### Abstract

It is well known that constraint satisfaction problems (CSPs) in the phase transition region are most difficult for complete search algorithms. On the other hand, for incomplete hill-climbing algorithms, problems in the phase transition region axe more difficult than problems beyond the phase transition region, i.e., more constrained problems. This result seems somewhat unnatural since these more constrained problems have fewer solutions than the phase transition problems. In this paper, we clarify the cause of this paradoxical phenomenon by exhaustively analyzing the state-space landscape of CSPs, which is formed by the evaluation values of states. The analyses show that by adding more constraints, while the number of solutions decreases, the number of local-minima also decreases, thus the number of states that are reachable to solutions increases. Furthermore, the analyses clarify that the decrease in local-minima is caused by a set of interconnected local-minima (basin) being divided into smaller regions by adding more constraints.

Original language | English |
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Title of host publication | Principles and Practice of Constraint Programming - CP 1997 - 3rd International Conference, CP 1997, Proceedings |

Editors | Gert Smolka |

Publisher | Springer Verlag |

Pages | 356-370 |

Number of pages | 15 |

ISBN (Print) | 3540637532, 9783540637530 |

Publication status | Published - Jan 1 1997 |

Externally published | Yes |

Event | 3rd International Conference on Principles and Practice of Constraint Programming, CP 1997 - Linz, Austria Duration: Oct 29 1997 → Nov 1 1997 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1330 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd International Conference on Principles and Practice of Constraint Programming, CP 1997 |
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Country | Austria |

City | Linz |

Period | 10/29/97 → 11/1/97 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Principles and Practice of Constraint Programming - CP 1997 - 3rd International Conference, CP 1997, Proceedings*(pp. 356-370). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1330). Springer Verlag.

**Why adding more constraints makes a problem easier for hill-climbing algorithms : Analyzing landscapes of CSPs.** / Yokoo, Makoto.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Principles and Practice of Constraint Programming - CP 1997 - 3rd International Conference, CP 1997, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1330, Springer Verlag, pp. 356-370, 3rd International Conference on Principles and Practice of Constraint Programming, CP 1997, Linz, Austria, 10/29/97.

}

TY - GEN

T1 - Why adding more constraints makes a problem easier for hill-climbing algorithms

T2 - Analyzing landscapes of CSPs

AU - Yokoo, Makoto

PY - 1997/1/1

Y1 - 1997/1/1

N2 - It is well known that constraint satisfaction problems (CSPs) in the phase transition region are most difficult for complete search algorithms. On the other hand, for incomplete hill-climbing algorithms, problems in the phase transition region axe more difficult than problems beyond the phase transition region, i.e., more constrained problems. This result seems somewhat unnatural since these more constrained problems have fewer solutions than the phase transition problems. In this paper, we clarify the cause of this paradoxical phenomenon by exhaustively analyzing the state-space landscape of CSPs, which is formed by the evaluation values of states. The analyses show that by adding more constraints, while the number of solutions decreases, the number of local-minima also decreases, thus the number of states that are reachable to solutions increases. Furthermore, the analyses clarify that the decrease in local-minima is caused by a set of interconnected local-minima (basin) being divided into smaller regions by adding more constraints.

AB - It is well known that constraint satisfaction problems (CSPs) in the phase transition region are most difficult for complete search algorithms. On the other hand, for incomplete hill-climbing algorithms, problems in the phase transition region axe more difficult than problems beyond the phase transition region, i.e., more constrained problems. This result seems somewhat unnatural since these more constrained problems have fewer solutions than the phase transition problems. In this paper, we clarify the cause of this paradoxical phenomenon by exhaustively analyzing the state-space landscape of CSPs, which is formed by the evaluation values of states. The analyses show that by adding more constraints, while the number of solutions decreases, the number of local-minima also decreases, thus the number of states that are reachable to solutions increases. Furthermore, the analyses clarify that the decrease in local-minima is caused by a set of interconnected local-minima (basin) being divided into smaller regions by adding more constraints.

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UR - http://www.scopus.com/inward/citedby.url?scp=84948981891&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84948981891

SN - 3540637532

SN - 9783540637530

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 356

EP - 370

BT - Principles and Practice of Constraint Programming - CP 1997 - 3rd International Conference, CP 1997, Proceedings

A2 - Smolka, Gert

PB - Springer Verlag

ER -