Optimization Problems with Interval Uncertainty: Branch and Bound Method

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• 作者：I. V Sergienko (1)
  Ol. O. Iemets
  Ol. O. Yemets
  
• 关键词：optimization ; interval uncertainty ; branch and bound method
• 刊名：Cybernetics and Systems Analysis
• 出版年：2013
• 出版时间：September 2013
• 年：2013
• 卷：49
• 期：5
• 页码：673-683
• 全文大小：129KB
• 参考文献：1. I. V. Sergienko, I. N. Parasyuka, nd M. F. Kaspshitskaya, 鈥淢odels and methods of fuzzy discrete optimization problems in diagnostic information technologies,鈥?Systemni Doslidzh. Inform. Tekhnol. No. 2, 7鈥?2 (2005).
  2. O. A. Yemets and A. A. Roskladka, 鈥淐ombinatorial optimization under uncertainty,鈥?Cybern. Syst. Analysis, ong class="a-plus-plus">44ong>, No. 5, 655鈥?63 (2008). oi.org/10.1007/s10559-008-9035-7">CrossRef
  3. Ol. O. Iemets and Ol. O. Yemets, Solving Combinatorial Optimization Problems on Fuzzy Sets [in Ukrainian], PUET, Poltava (2011), org.ua/handle/123456789/352" class="a-plus-plus">http://dspace.uccu.org.ua/handle/123456789/352.
  4. G. Alefeld and J. Herzberger, Introduction to Interval Computations, Academic Press (1983).
  5. Yu. G. Stoyan, Extended Space / I _{/ S} ( / R) of Centered Intervals [in Russian], Prepr. NAS Ukraine, Inst. for Mechanical Engineering Problems, No. 378, Kharkov (1994).
  6. Yu. G. Stoyan, Quasilinear Interval Mappings. The Interval Metrics [in Russian], Prepr. NAS Ukraine, Inst. for Mechanical Engineering Problems, No. 387, Kharkov (1995).
  7. Yu. I. Shokin, Interval Analysis [in Russian], Nauka, Novosibirsk (1981).
  8. L. T. Ashchepkov and D. V. Davydov, Universal Solutions of Interval Op timization and Control Problems [in Russian], Nauka, Moscow (2006).
  9. B. S. Dobronets, Interval Mathematics [in Russian], KGU, Krasnoyarsk (2004).
  10. Z. Kh. Yuldashev, Modeling of Linear Programming Problems by Interval Methods [in Russian], Prepr. IVT SO RAN, Novosibirsk (1994).
  11. M. Fidler, J. Nedoma, J. Romik, et al., Linear Optimization Problems with Imperfect Data [in Russian], RKhD, Moscow鈥揑zhevsk (2008).
  
• 作者单位：I. V Sergienko (1)
  Ol. O. Iemets
  Ol. O. Yemets
  
  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
  
• ISSN：1573-8337

文摘

An order on a set of centered intervals is introduced and is proved to be linear. An optimization problem is formulated over a set of centered intervals. The branch and bound method is proposed and substantiated to solve this problem. A number of theorems that substantiate estimates in the branch and bound method are proved.