Abstract:The motivation behind this paper is to focus on the solution of Fully Rough Three Level Large Scale Integer Linear Programming (FRTLLSILP) problem, in which all decision parameters and decision variables in the objective functions and the constraints are rough intervals, and have block angular structure of the constraints. The optimal values of decision rough variables are rough integer intervals. The proposed model is based on interval method and slice-sum method in an interactive model to find a compromised … Show more
The most widely used actions and decisions of the real-world tasks frequently appear as hierarchical systems. To deal with these systems, the multi-level programming problem presents the most flourished technique. However, practical situations involve some the impreciseness regarding some decisions and performances; RST provides a vital role by considering the lower and upper bounds of any aspect of uncertain decision. By preserving the advantages of it, in the present study, solving fully rough multi-level quadratic programming problems over the variables, parameters of the objective functions, and the constraints such as rough intervals are focused on. The proposed approach incorporates the interval method, slice-sum method, Frank and Wolfe algorithm, and the decomposition algorithm to reach optimal values as rough intervals. The proposed is validated by an illustrative example, and also environmental-economic power dispatch is investigated as a real application. Finally, the proposed approach is capable of handling the fully rough multi-level quadratic programming models.
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