MPC 2009, ISSUE 4

Mathematical Programming Computation, Volume 1, Issue 4, December 2009

A structure-conveying modelling language for mathematical and stochastic programming

Marco Colombo, Andreas Grothey, Jonathan Hogg, Kristian Woodsend, Jacek Gondzio

We present a structure-conveying algebraicmodelling language formathematical programming. The proposed language extends AMPL with object-oriented features that allows the user to construct models from sub-models, and is implemented as a combination of pre- and post-processing phases for AMPL. Unlike traditional modelling languages, the new approach does not scramble the block structure of the problem, and thus it enables the passing of this structure on to the solver. Interior point solvers that exploit block linear algebra and decomposition-based solvers can therefore directly take advantage of the problem’s structure. The language contains features to conveniently model stochastic programming problems, although it is designed with a much broader application spectrum.

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Mathematical Programming Computation, Volume 1, Issue 4, December 2009

Information-based branching schemes for binary linear mixed integer problems

Fatma Kilinc Karzan, George L. Nemhauser, Martin W.P. Savelsbergh

Branching variable selection can greatly affect the effectiveness and efficiency of a branch-and-bound algorithm. Traditional approaches to branching variable selection rely on estimating the effect of the candidate variables on the objective function. We propose an approach which is empowered by exploiting the information contained in a family of fathomed subproblems, collected beforehand from an incomplete branch-and-bound tree. In particular, we use this information to define new branching rules that reduce the risk of incurring inappropriate branchings. We provide computational results that demonstrate the effectiveness of the new branching rules on various benchmark instances.

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