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Decomposition Branching for Mixed Integer Programming
Operations Research, 2022Applications of mixed integer programming can be found in many industries, such as transportation, healthcare, energy, and finance, and their economic impact is significant. It is also well known that mixed integer programs (MIPs) can be very difficult to solve.
Baris Yildiz 0001 +2 more
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Mixed-integer programming for control
Proceedings of the 2005, American Control Conference, 2005., 2005The article describes how mixed-integer programming (MIP) can be employed for feedback control. MIP can be used to find optimal trajectories subject to integer constraints, which can encode discrete decisions or nonconvexity, for example. This optimization can be performed online within model predictive control (MPC) to implement a feedback control law.
Richards, AG, How, JP
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A Biobjective Perspective for Mixed-Integer Programming
IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2022A mixed-integer programming (MIP) problem contains not only constraints but also integer restrictions. Integer restrictions divide the feasible region defined by constraints into multiple discontinuous feasible parts with different sizes. Several popular methods (e.g., rounding and truncation) have been proposed to deal with integer restrictions ...
Jiao Liu 0006 +3 more
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Structure Detection in Mixed-Integer Programs
INFORMS Journal on Computing, 2018Despite vast improvements in computational power, many large-scale optimization problems involving integer variables remain difficult to solve. Certain classes, however, can be efficiently solved by exploiting special structure. One such structure is the singly bordered block-diagonal (BBD) structure that lends itself to Dantzig-Wolfe decomposition ...
Taghi Khaniyev +2 more
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Learning To Scale Mixed-Integer Programs
Proceedings of the AAAI Conference on Artificial Intelligence, 2021Many practical applications require the solution of numerically challenging linear programs (LPs) and mixed integer programs (MIPs). Scaling is a widely used preconditioning technique that aims at reducing the error propagation of the involved linear systems, thereby improving the numerical behavior of the dual simplex algorithm and, consequently, LP ...
Timo Berthold, Gregor Hendel
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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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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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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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