Displaying similar documents to “Column-generation in integer linear programming”

A branch-and-price-and-cut algorithm for the pattern minimization problem

Cláudio Alves, J. M. Valério de Carvalho (2008)

RAIRO - Operations Research - Recherche Opérationnelle

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In cutting stock problems, after an optimal (minimal stock usage) cutting plan has been devised, one might want to further reduce the operational costs by minimizing the number of setups. A setup operation occurs each time a different cutting pattern begins to be produced. The related optimization problem is known as the Pattern Minimization Problem, and it is particularly hard to solve exactly. In this paper, we present different techniques to strengthen a formulation proposed in the...

Column-Generation in Integer Linear Programming

Nelson Maculan, Marcos de Mendonça Passini, José André de Moura Brito, Irene Loiseau (2010)

RAIRO - Operations Research

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We present an exact method for integer linear programming problems that combines branch and bound with column generation at each node of the search tree. For the case of models involving binary column vectors only, we propose the use of so-called geometrical cuts to be added to the subproblem in order to eliminate previously generated columns. This scheme could be applied to general integer problems without specific structure. We report computational results on a successful application...

An algorithm for multiparametric 0-1-Integer Programming problems relative to a generalized min max objective function

José Luis Quintero, Alejandro Crema (2009)

RAIRO - Operations Research

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The multiparametric 0-1-Integer Programming (0-1-IP) problem relative to the objective function is a family of 0-1-IP problems which are related by having identical constraint matrix and right-hand-side vector. In this paper we present an algorithm to perform a complete multiparametric analysis relative to a generalized min max objective function such that the min sum and min max are particular cases.

An algorithm for multiparametric min max 0-1-integer programming problems relative to the objective function

José Luis Quintero, Alejandro Crema (2005)

RAIRO - Operations Research - Recherche Opérationnelle

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The multiparametric min max 0-1-Integer Programming (0-1-IP) problem relative to the objective function is a family of min max 0-1-IP problems which are related by having identical constraint matrix and right-hand-side vector. In this paper we present an algorithm to perform a complete multiparametric analysis relative to the objective function.

Enumerating the Set of Non-dominated Vectors in Multiple Objective Integer Linear Programming

John Sylva, Alejandro Crema (2008)

RAIRO - Operations Research

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An algorithm for enumerating all nondominated vectors of multiple objective integer linear programs is presented. The method tests different regions where candidates can be found using an auxiliary binary problem for tracking the regions already explored. An experimental comparision with our previous efforts shows the method has relatively good time performance.