Abstract
Ratios ? of the values of objective functions of optimal Boolean (or integer) to the values of greedy solutions for the knapsack problem are considered. The relationship of the parameter ? with the ratio Δ of the values of objective functions for the optimal solution of linear relaxation to the values of optimal integer solution was found. Two-sided estimates for ? and Δ were obtained. A computational experiment was conducted to investigate the ratio of ? of problems of one- and two-dimensional knapsack problems with Boolean variables. A hypothesis on asymptotic behavior of the ratio ? with growth of the number of problem variables was formulated.
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