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Mixed Integer Linear Programming Formulation Techniques
SIAM Review, 2015A wide range of problems can be modeled as Mixed Integer Linear Programming (MIP) problems using standard formulation techniques. However, in some cases the resulting MIP can be either too weak or too large to be effectively solved by state of the art ...
J. Vielma
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Integer Linear Programming (ILP)
2013The feasible region of the LP model is continuous in the sense that each variable is restricted to over a continuous interval. If variables are further restricted to integer values, it becomes an ILP model. As its feasible region consists of discrete points, ILP model differs from LP model essentially.
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On the greedy solution in integer linear programming
Zeitschrift f�r Operations Research, 1987The author generalizes a result of \textit{M. J. Magazine, G. L. Nemhauser} and \textit{L. E. Trotter} jun. [Oper. Res. 23, 207--217 (1975; Zbl 0305.90039)] from knapsack problems to arbitrary integer programs. He states a greedy method for integer programs based on the natural partial order in \(\mathbb R^ n\) and characterizes a class of problems for
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New Integer Linear Programming Models for the Vertex Coloring Problem
Latin American Symposium on Theoretical Informatics, 2017The vertex coloring problem asks for the minimum number of colors that can be assigned to the vertices of a given graph such that for all vertices v the color of v is different from the color of any of its neighbors. The problem is NP-hard.
Adalat Jabrayilov, Petra Mutzel
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A Note on Linear Programming and Integer Feasibility
Operations Research, 1968This paper proves a theorem that provides new strategies for solving integer programming problems, based on finding certain types of basic solutions to linear programs. The theorem is motivated by and extends ideas of Cabot and Hurter. An integer programming method based on the theorem is outlined.
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A parallel integer linear programming algorithm
European Journal of Operational Research, 1988zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Billy E. Gillett +2 more
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Nonlinear and Mixed Integer Linear Programming
2012In this chapter we compare continuous nonlinear optimization with mixed integer optimization of water supply networks by means of a meso scaled network instance. We introduce a heuristic approach, which handles discrete decisions arising in water supply network optimization through penalization using nonlinear programming.
Kolb, Oliver +3 more
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Duality in mathematics and linear and integer programming
Journal of Optimization Theory and Applications, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Linear Programming Tools for Integer Programming
1989Abstract : The motivation for this work has been the need for a practical procedure to solve the maximum-weight cut problem (MCP) in undirected graphs. Our primary focus has been on problems arising from considerations in statistical mechanics. These problems are typically posed on grid graphs and some natural variants.
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Termination of Integer Linear Programs [PDF]
, 2006 We show that termination of a simple class of linear loops over the integers is decidable. Namely we show that termination of deterministic linear loops is decidable over the integers in the homogeneous case, and over the rationals in the general case. This is done by analyzing the powers of a matrix symbolically using its eigenvalues.
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