Progress in computational mixed integer programming—A look back from the other side of the tipping point

By Robert E. Bixby, Edward E. Rothberg. 2007

233 citations recorded by the source corpus.

Subfields: Industrial and Manufacturing Engineering, Management Science and Operations Research

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Citations in the corpus

Supersparse linear integer models for optimized medical scoring systems (2015, methodology): “In comparison to current methods for sparse linear classification, SLIM can produce scoring systems that are fully optimized for accuracy and sparsity, and that satisfy a wide range of complicated operational constraints without any parameter tuning.”
Journal of the American Statistical Association Using Mixed Integer Programming for Matching in an Observational Study of Kidney Failure after Surgery Using Mixed Integer Programming for Matching in an Observational Study of Kidney Failure after Surgery (unknown): “…solution space are needed with the branch-and-bound algorithm, and, on the other hand, to avoid the slow convergence rates of the addition of too many constraints, which presents numerical difficulties for solvers with the cutting plane algorithm (Bixby and Rothberg 2007; Linderoth and Lodi 2010).”
The SCIP Optimization Suite 3.2 (2016, background): “In regards to mixed-integer nonlinear programming this release includes improvements to separation, propagation and constraint upgrading processes.”
Algorithms and Software for Convex Mixed Integer Nonlinear Programs (2012, background): “Combining both integrality and nonlinearity can lead to examples of MINLP that are undecidable [68].”
On the Computational Studies of Deterministic Global Optimization of Head Dependent Short-Term Hydro Scheduling (2013, methodology): “This work is motivated by the current trend to develop more detailed MINLP models for the STHS, and is supported by the following advancements: 1) global optimization for nonconvex MINLP problems; 2) availability of affordable multiple threads computer hardware; and 3) increasing sophistication of M”
Tight and Compact MILP Formulation for the Thermal Unit Commitment Problem (2013, background): “2) Performance Metrics: In order to summarize comparison results between formulations, geometric means of ratios are used since arithmetic means can be quite misleading when applied to a set of ratios [10], [14], that is, a number of model characteristics between two formulations, e.”
Mixed Integer Linear Programming Formulation Techniques (2015, background): “For more details on basic branch-and-bound and state-of-the-art solvers, we refer the reader to [22, 36, 131, 166] and [1, 2, 25, 23, 92, 112, 24], respectively.”
A Review of Operations Research in Mine Planning (2010, background): “Bixby and Rothberg (2007) remind us of the continued improvements in hardware and software capabilities.”
Progress in presolving for mixed integer programming (2015, background): “11, 91058 Erlangen, Germany 1 The impact of presolving on the entire solution process of mixed integer linear problems was published in Bixby and Rothberg [12].”
Dynamic vehicle routing problems: Three decades and counting (2016, background): “Bixby and Rothberg [20] report that in 2004 an LP was solved, by Cplex 8, a million times faster than it was by Cplex 1 in 1990.”