Programs featuring “on/off” constraints. We study the simple set defined by o...

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Bibliographic Details
Published inElectronic notes in discrete mathematics Vol. 36; pp. 1153 - 1160
Main Authors Hijazi, Hassan, Bonami, Pierre, Cornuéjols, Gérard, Ouorou, Adam
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2010
Subjects
delay constraints
Disjunctive Programming
on/off constraints
routing problems
on/off constraints
Disjunctive Programming
routing problems
delay constraints
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Summary:We call “on/off” constraint an algebraic constraint that is activated if and only if a corresponding boolean variable equals 1. Our main subject of interest is to derive tight convex formulations of Mixed Integer NonLinear Programs featuring “on/off” constraints. We study the simple set defined by one “on/off” constraint with bounded variables. Using Disjunctive Programming, we introduce convex hull formulations of this set defined in higher dimensional spaces. Because the large number of variables in these formulations appears to be practically disadvantageous, we concentrate our efforts on defining explicit projections into lower dimensional spaces. Based on these results, we present new formulations to a well-known telecommunication problem: routing several commodities subject to multiple delay constraints. Numerical results are presented to assess the efficiency of the new models.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2010.05.146