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Mixed-integer quadratic programming
Mathematical Programming, 1982This paper considers mixed-integer quadratic programs in which the objective function is quadratic in the integer and in the continuous variables, and the constraints are linear in the variables of both types. The generalized Benders' decomposition is a suitable approach for solving such programs.
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Integer and Mixed-Integer Programming
1997We survey techniques for sensitivity analysis of integer programming and related problems. The emphasis is on finding analogues from linear programming.
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Mixed Integer Programming Computation
2009The first 50 years of Integer and Mixed-Integer Programming have taken us to a very stable paradigm for solving problems in a reliable and effective way. We run over these 50 exciting years by showing some crucial milestones and we highlight the building blocks that are making nowadays solvers effective from both a performance and an application ...
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Genetic Programming Applied to Mixed Integer Programming
2004We present the application of Genetic Programming (GP) in Branch and Bound (B&B) based Mixed Integer Linear Programming (MIP). The hybrid architecture introduced employs GP as a node selection expression generator: a GP run, embedded into the B&B process, exploits the characteristics of the particular MIP problem being solved, evolving a problem ...
Konstantinos Kostikas +1 more
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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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Learning to Branch in Mixed Integer Programming
Proceedings of the AAAI Conference on Artificial Intelligence, 2016The design of strategies for branching in Mixed Integer Programming (MIP) is guided by cycles of parameter tuning and offline experimentation on an extremely heterogeneous testbed, using the average performance. Once devised, these strategies (and their parameter settings) are essentially input-agnostic.
Elias Boutros Khalil +4 more
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Progress in presolving for mixed integer programming
Mathematical Programming Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gerald Gamrath +4 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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Cross decomposition for mixed integer programming
Mathematical Programming, 1983Many methods for solving mixed integer programming problems are based either on primal or on dual decomposition, which yield, respectively, a Benders decomposition algorithm and an implicit enumeration algorithm with bounds computed via Lagrangean relaxation. These methods exploit either the primal or the dual structure of the problem. We propose a new
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Mixed-integer bilinear programming problems
Mathematical Programming, 1993This paper considers the bilinear programming problem with one set of variables restricted to be binary values. The authors describe some special cases of the problem which admit more efficient solution procedures. A composite Lagrangian relaxation cutting plane algorithm is given for the more general case.
Warren P. Adams, Hanif D. Sherali
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