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On the Choice of Explicit Stabilizing Terms in Column Generation by Hatem M.T. Ben Amor; Jacques Desrosiers; Antonio Frangioni is a Computer Science article available to read on EtoBox.

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## a b s t r a c t Column generation algorithms are instrumental in many areas of applied optimization, where linear programs with an enormous number of columns need to be solved. Although successfully employed in many applications, these approaches suffer from well-known instability issues that somewhat limit their efficiency. Building on the theory developed for nondifferentiable optimization algorithms, a large class of stabilized column generation algorithms can be defined which avoid the instability issues by using an explicit stabilizing term in the dual; this amounts at considering a (generalized) augmented Lagrangian of the primal master problem. Since the theory allows for a great degree of flexibility in the choice and in the management of the stabilizing term, one can use piecewiselinear or quadratic functions that can be efficiently dealt with using off-the-shelf solvers. The practical effectiveness of this approach is demonstrated by extensive computational experiments on large-scale Vehicle and Crew Scheduling problems. Also, the results of a detailed computational study on the impact of the different choices in the stabilization term (shape of the function, parameter

Who reads On the Choice of Explicit Stabilizing Terms in Column Generation?

Author

Hatem M.T. Ben Amor; Jacques Desrosiers; Antonio Frangioni

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0166-218X)

Published

2009

Language

EN

Field

Computer Science (Physical Sciences)