FINDING A GUARANTEED SUB-OPTIMAL SOLUTION ON THE CONSTRAINTS IN THE INTEGRATED KNOCKET PROBLEM
Abstract
In this article, the concepts of a guaranteed solution and a guaranteed suboptimal solution for the integer knapsack problem are derived. A method for finding a guaranteed suboptimal solution has been developed on the basis of one economic interpretation. Using this method, one specific problem was solved.
References
Korbut A.A., Finkelstein Yu.Yu. Discrete programming. M .: Science,1969, 368 p.
Finkelstein Yu.Yu. Approximate methods and applied problems of discrete programming. Moscow: Nauka, 1976.
Emelichev V.A., Komlik V.N. A method for constructing a sequence of plans for solving discrete optimization problems. M .:Nauka, 1981, 208 p.
Martello S., Toth P. Knapsack problems, Algorithm and Computers implementations. John Wiley & Sons, Chichster, 1990, 296 p.
Kellerer H., Pferschy U., Pisinger D. Knapsack problems. Springer-Verlag, Berlin, Heidelberg, NewYork, 2004, 546 p.
Sigal I.Kh. , Ivanova A.P. An introduction to applied discrete programming of a computer model and an algorithm. M. Fizmat lit. , 2007, 304 p.
Mamedov K.Sh. Research on integer optimization (methods, algorithms and computational experiments). Lambert Academic Publishing, (Germany) 2012, 276 p.
Mamedov K.Sh. Methods for solving various classes of discrete optimization problems. Baku- "ELM" -2011. 343st.
Gary M., Johnson D. Computing machines and intractable problems. M .: Mir, 1982. Page 416
Kovalev M.M. Discrete optimization (integer programming). M. URSS, 2003, 246 art.
Mansimov KB, Mamedov KK A method for solving a partially-integer knapsack problem by narrowing the boundary of values of the objective function and variables. Automation and computer technology No. 4, Riga, 2010, p. 40 - 53.
Mamedov K. Sh., Mamedov K. K., Elchueva S. K. Solving the Mixed-Integer Knapsack Problem by Decrease of Dimension and use of Dynamic programming. Automatic Control and Computer Sience, 2015, vol 49, no 4, pp 231-238. Mamedov K.Sh., Mamedov N.N., The concept of a guaranteed solution and finding it in a Boolean programming problem. "Reports" of the National Academy of Sciences of Azerbaijan, 2012, No. 6, art. 19-26. (In Azerb. Language.)
Mamedov K.Sh., Mamedov NN, Algorithms for constructing a guaranteed solution and a guaranteed approximate solution of the multidimensional knapsack problem. International scientific and technical journal "Problems Management and Informatics "2014, No. 5, p. 30-37.
K. Sh. Mamedov, N. N. Mamedov“Guaranteed Solution and its Finding in the Integer Programming Problems” International Journal of Applied Science and Technology Vol. 5, No. 4, August 2015, p. 46-54.
Mamedov K.Sh., Mamedov N. N The concept of a guaranteed solution by functional for a multidimensional knapsack problem. International scientific and technical journal "Radioelectronics, Informatics, Management" 2018, No. 1 (44), with. 167-174. 16. Mamedov K.Sh., Mamedov NN, Methods for finding a guaranteed solution and a guaranteed suboptimal solution in an integer programming problem. Baku "Elm", 2018, 206 st. ... (In Azerb. Language.)
CC BY-ND
A work licensed in this way allows the following:
1. The freedom to use and perform the work: The licensee must be allowed to make any use, private or public, of the work.
2. The freedom to study the work and apply the information: The licensee must be allowed to examine the work and to use the knowledge gained from the work in any way. The license may not, for example, restrict "reverse engineering."
2. The freedom to redistribute copies: Copies may be sold, swapped or given away for free, in the same form as the original.