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122
Bayesian network learning with cutting planes.
- In Proceedings of the Twenty-Seventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-11),
, 2011
"... Abstract The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises log marginal likelihood (BDe score). Integer ..."
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Cited by 46 (7 self)
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Abstract The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises log marginal likelihood (BDe score). Integer programming, specifically the SCIP framework, is used to solve this optimisation problem. Acyclicity constraints are added to the integer program (IP) during solving in the form of cutting planes. Finding good cutting planes is the key to the success of the approach-the search for such cutting planes is effected using a sub-IP. Results show that this is a particularly fast method for exact BN learning.
Cutting to the Chase -- Solving Linear Integer Arithmetic
"... We describe a new algorithm for solving linear integer programming problems. The algorithm performs a DPLL style search for a feasible assignment, while using a novel cut procedure to guide the search away from the conflicting states. ..."
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Cited by 15 (5 self)
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We describe a new algorithm for solving linear integer programming problems. The algorithm performs a DPLL style search for a feasible assignment, while using a novel cut procedure to guide the search away from the conflicting states.
Experiments with a Generic Dantzig-Wolfe Decomposition for Integer Programs
"... Abstract We report on experiments with turning the branch-price-andcut framework SCIP into a generic branch-price-and-cut solver. That is, given a mixed integer program (MIP), our code performs a Dantzig-Wolfe decomposition according to the user’s specification, and solves the resulting re-formulati ..."
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Cited by 12 (3 self)
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Abstract We report on experiments with turning the branch-price-andcut framework SCIP into a generic branch-price-and-cut solver. That is, given a mixed integer program (MIP), our code performs a Dantzig-Wolfe decomposition according to the user’s specification, and solves the resulting re-formulation via branch-and-price. We take care of the column generation subproblems which are solved as MIPs themselves, branch and cut on the original variables (when this is appropriate), aggregate identical subproblems, etc. The charm of building on a well-maintained framework lies in avoiding to re-implement state-of-the-art MIP solving features like pseudo-cost branching, preprocessing, domain propagation, primal heuristics, cutting plane separation etc. 1
An exact rational mixed-integer programming solver
, 2010
"... We present an exact rational solver for mixed-integer linear programming which avoids the numerical inaccuracies inherent in the floating-point computations adopted in existing software. This allows the solver to be used for establishing fundamental theoretical results and in applications where corr ..."
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Cited by 8 (1 self)
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We present an exact rational solver for mixed-integer linear programming which avoids the numerical inaccuracies inherent in the floating-point computations adopted in existing software. This allows the solver to be used for establishing fundamental theoretical results and in applications where correct solutions are critical due to legal and financial consequences. Our solver is a hybrid symbolic/numeric implementation of LP-based branch-andbound, using numerically-safe bounding methods for all binding computations in the search tree. Computing provably accurate solutions by dynamically choosing the fastest of several available methods depending on the structure of the instance, our exact solver is only moderately slower compared to an inexact floating-point branch-and-bound solver. The software is incorporatedinto the SCIPoptimization framework,using the exact LP solverQSopt ex and the GMP arithmetic library. Computational results are presented for a suite of test instances taken from the Miplib and Mittelmann collections.
Integrating operations research in constraint programming
, 2010
"... This paper presents Constraint Programming as a natural formalism for modelling problems, and as a flexible platform for solving them. CP has a range of techniques for handling constraints including several forms of propagation and tailored algorithms for global constraints. It also allows linear p ..."
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Cited by 7 (0 self)
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This paper presents Constraint Programming as a natural formalism for modelling problems, and as a flexible platform for solving them. CP has a range of techniques for handling constraints including several forms of propagation and tailored algorithms for global constraints. It also allows linear programming to be combined with propagation and novel and varied search techniques which can be easily expressed in CP. The paper describes how CP can be used to exploit linear programming within different kinds of hybrid algorithm. In particular it can enhance techniques such as Lagrangian relaxation, Benders decomposition and column generation.
Branch-Price-and-Cut Algorithms
- CONTRIBUTED TO THE WILEY ENCYCLOPEDIA OF OPERATIONS RESEARCH AND MANAGEMENT SCIENCE (EORMS)
, 2010
"... In many mixed integer programs there is some embedded problem structure which can be exploited, often by a decomposition. When the relaxation in each node of a branch-andbound tree is solved by column generation, one speaks of branch-and-price. Optionally, cutting planes can be added in order to str ..."
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Cited by 7 (0 self)
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In many mixed integer programs there is some embedded problem structure which can be exploited, often by a decomposition. When the relaxation in each node of a branch-andbound tree is solved by column generation, one speaks of branch-and-price. Optionally, cutting planes can be added in order to strengthen the relaxation, and this is called branch-price-and-cut. We introduce the common concepts of convexification and discretization to arrive at a Dantzig-Wolfe type reformulation of a mixed integer program. The relation between the original and the extended formulations helps us understand how cutting planes should be formulated and how branching decisions can be taken while keeping the column generation subproblems manageable.
Active network management: planning under uncertainty for exploiting load modulation
- In Proceedings of the 2013 IREP Symposium - Bulk Power Systems Dynamics and Control - IX, Rethymnon
, 2013
"... This paper addresses the problem faced by a distribution system operator (DSO) when planning the operation of a network in the short-term. The problem is formulated in the context of high penetration of renewable energy sources (RES) and distributed generation (DG), and when flexible demand is avail ..."
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Cited by 7 (4 self)
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This paper addresses the problem faced by a distribution system operator (DSO) when planning the operation of a network in the short-term. The problem is formulated in the context of high penetration of renewable energy sources (RES) and distributed generation (DG), and when flexible demand is available. The problem is expressed as a sequential decision-making problem under uncertainty, where, in the first stage, the DSO has to decide whether or not to reserve the availability of flexible demand, and, in the subsequent stages, can curtail the generation and modulate the available flexible loads. We analyze the relevance of this formulation on a small test system, discuss the assumptions made, compare our approach to related work, and indicate further research directions.
Intersection cuts for nonlinear integer programming: Convexification techniques for structured sets
- Mathematical Programming
"... We study the generalization of split and intersection cuts from Mixed Integer Linear Pro-gramming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference of two convex sets with specific geometric structures. We introduce two ..."
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Cited by 6 (0 self)
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We study the generalization of split and intersection cuts from Mixed Integer Linear Pro-gramming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference of two convex sets with specific geometric structures. We introduce two techniques to give precise characterizations of such convex hulls and use them to construct split and intersection cuts for several classes of sets. In particular, we give simple formulas for split cuts for essentially all convex sets described by a single quadratic inequality and for more general intersection cuts for a wide variety of convex quadratic sets.
