N.O. Shukurova.
Theoretical substantiation and experimental analysis of the method for finding the upper bound for the interval problem of mixed-Boolean programming
There are various methods for finding an approximate solution to a mixed-Boolean programming problem. Obviously, after finding such approximate solutions that corresponding to the value of the objective function, it is necessary to estimate the proximity of this value to the optimal one. For this, the corresponding linear programming problems are usually solved (i.e., the integer condition is discarded). This approach can be ineffective in the case of large dimensions, since the coordinates of the optimal solution and the optimal value of the objective function are determined. Obviously, to find the absolute and relative errors, there is no need to find the coordinates of the optimal solution, however, the approximate values of the functional and its upper bound are needed. For this purpose, in this paper, an algorithm for finding the upper bound of the interval problem of mixed-Boolean programming has been developed. For this, the majorizing function of the Lagrange-type for this problem is minimized.
Keywords: Interval problem of mixed-Boolean programming, Lagrange-type function, Upper limit of the optimum, Relative errors, Computational experiments
DOI: https://doi.org/10.54381/icp.2022.2.06
Theoretical substantiation and experimental analysis of the method for finding the upper bound for the interval problem of mixed-Boolean programming
There are various methods for finding an approximate solution to a mixed-Boolean programming problem. Obviously, after finding such approximate solutions that corresponding to the value of the objective function, it is necessary to estimate the proximity of this value to the optimal one. For this, the corresponding linear programming problems are usually solved (i.e., the integer condition is discarded). This approach can be ineffective in the case of large dimensions, since the coordinates of the optimal solution and the optimal value of the objective function are determined. Obviously, to find the absolute and relative errors, there is no need to find the coordinates of the optimal solution, however, the approximate values of the functional and its upper bound are needed. For this purpose, in this paper, an algorithm for finding the upper bound of the interval problem of mixed-Boolean programming has been developed. For this, the majorizing function of the Lagrange-type for this problem is minimized.
Keywords: Interval problem of mixed-Boolean programming, Lagrange-type function, Upper limit of the optimum, Relative errors, Computational experiments
DOI: https://doi.org/10.54381/icp.2022.2.06