If all of the unknown variables are required to be integers, then the problem is called an integer programming ( IP ) or "'integer linear programming "'( ILP ) problem.
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Some research literature considers discrete optimization to consist of integer programming together with combinatorial optimization ( which in turn is composed of optimization problems dealing with graph structures ) although all of these topics have closely intertwined research literature.
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Tayur is recognized for his Operations Research work in developing novel algorithms for models in stochastic inventory theory ( using Infinitesimal Perturbation Analysis ), integer programming ( using Hilbert's Nullstellensatz, Algebraic Geometry, and Gr�bner Basis Theory)
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"' SCIP "'( "'Solving Constraint Integer Programs "') is a mixed integer programming solver and a framework for Branch and cut and Branch and price, developed primarily at Zuse Institute Berlin.
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Additionally, many computer scientists use the phrase polyhedral combinatorics to describe research into precise descriptions of the faces of certain specific polytopes ( especially 0-1 polytopes, whose vertices are subsets of a hypercube ) arising from integer programming problems.
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S . K . Sen, H . Agarwal, and Sagar Sen, Chemical equation balancing : an integer programming approach, Mathematical and Computer Modelling, 44, Issues 7-8, 678-691, October 2006, Available online at www . sciencedirect . com
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This relaxation technique transforms an NP-hard optimization problem ( integer programming ) into a related problem that is solvable in polynomial time ( linear programming ); the solution to the relaxed linear program can be used to gain information about the solution to the original integer program.
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Proposed is an integer programming approach which is polynomial-time and is used for most chemical equation balancing ( Mathematical and Computer Modelling, Elsevier, 44, Issues 7-8, 678-691, October 2006; also available online at www . sciencedirect . com ).
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ILP solvers depend on linear programming ( LP ) algorithms, such as the primal instances of the integer programming, but in order to maintain guarantees on optimality, they are most useful when used to approximate the dual of the protein design problem, because approximating the dual guarantees that no solutions are missed.
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Levine produced a research paper that attempts to offer a solution to the Nurse Rostering Problems ( NRP ), in which a hybrid algorithm was proposed that makes use of Integer Programming ( IP ), and Variable Neighbourhood Search ( VNS ) algorithms due to the difficulty in solving this problem from a single approach.
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