Open AccessFINDING OF OPTIMAL SUBSET STRUCTURE IN THE KNAPSACK PROBLEM
Author(s) -
Sergey V. Chebakov,
Л. В. Серебряная
Publication year - 2019
Publication title -
doklady belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki
Language(s) - English
Resource type - Journals
eISSN - 2708-0382
pISSN - 1729-7648
DOI - 10.35596/1729-7648-2019-124-6-72-79
Subject(s) - knapsack problem , continuous knapsack problem , mathematics , set (abstract data type) , mathematical optimization , change making problem , pareto principle , pareto optimal , value (mathematics) , multi objective optimization , computer science , statistics , programming language
An algorithm for solving the knapsack problem based on the proposed multi-criteria model is considered. The implementation of this algorithm allows to define the structure of the optimal subset as a union of certain elements of a Pareto layers group into which a initial data set is divided. The first such layer is the Pareto set. The optimal subset allows to find a specific subset of the initial data. Its elements as a result of belonging to the Pareto layers with large numbers cannot enter the optimal subset. The most expensive in terms of the number of operations required are knapsack problems, in which the number of elements in the set of initial data is quite large. The article shows that with a relatively small value of the knapsack volume, the number of elements required to find the optimal subset is significantly less than their total number in the original set. It can lead to a significant decrease in the total time to solve the combinatorial problem.