Properties of linear unconditional optimization problems on arrangements under probabilistic uncertainty

1Iemets, OO
2Barbolina, TM
1Poltava University of Economics and Trade
2V.G. Korolenko Poltava National Pedagogical University
Dopov. Nac. akad. nauk Ukr. 2016, 2:31-37
https://doi.org/10.15407/dopovidi2016.02.031
Section: Information Science and Cybernetics
Language: Ukrainian
Abstract: 

The properties of linear unconditional optimization problems on arrangements, when a feasible region is defined with probabilistic uncertainty, are studied. We formulate and prove the condition as a base of solution's search and ways of solution's construction in particular cases. We demonstrate that the solution of the unconditional optimization problem on arrangements with discrete random variables as coefficients of the goal function can be reduced to that of the examined problem.

Keywords: discrete random variable, Euclidean problem of combinatorial optimization, linear unconditional optimization problem on arrangements, probabilistic uncertainty
References: 
  1. Sergienko I. V., Kaspshitskaya M. F. Models and methods of solving combinatorial optimization problems by comput. Kiev: Nauk. Dumka, 1981 (in Russian).
  2. Stoyan Yu. G., Iemets O. O. Theory and methods of euclidian combinatorial optimization, Kyiv: Instytut systemnykh doslidzhen osvity, 1993 (in Ukrainian).
  3. Iemets O. A., Barbolina T. N. Combinatorial optimization on arrangements, Kyiv: Nauk. Dumka, 2008 (in Russian).
  4. Donets G. A., Kolechkina L. M. Extremal problems on combinatorial configurations, Poltava: RVV PUET, 2011 (in Ukrainian).
  5. Sergienko I. V., Mikhalevich M. V. System Research and Information Technologies, 2004, No 4: 7–29 (in Russian).
  6. Haivoronskyy O. O., Ermoliev Yu. M., Knopov P. S., Norkin V. I. Cybernetics and Systems Analysis, 2015, 51, No 1: 64–73 (in Russian). https://doi.org/10.1007/s10559-015-9700-6
  7. Kan Yu. S., Kibzun A. I. Stochastic programming problems with probability functions, Moscow: FIZMATLIT, 2009 (in Russian).
  8. Marti K. Stochastic Optimization Methods, Berlin: Springer, 2008. https://doi.org/10.1007/978-3-540-79458-5
  9. Sergienko I. V., Iemets O. O., Yemets O. O. Cybernetics and Systems Analysis, 2013, 49, No 5: 673–683 (in Russian). https://doi.org/10.1007/s10559-013-9554-8
  10. Iemets O. O., Yemets O. O. Solving combinatorial optimization problems on fuzzy sets, Poltava: PUET, 2011 (in Ukrainian).
  11. Iemets O. O., Barbolina T. M. Dopov. Nac. akad. nauk Ukr., 2014, No 11: 40–45 (in Ukrainian).
  12. Iemets O. O., Barbolina T. M. Visnyk Cherkaskoho universytetu. Seria Prykladna matematyka. Informatyka, 2014, No 18: 3–11 (in Ukrainian).