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## Pseudo-Boolean and Finite Domain Constraint Programming: A Case Study

Citations: | 1 - 0 self |

### Citations

1415 |
Integer and Combinatorial Optimization,
- Nemhauser, Wolsey
- 1999
(Show Context)
Citation Context ...acing each of the constraints n X j=1 G ijsn \Delta W i (2) for i = 1; : : : ; m, with n individual constraints G i1sW i ; . . . G insW i : (3) This reformulation is well-known in operations research =-=[14, 11]-=-. Summing up the constraints in (3) yields the constraint (2), which shows that (3) implies (2). Concerning 0-1 solutions, the two formulations are equivalent. However, if we compare their linear rela... |

429 |
Parallel constraint satisfaction in logic programming: Preliminary results of chip within PEPSys.
- Hentenryck
- 1989
(Show Context)
Citation Context ...ated over finite domains, i.e. the variables take their values in finite sets of non-negative integer numbers. Many practical problems can be modeled naturally using such constraints (see for example =-=[12, 1]-=-). A special case of finite domain constraints are pseudo-Boolean constraints [6], where all variables are defined over the domain f0; 1g. This corresponds to 0-1 integer programming in operations res... |

368 |
Or-library: distributing test problems by electronic mail,
- Beasley
- 1990
(Show Context)
Citation Context ... that if a customer is supplied by some warehouse then this warehouse must be open. 3.4 Computational experience with the weak 0-1 model We compared the two models on 12 instances from the OR-Library =-=[5]-=-. Each of these examples has 50 customers. The number of warehouses ranges from 16 to 50. All floating point numbers in the data were truncated in order to get integer numbers. In Tab. 1, the problem ... |

270 |
The constraint logic programming language CHIP,” in
- Dincbas, Hentenryck, et al.
- 1988
(Show Context)
Citation Context ...pt gives the optimal cost of the problem and the column LP-Opt the cost of an optimal solution to the linear relaxation of the weak 0-1 model (1). The finite domain model was solved with Chip V.4.1.0 =-=[10, 2]-=-, the 0-1 model with our polyhedral branch-and-cut solver Yazoo [9], where we compared two solution strategies: ffl Branch-and-Bound with linear programming relaxations (B&B) ffl Branch-and-Cut with l... |

246 | A lift-and-project cutting plane algorithm for mixed 0-1 integer programs.
- Balas, Ceria, et al.
- 1993
(Show Context)
Citation Context ... the separation phase to find strong valid inequalities that cut off some part of the linear relaxation and thus improve the current upper bound. In our solver, we use lift-and-project cutting planes =-=[3]-=-. After cutting planes have been generated, they are added to the current subproblem and the relaxation is reoptimized. 2.3 Incrementality This branch-and-cut approach fits perfectly well the demands ... |

121 |
Model Building in Mathematical Programming,
- Williams
- 1999
(Show Context)
Citation Context ...acing each of the constraints n X j=1 G ijsn \Delta W i (2) for i = 1; : : : ; m, with n individual constraints G i1sW i ; . . . G insW i : (3) This reformulation is well-known in operations research =-=[14, 11]-=-. Summing up the constraints in (3) yields the constraint (2), which shows that (3) implies (2). Concerning 0-1 solutions, the two formulations are equivalent. However, if we compare their linear rela... |

28 |
Generality versus specificity: An experience with AI and OR techniques
- Hentenryck, Carillon
- 1988
(Show Context)
Citation Context ...can be used globally at all other nodes. 3 Warehouse location revisited We now focus on a classical application of finite domain constraint programming, the (uncapacitated) warehouse location problem =-=[13, 12, 2]-=-. We will present three formulations of the problem, one finite domain and two 0-1 models, and compare their efficiency. 3.1 Problem Description Given a number of customers and possible warehouse loca... |

17 |
Logic programming with pseudo-Boolean constraints
- Bockmayr
- 1993
(Show Context)
Citation Context ...negative integer numbers. Many practical problems can be modeled naturally using such constraints (see for example [12, 1]). A special case of finite domain constraints are pseudo-Boolean constraints =-=[6]-=-, where all variables are defined over the domain f0; 1g. This corresponds to 0-1 integer programming in operations research. Finite domain constraints are usually solved with local consistency techni... |

5 | Finite Domain and Cutting Plane Techniques in CLP(3
- BARTH, BOCKMAYR
- 1995
(Show Context)
Citation Context ...nstraint set is full-dimensional, then the domains of the variables cannot be reduced. Even if the domains could be reduced, consistency techniques that work locally are often not able to detect this =-=[4]-=-. To overcome these problems and in order to infer more information from a given constraint set, we have developed a new approach for pseudo-Boolean constraint solving. It uses techniques from mathema... |

5 | Cutting planes in constraint logic programming
- Bockmayr
- 1994
(Show Context)
Citation Context ...new approach for pseudo-Boolean constraint solving. It uses techniques from mathematical programming and is based on the idea of generating strong valid inequalities within a branch-and-cut framework =-=[7, 8]-=-. Often a given practical problem can be modeled in different ways. We may use either a ffl finite domain model, where every variable takes its value in some finite set of natural numbers, or a ffl 0-... |

5 |
Solving Pseudo-Boolean Constraints
- BOCKMAYR
- 1995
(Show Context)
Citation Context ...new approach for pseudo-Boolean constraint solving. It uses techniques from mathematical programming and is based on the idea of generating strong valid inequalities within a branch-and-cut framework =-=[7, 8]-=-. Often a given practical problem can be modeled in different ways. We may use either a ffl finite domain model, where every variable takes its value in some finite set of natural numbers, or a ffl 0-... |

1 |
Implementing a polyhedral branch-and-cut solver for pseudo-Boolean constraint programming
- Bockmayr, Kasper
- 1996
(Show Context)
Citation Context ... of an optimal solution to the linear relaxation of the weak 0-1 model (1). The finite domain model was solved with Chip V.4.1.0 [10, 2], the 0-1 model with our polyhedral branch-and-cut solver Yazoo =-=[9]-=-, where we compared two solution strategies: ffl Branch-and-Bound with linear programming relaxations (B&B) ffl Branch-and-Cut with lift-and-project cutting planes (B&C). The underlying linear program... |