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Complexity of Max-SAT using stochastic algorithms

Published: 12 July 2008 Publication History

Abstract

Hill-climbing has been shown to be more effective than exhaustive search in solving satisfiability problems. Also, it has been used either by itself or in combination with other methods to solve the most difficult region of SAT, the phase transition. We show that hill-climbing also finds SAT problems difficult around the phase transition. It too follows an easy-hard-eays transition.

References

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J. M. Crawford and L. D. Auton. Experimental results on the crossover point in random 3-SAT. Artificial Intelligence, 81(1-2):31--57, 1996.
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D. Mitchell, B. Selman, and H. Levesque. Hard and easy distributions of SAT problems. pages 459--465, San Jose, CA, USA, 1992. Publ by AAAI, Menlo Park, CA, USA.
[3]
R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, and L. Troyansky. Determining computational complexity from characteristic ‘phase transitions'. Nature, 400(6740):133--7, 1999.
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B. Selman. Stochastic search and phase transitions: AI meets physics. volume vol.1 of IJCAI-95. Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence, pages 998--1002, Montreal, Que., Canada, 1995. Morgan Kaufmann Publishers.
[5]
Z. Weixiong. Phase transitions and backbones of 3-SAT and maximum 3-SAT. Principles and Practice of Constraint Programming -- CP 2002. 7th International Conference, CP 2001. Proceedings (Lecture Notes in Computer Science Vol.2239), pages 153--67, Paphos, Cyprus, 2001. Springer-Verlag.

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Published In

cover image ACM Conferences
GECCO '08: Proceedings of the 10th annual conference on Genetic and evolutionary computation
July 2008
1814 pages
ISBN:9781605581309
DOI:10.1145/1389095
  • Conference Chair:
  • Conor Ryan,
  • Editor:
  • Maarten Keijzer
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 12 July 2008

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Author Tags

  1. hill-climbing.
  2. maximum satisfiability
  3. phase transition
  4. satisfiability

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Cited By

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  • (2021)How to exploit fitness landscape properties of timetabling problem: A new operator for quantum evolutionary algorithmExpert Systems with Applications10.1016/j.eswa.2020.114211168(114211)Online publication date: Apr-2021
  • (2015)Quadratic assignment problem: a landscape analysisEvolutionary Intelligence10.1007/s12065-015-0132-z8:4(165-184)Online publication date: 22-May-2015
  • (2011)Memetic AlgorithmsWiley Encyclopedia of Operations Research and Management Science10.1002/9780470400531.eorms0515Online publication date: 14-Jan-2011
  • (2010)Learning the large-scale structure of the MAX-SAT landscape using populationsIEEE Transactions on Evolutionary Computation10.1109/TEVC.2009.203357914:4(518-529)Online publication date: 1-Aug-2010
  • (2010)A Modern Introduction to Memetic AlgorithmsHandbook of Metaheuristics10.1007/978-1-4419-1665-5_6(141-183)Online publication date: 12-Aug-2010
  • (2009)Improving Performance in Combinatorial Optimisation Using Averaging and ClusteringProceedings of the 9th European Conference on Evolutionary Computation in Combinatorial Optimization10.1007/978-3-642-01009-5_16(180-191)Online publication date: 10-Apr-2009

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