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MIPLIB 2010  Mixed Integer Programming Library version 5
, 2011
"... ... Mixed Integer Programming Library. The miplib 2010 is the first miplib release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the ne ..."
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... Mixed Integer Programming Library. The miplib 2010 is the first miplib release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the needs of the community. The new version comprises 361 instances sorted into several groups. This includes the main benchmark test set of 87 instances, which
ILP Modulo Theories
"... Abstract. We present Integer Linear Programming (ILP) Modulo Theories (IMT). An IMT instance is an Integer Linear Programming instance, where some symbols have interpretations in background theories. In previous work, the IMT approach has been applied to industrial synthesis and design problems with ..."
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Abstract. We present Integer Linear Programming (ILP) Modulo Theories (IMT). An IMT instance is an Integer Linear Programming instance, where some symbols have interpretations in background theories. In previous work, the IMT approach has been applied to industrial synthesis and design problems with realtime constraints arising in the development of the Boeing 787. Many other problems ranging from operations research to software verification routinely involve linear constraints and optimization. Thus, a general ILP Modulo Theories framework has the potential to be widely applicable. The logical next step in the development of IMT and the main goal of this paper is to provide theoretical underpinnings. This is accomplished by means of BC(T), the Branch and Cut Modulo T abstract transition system. We show that BC(T) provides a sound and complete optimization procedure for the ILP Modulo T problem, as long as T is a decidable, stablyinfinite theory. We compare a prototype of BC(T) against leading SMT solvers. 1
Restricted Risk Measures and Robust Optimization
, 2014
"... In this paper we consider characterizations of the robust uncertainty sets associated with coherent and distortion risk measures. In this context we show that if we are willing to enforce the coherent or distortion axioms only on random variables that are affine or linear functions of the vector of ..."
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In this paper we consider characterizations of the robust uncertainty sets associated with coherent and distortion risk measures. In this context we show that if we are willing to enforce the coherent or distortion axioms only on random variables that are affine or linear functions of the vector of random parameters, we may consider some new variants of the uncertainty sets determined by the classical characterizations. We also show that in the finite probability case these variants are simple transformations of the classical sets. Finally we present results of computational experiments that suggest that the risk measures associated with these new uncertainty sets can help mitigate estimation errors of the Conditional ValueatRisk. 1
On the safety of Gomory cut generators
, 2012
"... Gomory mixedinteger cuts are one of the key components in BranchandCut solvers for mixedinteger linear programs. The textbook formula for generating these cuts is not used directly in opensource and commercial software due to the limited numerical precision of the computations: Additional steps ..."
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Gomory mixedinteger cuts are one of the key components in BranchandCut solvers for mixedinteger linear programs. The textbook formula for generating these cuts is not used directly in opensource and commercial software due to the limited numerical precision of the computations: Additional steps are performed to avoid the generation of invalid cuts. This paper studies the impact of some of these steps on the safety of Gomory mixedinteger cut generators. As the generation of invalid cuts is a relatively rare event, the experimental design for this study is particularly important. We propose an experimental setup that allows statistically significant comparisons of generators. We also propose a parameter optimization algorithm and use it to find a Gomory mixedinteger cut generator that is as safe as a benchmark cut generator from a commercial solver even though it generates many more cuts.
SOFTWARE Open Access
"... Robust flux balance analysis of multiscale biochemical reaction networks ..."
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On lifting poorlyscaled flux balance analysis problems
"... Background Biological processes such as metabolism, signaling, and macromolecular synthesis can be modeled as large networks of biochemical reactions. Large and comprehensive networks, like MetabolicExpression networks that explicitly accounts for the demands of macromolecular synthesis at single n ..."
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Background Biological processes such as metabolism, signaling, and macromolecular synthesis can be modeled as large networks of biochemical reactions. Large and comprehensive networks, like MetabolicExpression networks that explicitly accounts for the demands of macromolecular synthesis at single nucleotide resolution, are inherently multiscale because reaction rates can vary over many orders of magnitude. Naively using standard optimization systems to conduct flux balance analysis can produce inaccurate or infeasible results. Results We describe lifting techniques that enable offtheshelf optimization software to compute accurate solutions to the poorly scaled optimization problems arising from flux balance analysis of multiscale biochemical reaction networks. We demonstrate the benefits of lifting using the first integrated reconstruction of metabolism and macromolecular synthesis for E. coli. Conclusion Lifting techniques enable accurate flux balance analysis of multiscale networks using offtheshelf optimization software. Although we describe these techniques in the context of flux balance analysis, our methods can be used to handle a variety of optimization problems arising from analysis of multiscale network reconstructions.