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A new communication platform for smart EMS using a mixed-integer-linear-programming
Energy Systems, 2023B. Alhasnawi +3 more
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Symmetry in Integer Linear Programming
2009An integer linear program (ILP) is symmetric if its variables can be permuted without changing the structure of the problem. Areas where symmetric ILPs arise range from applied settings (scheduling on identical machines), to combinatorics (code construction), and to statistics (statistical designs construction).
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Optima of dual integer linear programs
Combinatorica, 1988Let \(A\) be a 0-1 matrix of dimension \(n\cdot m\). Consider the following pair of linear programs \[ \text{(L)}\quad \max x\cdot 1,\quad Ax\leq 1,\quad x\geq 0;\quad \text{(D)}\quad \min y\cdot 1,\quad yA\geq 1,\quad y\geq 0. \] If integral solution constraints are added, they become dual pairs of packing and covering integer linear programs. Let \(z\
Nathan Linial, Ron Aharoni, Paul Erdös
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On the foundations of linear and integer linear programming I
Mathematical Programming, 1975In this paper we consider the question: how does the flow algorithm and the simplex algorithm work? The usual answer has two parts: first a description of the "improvement process", and second a proof that if no further improvement can be made by this process, an optimal vector has been found.
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Linear and Integer Programming in Practice
2016Ultimately, we learn about linear programming and integer programming because we wish to solve real-world problems using these techniques. In this chapter, we first discuss how problems can be formulated as linear and integer programs. We then give example formulation techniques that go well beyond the conversions used to obtain equivalent formulations
Andrew B. Kahng, T. C. Hu
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GRASP for Linear Integer Programming
2003In this paper, we introduce a GRASP for the solution of general linear integer problems. The strategy is based on the separation of the set of variables into the integer subset and the continuous subset. The integer variables are fixed by GRASP and replaced in the original linear problem.
João Pedro Pedroso, Teresa Neto
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Experiments in mixed-integer linear programming
Mathematical Programming, 1971This paper presents a “branch and bound” method for solving mixed integer linear programming problems. After briefly discussing the bases of the method, new concepts called pseudo-costs and estimations are introduced. Then, the heuristic rules for generating the tree, which are the main features of the method, are presented.
Jean-Michel Gauthier +5 more
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Mixed-Integer Linear Programming Formulations
2014In this chapter, (mixed-)integer linear programming formulations of the resource-constrained project scheduling problem are presented. Standard formulations from the literature and newly proposed formulations are classified according to their size in function of the input data.
Artigues, Christian +3 more
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A note on integer linear fractional programming
Naval Research Logistics Quarterly, 1980AbstractThis note consists of developing a method for enforcing additional constraints to linear fractional programs and showing its usefulness in solving integer linear fractional programs.
M. Chandramohan, Suresh Chandra
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Metric aspects of integer linear programming
Discrete Mathematics and Applications, 1994Summary: Explicit bounds for the ratio of the optima of primal and dual integer linear programs in the worst case and similar bounds for the ratio of the integer and rational optima of linear programs are obtained. It is proved that for non-negative input data these ratios are linear in the number of variables and the maximum of absolute values of the ...
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