39 research outputs found

    SCIL - Symbolic Constraints in Integer Linear Programming

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    We describe SCIL. SCIL introduces symbolic constraints into branch-and-cut-and-price algorithms for integer linear programs. Symbolic constraints are known from constraint programming and contribute significantly to the expressive power, ease of use, and efficiency of constraint programs

    Detecting semantic groups in MIP models

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    Computing H/D-Exchange rates of single residues from data of proteolytic fragments

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    <p>Abstract</p> <p>Background</p> <p>Protein conformation and protein/protein interaction can be elucidated by solution-phase Hydrogen/Deuterium exchange (sHDX) coupled to high-resolution mass analysis of the digested protein or protein complex. In sHDX experiments mutant proteins are compared to wild-type proteins or a ligand is added to the protein and compared to the wild-type protein (or mutant). The number of deuteriums incorporated into the polypeptides generated from the protease digest of the protein is related to the solvent accessibility of amide protons within the original protein construct.</p> <p>Results</p> <p>In this work, sHDX data was collected on a 14.5 T FT-ICR MS. An algorithm was developed based on combinatorial optimization that predicts deuterium exchange with high spatial resolution based on the sHDX data of overlapping proteolytic fragments. Often the algorithm assigns deuterium exchange with single residue resolution.</p> <p>Conclusions</p> <p>With our new method it is possible to automatically determine deuterium exchange with higher spatial resolution than the level of digested fragments.</p

    Compact and Extended Formulations for Range Assignment Problems

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    We devise two new integer programming models for range assignment problems arising in wireless network design. Building on an arbitrary set of feasible network topologies, e.g., all spanning trees, we explicitly model the power consumption at a given node as a weighted maximum over edge variables. We show that the standard ILP model is an extended formulation of the new models. For all models, we derive complete polyhedral descriptions in the unconstrained case where all topologies are allowed. These results give rise to tight relaxations even in the constrained case. We can show experimentally that the compact formulations compare favorably to the standard approach

    Compact and Extended Formulations for Range Assignment Problems

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    We devise two new integer programming models for range assignment problems arising in wireless network design. Building on an arbitrary set of feasible network topologies, e.g., all spanning trees, we explicitly model the power consumption at a given node as a weighted maximum over edge variables. We show that the standard ILP model is an extended formulation of the new models. For all models, we derive complete polyhedral descriptions in the unconstrained case where all topologies are allowed. These results give rise to tight relaxations even in the constrained case. We can show experimentally that the compact formulations compare favorably to the standard approach

    An Algorithm-Independent Measure of Progress for Linear Constraint Propagation

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    Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite convergence. However, these heuristic stopping criteria can pose difficulties for fairly comparing the efficiency of different implementations of iterative propagation algorithms in a real-world setting. Most significantly, the presence of unbounded variable domains in the problem formulation makes it difficult to quantify the relative size of reductions performed on them. In this work, we develop a method to measure - independently of the algorithmic design - the progress that a given iterative propagation procedure has made at a given point in time during its execution. Our measure makes it possible to study and better compare the behavior of bounds propagation algorithms for linear constraints. We apply the new measure to answer two questions of practical relevance: (i) We investigate to what extent heuristic stopping criteria can lead to premature termination on real-world MIP instances. (ii) We compare a GPU-parallel propagation algorithm against a sequential state-of-the-art implementation and show that the parallel version is even more competitive in a real-world setting than originally reported

    Fifth Biennial Report : June 1999 - August 2001

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    Sixth Biennial Report : August 2001 - May 2003

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