Why adding more constraints makes a problem easier for hill-climbing algorithms: Analyzing landscapes of CSPs

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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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 languageEnglish
Title of host publicationPrinciples and Practice of Constraint Programming - CP 1997 - 3rd International Conference, CP 1997, Proceedings
EditorsGert Smolka
PublisherSpringer Verlag
Pages356-370
Number of pages15
ISBN (Print)3540637532, 9783540637530
DOIs
Publication statusPublished - 1997
Externally publishedYes
Event3rd International Conference on Principles and Practice of Constraint Programming, CP 1997 - Linz, Austria
Duration: Oct 29 1997Nov 1 1997

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1330
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other3rd International Conference on Principles and Practice of Constraint Programming, CP 1997
CountryAustria
CityLinz
Period10/29/9711/1/97

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Yokoo, M. (1997). Why adding more constraints makes a problem easier for hill-climbing algorithms: Analyzing landscapes of CSPs. In G. Smolka (Ed.), 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. https://doi.org/10.1007/bfb0017451