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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.
Michel Bénichou +5 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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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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Safe bounds in linear and mixed-integer linear programming
Mathematical Programming, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arnold Neumaier, Oleg Shcherbina
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An optimality cut for mixed integer linear programs
European Journal of Operational Research, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gilbert Laporte, Frédéric Semet
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The Mixed Integer Linear Bilevel Programming Problem
Operations Research, 1990A two-person, noncooperative game in which the players move in sequence can be modeled as a bilevel optimization problem. In this paper, we examine the case where each player tries to maximize the individual objective function over a jointly constrained polyhedron. The decision variables are variously partitioned into continuous and discrete sets. The
James T. Moore, Jonathan F. Bard
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Multiobjective Integer and Mixed-Integer Linear Programming
2016The introduction of discrete variables into multiobjective programming problems leads to all-integer or mixed-integer problems that are more difficult to tackle, even if they have linear objective functions and constraints. The feasible set is no longer convex, and the additional difficulties go beyond those of changing from single objective linear ...
Carlos Henggeler Antunes +2 more
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From Mixed-Integer Linear to Mixed-Integer Bilevel Linear Programming
2017Bilevel Optimization is a very challenging framework where two players (with different objectives) compete for the definition of the final solution. In this paper we address a generic mixed-integer bilevel linear program, i.e., a bilevel optimization problem where the objective functions and constraints are all linear, and some variables are required ...
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A DC Programming Approach for Mixed-Integer Linear Programs
2008In this paper, we propose a new efficient algorithm for globally solving a class of Mixed Integer Program (MIP). If the objective function is linear with both continuous variables and integer variables, then the problem is called a Mixed Integer Linear Program (MILP). Researches on MILP are important in both theoretical and practical aspects.
Yi-Shuai Niu, Pham Dinh Tao
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Bivium as a Mixed-Integer Linear Programming Problem
2009Trivium is a stream cipher proposed for the eSTREAM project. Raddum introduced some reduced versions of Trivium, named Bivium A and Bivium B. In this article we present a numerical attack on the Biviums. The main idea is to transform the problem of solving a sparse system of quadratic equations over GF (2) into a combinatorial optimization problem.
Julia Borghoff +2 more
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