## Analyzing a Heuristic Strategy for Constraint-Satisfaction and Scheduling (1994)

Venue: | in Intelligent Scheduling |

Citations: | 26 - 3 self |

### BibTeX

@INPROCEEDINGS{Johnston94analyzinga,

author = {Mark D. Johnston and Steven Minton},

title = {Analyzing a Heuristic Strategy for Constraint-Satisfaction and Scheduling},

booktitle = {in Intelligent Scheduling},

year = {1994},

pages = {257--289},

publisher = {Morgan}

}

### OpenURL

### Abstract

This paper describes a simple heuristic approach to solving large-scale constraint satisfaction and scheduling problems. In this approach one starts with an inconsistent assignment for a set of variables and searches through the space of possible repairs. The search can be guided by a value-ordering heuristic, the min-conflicts heuristic, that attempts to minimize the number of constraint violations after each step. The heuristic can be used with a variety of different search strategies. On the n-queens problem, a technique based on this approach performs orders of magnitude better than traditional backtracking techniques. The technique has also been used for scheduling the Hubble Space telescope. A theoretical analysis is presented both to explain why this method works well on certain types of problems and to predict when it is likely to be most effective. 1 Introduction One of the most promising general approaches for solving combinatorial search problems is to generate an initial...

### Citations

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Citation Context ...AI repair-based approaches may be more generally useful than previously thought. Additional evidence also comes from some recent flurry of related studies. For instance, Selman, Levesque and Mitchell =-=[37]-=-, showed that GSAT, a repair-based algorithm that uses a form of min-conflicts for satisfiability problems, outperforms traditional satisfiability algorithms. Specifically, they demonstrated that GSAT... |

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Citation Context ...ffective. 1 Introduction One of the most promising general approaches for solving combinatorial search problems is to generate an initial, suboptimal solution and then to apply local repair heuristics=-=[37, 26, 31, 27, 44, 39, 15]-=-. Techniques based on this approach have met with empirical success on many combinatorial problems, including the traveling salesman and graph partitioning problems[16]. Such techniques also have a lo... |

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Citation Context ...d to produce a solution to any instance of the n-queens problem. Nevertheless, the problem has been perceived as relatively "hard" for heuristic search methods. Several studies of the nqueen=-=s problem [40, 12, 23]-=- have compared heuristic backtracking methods such as search rearrangement backtracking (e.g., most-constrained first), forward checking, dependency-directed backtracking, etc. To solve the n-queens p... |

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Citation Context ...ison with other approaches. Both of these areas are discussed in this section. Hubble Space Telescope The Hubble Space Telescope scheduling problem can be considered a constrained optimization problem=-=[9, 7]-=- where we must maximize both the number and the importance of the constraints that are satisfied. As noted in [27, 28], the initial scheduling system developed for this application had difficulty prod... |

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Citation Context ... 19] for use in Spike [17], a system for scheduling astronomical observations on the Hubble Space Telescope. The min-conflicts heuristic was distilled from an analysis of the network, as described in =-=[27, 28, 29]-=-. The heuristic has now replaced the neural network in the Spike system, since it can be implemented in a very simple and efficient fashion. We begin the paper with a description of the min-conflicts ... |

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Citation Context ...uristics[37, 26, 31, 27, 44, 39, 15]. Techniques based on this approach have met with empirical success on many combinatorial problems, including the traveling salesman and graph partitioning problems=-=[16]-=-. Such techniques also have a long tradition in AI, most notably in problem-solving systems that operate by debugging initial solutions [38, 41]. In this paper, we describe how this idea can be extend... |

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Citation Context ...ison with other approaches. Both of these areas are discussed in this section. Hubble Space Telescope The Hubble Space Telescope scheduling problem can be considered a constrained optimization problem=-=[9, 7]-=- where we must maximize both the number and the importance of the constraints that are satisfied. As noted in [27, 28], the initial scheduling system developed for this application had difficulty prod... |

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Citation Context ...couraging studies on repair-based algorithms include Sosic and Gu's work with N-queens[39], Morris's work on constraint-satisfaction problems[30, 31, 32] and a variety of studies on Tabu Search (e.g. =-=[10, 13]-=-), a hill-climbing, local search technique that maintains a list of forbidden moves in order to avoid cycles. 5 Future Work The min-conflicts method outlined in this paper, and repair-based methods in... |

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Citation Context ...pecifically, we compared the min-conflicts method to a simple constructive backtracking algorithm that is known to perform well on graph-coloring problems. The algorithm, originally proposed by Brelaz=-=[4, 42]-=-, can be described as the repeated application of the following rule for choosing a node to color: Find the uncolored node that has the fewest consistent colorings with its neighbors. If there is more... |

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Citation Context ...ew problem. There has also been related work in AI on sophisticated methods for measuring the contention between resources in scheduling problems. This information can then be used in heuristic search=-=[8, 33, 36]. The use of "c-=-onflict counts" can be viewed as a simple measure of resource contention. The fact that the min-conflicts approach performs well on n-queens, a well-studied, "standard" constraintsatisf... |

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Citation Context ...ion (in terms of the minimum number of repairs that are required) affects the expected utility of the heuristic. The work described in this paper was inspired by a neural network originally developed =-=[20, 2, 19]-=- for use in Spike [17], a system for scheduling astronomical observations on the Hubble Space Telescope. The min-conflicts heuristic was distilled from an analysis of the network, as described in [27,... |

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Citation Context ...ffective. 1 Introduction One of the most promising general approaches for solving combinatorial search problems is to generate an initial, suboptimal solution and then to apply local repair heuristics=-=[37, 26, 31, 27, 44, 39, 15]-=-. Techniques based on this approach have met with empirical success on many combinatorial problems, including the traveling salesman and graph partitioning problems[16]. Such techniques also have a lo... |

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Citation Context ...d to produce a solution to any instance of the n-queens problem. Nevertheless, the problem has been perceived as relatively "hard" for heuristic search methods. Several studies of the nqueen=-=s problem [40, 12, 23]-=- have compared heuristic backtracking methods such as search rearrangement backtracking (e.g., most-constrained first), forward checking, dependency-directed backtracking, etc. To solve the n-queens p... |

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Citation Context ...on of his "micro-opportunistic" scheduler with other techniques, including some of the major current approaches from the operations research community. These same problems were also used by =-=Muscettola[33] to evalua-=-te his "conflict partition scheduling" approach. We have applied Spike to these problems, using the current Spike version of the min-conflicts algorithm that has superseded the GDS network. ... |

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Citation Context ...d independently.) While both methods are specific to n-queens, one method is a repair-based method that is similar to ours in spirit[39], whereas the other employs a constructive backtracking approach=-=[21]-=-. This latter method uses a combination of variable and value-ordering heuristics which take advantage of the particular structure inherent in n-queens. This shows that one can solve n-queens problems... |

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Citation Context ...schedule ground maintenance for the space shuttle. Other encouraging studies on repair-based algorithms include Sosic and Gu's work with N-queens[39], Morris's work on constraint-satisfaction problems=-=[30, 31, 32]-=- and a variety of studies on Tabu Search (e.g. [10, 13]), a hill-climbing, local search technique that maintains a list of forbidden moves in order to avoid cycles. 5 Future Work The min-conflicts met... |

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