J. N. Hooker and G. Ottosson, Logic-based Benders decomposition, Mathematical Programming 96 (2003) 33-60. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Branch-and-Check: A Hybrid Framework Integrating Mixed Integer .. - Thorsteinsson (2001) (2 citations) (Correct)
....0; q 2 Q 2 ; 4) x 2 D; where u q is the dual solution to the subproblem when the subproblem is feasible in iterations q 2 Q 1 , and infeasible in iterations q 2 Q 2 , before resolving the master problem in the next iteration. A more detailed description of Benders Decomposition can found in [1, 8, 11, 14, 17]. 2.2 Previous Integration Schemes Properties of a number of di erent problems were considered by Darby Dowman and Little in [4, 5] and their e ect on the performance of CLP and MIP approaches were presented. They reported experimental results that illustrate some key properties of the ....
....the lower bounds and nogoods (13) 14) It is true that if the subproblem is not an LP, or more accurately if duality theory is not available, more work has to be put into deriving the lower bounds and nogoods. A survey of di erent duality concepts for a variety of problem classes can be found in [14]. It is not uncommon in CLP and MIP, however, to have to tailor methods for speci c structures. For example, global constraints in CLP require that propagation algorithms be designed for each one and in MIP, problem speci c cutting planes are widely used. In a similar fashion, when integrating CLP ....
John N. Hooker and Greger Ottosson. Logic-based Benders decomposition. Mathematical Programming, 2000. Submitted.
Logic-Based Methods for Global Optimization - Hooker (2003) Self-citation (Hooker) (Correct)
No context found.
J. N. Hooker and G. Ottosson, Logic-based Benders decomposition, Mathematical Programming 96 (2003) 33-60.
Logic, Optimization, and Constraint Programming - Hooker (2000) Self-citation (Hooker) (Correct)
....the next subproblem. If the subproblem is infeasible, one generates the next Benders cut B x K (x) The procedure terminates when the subproblem is feasible, or when the master problem becomes infeasible. In the latter case, 11) is infeasible. Logic based Benders decomposition was introduced in [85, 89]. Jain and Grossmann [96] used what is essentially the above framework to solve a machine assignment and scheduling problem. Each job is assigned to one of several machines (which operate at di#erent speeds) where each assignment incurs a processing cost. There is release date and a due date for ....
....approach can be generalized so that the subproblem is an optimization problem. Just as a classical Benders cut is obtained by solving the linear programming dual of the subproblem, a generalized cut can be obtained by solving the inference dual of the subproblem. These ideas are developed in [85, 89]. 4.2 Relaxations A key step in the integration of constraint programming and optimization is to find good relaxations for global constraints and the other versatile modeling constructs 24 of constraint programming. In many cases, useful continuous relaxations exist. In other cases, such as ....
Hooker, J. N. and G. Ottosson, Logic-based Benders decomposition, manuscript, Carnegie Mellon University (1998).
A Scheme for Unifying Optimization and Constraint.. - Hooker, Ottosson, .. (2000) (6 citations) Self-citation (Hooker Ottosson) (Correct)
.... x, we have the nogood z B x (x) u x b u x g(x) also known as a Benders cut. When the subproblem (17) is solved by branching, one may be able to construct a boolean formula P (x) such that the branching tree remains a proof of optimality of y x whenever P (x) 1. It is shown in [29], for example, that in integer programming the branching proof can be viewed as encoding a resolution proof whose premises are implied by constraints that are violated at the leaf nodes of the tree. The violated constraints imply the premises when x = x. One can let P (x) 1 for all values of x ....
John N. Hooker and Greger Ottosson. Logic-based benders decomposition. In preparation. , 1999.
A Scheme for Unifying Optimization and Constraint.. - Hooker, Ottosson, .. (1999) (6 citations) Self-citation (Hooker Ottosson) (Correct)
....very difficult. Both optimization and constraint satisfaction problems could benefit from the inference duality approach. The branch and bound tree for an integer programming problem, for example, can be analyzed to determine under what problem perturbations the tree remains a proof of optimality [16]. If branching and domain reduction prove a problem instance to be infeasible, one can examine for what problem perturbations this proof remains valid. More generally, a solution of the inference dual provides a explanation (in the form of a proof) for why a solution is optimal, or why the problem ....
....we have the nogood z B x (x) u x b Gamma u x g(x) also known as a Benders cut. When the subproblem (17) is solved by branching, one may be able to construct a boolean formula P (x) such that the branching tree remains a proof of optimality of y x whenever P (x) 1. It is shown in [16], for example, that in integer programming the branching proof can be viewed as encoding a resolution proof whose premises are implied by constraints that are violated at the leaf nodes of the tree. The violated constraints imply the premises when x = x. One can let P (x) 1 for all values of x ....
J. N. Hooker and G. Ottosson. Logic-based benders decomposition. Knowledge Engineering Review, special issue on AI/OR, submitted, 1999.
Constraint Satisfaction Methods For Generating Valid Cuts - Hooker (1998) (5 citations) Self-citation (Hooker) (Correct)
....to be gained by synthesizing the two fields. Logic based methods, for example, are much more evident in the constraint satisfaction literature than polyhedral methods. This literature also discusses the use of nogoods is a constraint based search, which generalizes the use of Benders cuts (see Hooker, 1995). It presents a more systematic analysis of exhaustive search methods that views traditional branching as a very special case (see Ginsberg, 1993; Ginsberg and McAllester, 1994; McAllester, 1993) The idea of a declarative formulation is already implicit in logic programming. In fact, logic ....
Hooker, J. N. (1995). Logic-based Benders decomposition, available on http://www.gsia.cmu.edu/afs/andrew/gsia/jh38/jnh.html.
Mixed Logical/Linear Programming - Hooker, Osorio (1997) (5 citations) Self-citation (Hooker) (Correct)
....ffl Optimal separating cuts have not been tested computationally, but the success of separating cuts and lift and project cuts (to which they are analogous) suggests that they could be useful. It may also be beneficial to use Benders cuts, which can be generalized to a logic based setting [34]. ffl It may be possible to construct useful linear relaxations of common logical formulas that contain multivalued discrete variables (other than integer variables) such as all different constraints. This issue is now under investigation. A software package based on MLLP would probably require ....
Hooker, J. N., Logic-based Benders decomposition, available at http://www.gsia.cmu.edu/afs/andrew/gsia/jh38/jnh.html (1995).
Hybrid Benders Decomposition Algorithms in Constraint Logic.. - Eremin, Wallace (2001) (1 citation) (Correct)
No context found.
J. N. Hooker and G. Ottosson. Logic-based benders decomposition. http://ba.gsia.cmu.edu/jnh/papers.html, 1999.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC