# Bounding the Optimum of Constraint Optimization Problems

@inproceedings{Givry1997BoundingTO, title={Bounding the Optimum of Constraint Optimization Problems}, author={Simon de Givry and G{\'e}rard Verfaillie and T. Schiex}, booktitle={CP}, year={1997} }

Solving constraint optimization problems is computationally so expensive that it is often impossible to provide a guaranteed optimal solution, either when the problem is too large, or when time is bounded. In these cases, local search algorithms usually provide good solutions. However, and even if an optimality proof is unreachable, it is often desirable to have some guarantee on the quality of the solution found, in order to decide if it is worthwile to spend more time on the problem.
This…

## 40 Citations

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## References

SHOWING 1-10 OF 25 REFERENCES

### Russian Doll Search for Solving Constraint Optimization Problems

- Computer ScienceAAAI/IAAI, Vol. 1
- 1996

The Russian Doll Search algorithm is introduced, which replaces one search by n successive searches on nested subproblems, records the results of each search and uses them later, when solving larger subpro problems, in order to improve the lower bound on the global valuation of any partial assignment.

### Analysis of Heuristic Methods for Partial Constraint Satisfaction Problems

- Computer ScienceCP
- 1996

An important finding is that a version of min-conflicts that incorporates the random walk strategy, with a good value for the walk probability appears to be as efficient in this domain as several of the more elaborate methods for improving local search that have been proposed in recent years.

### An Optimal Admissible Tree Search

- Computer Science
- 1985

This heuristic depth-first iteratiw-deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the Fifeen Puzzle within practical resource limits.

### Directed Arc Consistency Preprocessing

- Computer ScienceConstraint Processing, Selected Papers
- 1995

This work describes a family of strategies based on directed arc consistency testing during preprocessing that retain the benefits of full arc consistency checking, while improving lower bound calculations.

### Local Search in Combinatorial Optimisation.

- Business
- 1997

This book is an important reference volume and an invaluable source of inspiration for advanced students and researchers in discrete mathematics, computer science, operations research, industrial engineering and management science.

### Nogood Recording for static and dynamic constraint satisfaction problems

- Computer ScienceProceedings of 1993 IEEE Conference on Tools with Al (TAI-93)
- 1993

A new class of constraint recording algorithms called Nogood Recording is proposed that may be used for solving both static and dynamic CSPs and offers an interesting compromise, polynomially bounded in space, between an ATMS-like approach and the usual static constraint satisfaction algorithms.

### Valued Constraint Satisfaction Problems: Hard and Easy Problems

- Computer ScienceIJCAI
- 1995

A simple algebraic framework is considered, related to Partial Constraint Satisfaction, which subsumes most of these proposals and is used to characterize existing proposals in terms of rationality and computational complexity.

### MAC and Combined Heuristics: Two Reasons to Forsake FC (and CBJ?) on Hard Problems

- Computer Science, BusinessCP
- 1996

This paper tries to convince once and for all the CSP community that MAC is not only more efficient than FC to solve large practical problems, but it is also really more efficient on hard and large random problems.

### Nogood recording for valued constraint satisfaction problems

- Computer ScienceProceedings Eighth IEEE International Conference on Tools with Artificial Intelligence
- 1996

This study aims to use Nogood Recording in the wider scope of the Valued CSP framework (VCSP) to enhance the branch and bound algorithm and uses nogoods to increase the lower bound used by the branches and bound to prune the search.