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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 5, Pages 788–807 (Mi zvmmf137)  

This article is cited in 7 scientific papers (total in 7 papers)

Computational bounds for local search in combinatorial optimization

Yu. A. Kochetov

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia

Abstract: The results related to finding local optima in combinatorial optimization are overviewed. The class of polynomial-time local search problems (class PLS) is considered. By analogy with Cook's theorem, the existence of most complicated problems in this class is established. The number of steps in local descent algorithms is estimated in the worst and average cases. The local search determination of exact and approximate solutions with guaranteed error bounds is discussed.

Key words: local search, PLS-complete problems, metaheuristics, overview.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:5, 747–763

Bibliographic databases:

UDC: 519.658
Received: 12.10.2007

Citation: Yu. A. Kochetov, “Computational bounds for local search in combinatorial optimization”, Zh. Vychisl. Mat. Mat. Fiz., 48:5 (2008), 788–807; Comput. Math. Math. Phys., 48:5 (2008), 747–763

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Kononov, Yu. A. Kochetov, A. V. Plyasunov, “Competitive facility location models”, Comput. Math. Math. Phys., 49:6 (2009), 994–1009  mathnet  crossref  zmath  isi
    2. A. V. Eremeev, “Genetic algorithm with tournament selection as a local search method”, J. Appl. Industr. Math., 6:3 (2012), 286–294  mathnet  crossref  mathscinet
    3. Yu. A. Kochetov, A. V. Plyasunov, “Genetic local search the graph partitioning problem under cardinality constraints”, Comput. Math. Math. Phys., 52:1 (2012), 157–167  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Kochetov Yu.A., Kochetova N.A., “Zadacha balansirovki nagruzki na servery”, Vestnik Novosibirskogo gosudarstvennogo universiteta. Seriya: Informatsionnye tekhnologii, 11:4 (2013), 71–76  elib
    5. V. P. Il'ev, S. D. Il'eva, A. A. Navrotskaya, “Approximate solution of the $p$-median minimization problem”, Comput. Math. Math. Phys., 56:9 (2016), 1591–1597  mathnet  crossref  crossref  isi  elib
    6. S. M. Lavlinskii, A. A. Panin, A. V. Plyasunov, “Comparison of models of planning public-private partnership”, J. Appl. Industr. Math., 10:3 (2016), 356–369  mathnet  crossref  crossref  mathscinet  elib
    7. Starostin N.D., Mironov K.V., Mironov K.V., “Algorithm Modification of the Level-By-Level Approximation to the Minimum Route”, 2017 IEEE International Symposium on Signal Processing and Information Technology (Isspit), IEEE International Symposium on Signal Processing and Information Technology, IEEE, 2017, 270–275  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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