## Enhancements of Branch and Bound Methods for the Maximal Constraint Satisfaction Problem (1996)

Venue: | Proc. of AAAI-96 |

Citations: | 17 - 0 self |

### BibTeX

@INPROCEEDINGS{Wallace96enhancementsof,

author = {Richard J. Wallace},

title = {Enhancements of Branch and Bound Methods for the Maximal Constraint Satisfaction Problem},

booktitle = {Proc. of AAAI-96},

year = {1996},

pages = {188--195}

}

### OpenURL

### Abstract

Two methods are described for enhancing performance of branch and bound methods for overconstrained CSPs. These methods improve either the upper or lower bound, respectively, during search, so the two can be combined. Upper bounds are improved by using heuristic repair methods before search to find a good solution quickly, whose cost is used as the initial upper bound. The method for improving lower bounds is an extension of directed arc consistency preprocessing, used in conjunction with forward checking. After computing directed arc consistency counts, inferred counts are computed for all values based on minimum counts for values of adjacent variables that are later in the search order. This inference process can be iterated, so that counts are cascaded from the end to the beginning of the search order, to augment the initial counts. Improvements in time and effort are demonstrated for both techniques using random problems. Introduction Constraint satisfaction problems (CSPs) invol...

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Citation Context ... critical value. This explains why difficult problems are found for every combination of problems parameters, and the difficulty is greater when there are more inconsistencies in an optimal solution (=-=Freuder & Wallace 1992-=-) (Schiex et al. 1995). These considerations underscore the importance of efficient complete algorithms for solving overconstrained problems. This paper describes new methods for enhancing the perform... |

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Citation Context ...cedures described in the literature were altered to enhance performance. The procedures were, (i) min-conflicts hillclimbing (Minton et al. 1990), with a random walk component, as described for GSAT (=-=Selman & Kautz 1993-=-); the probability of random walk was set to 0.10, since this had been found to be a good value in earlier work, (ii) the breakout procedure (Morris 1993), (iii) weak commitment search (Yokoo 1994), w... |

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Citation Context ...walk component, as described for GSAT (Selman & Kautz 1993); the probability of random walk was set to 0.10, since this had been found to be a good value in earlier work, (ii) the breakout procedure (=-=Morris 1993-=-), (iii) weak commitment search (Yokoo 1994), without the addition of nogoods during search; in earlier work it was found that the proliferation of these nogoods quickly slows down search, while the r... |

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Citation Context ...rc consistency for MAX-CSPs. Here, checking is in forward direction, i. e., each value is tested for support in domains of future variables. In forward checking for MAX-CSPs (Freuder & Wallace 1992) (=-=Shapiro & Haralick 1981-=-), a value a being considered for assignment to variable v i is tested against values in the domain of each uninstantiated (future) variable v j , that shares a constraint with v i . If b, in the doma... |

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Citation Context ...main, three heuristic repair procedures were tested. In some cases the procedures described in the literature were altered to enhance performance. The procedures were, (i) min-conflicts hillclimbing (=-=Minton et al. 1990-=-), with a random walk component, as described for GSAT (Selman & Kautz 1993); the probability of random walk was set to 0.10, since this had been found to be a good value in earlier work, (ii) the bre... |

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Citation Context ...retrospective algorithms, and (ii) decreasing degree of a node, which is very effective with prospective algorithms. These heuristics work best when problems have relatively sparse constraint graphs (=-=Wallace & Freuder 1993-=-) (Wallace 1995). Ordering values by increasing number of inconsistencies, determined either during preprocessing or in the course of search, also improves search efficiency. Upper Bound Techniques Us... |

14 |
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Citation Context ...ect of the initial upper bound value on both weaker and stronger algorithms. (Note that, given the marked difficulty of partial CSPs, this problem size is within the usual range of those tested, cf. (=-=Larrosa & Meseguer 1995-=-) (Schiex et al. 1995). In addition, 30-variable problems were tested to confirm results with smaller problems and to assess the effect of problem size. In this case only the more efficient prospectiv... |

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Citation Context ...nt method is based on a specialized type of inconsistency count, called directed arc consistency counts (DACCs), that refer to variables before or after the current value in a specified search order (=-=Wallace 1995-=-). The new method uses DACCs for variables later in the search order to infer inconsistencies for the values of variables that will be instantiated earlier. For example, if value a in the domain of v ... |

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