DEFINITIONS OF SUBOPTIMISTIC AND SUBPESSIMISTIC SOLUTIONS AND THEIR CONSTRUCTION IN THE INTERVAL BOOLEAN PROGRAMMING PROBLEM
К. Sh. Mamedov, A. H. Mamedova · Radio Electronics Computer Science Control · 2016
The work considers an interval examples of Bulian programming.Given some economic interpretation to this problem which result in theconstructed economic-mathematical model.Introduced the definitions of optimistic, pessimistic, and suboptimistic, subpessimistic solutionsfor the Boolean programming problem with integer interval data are introduced. On the basis of the economic interpretation of the problemtwo algorithms are developed for the constructing of the suboptimistic and subpessimistic solutions of this task. Of course, when solutions maydifferent from suboptimistic and subpessimistic solutions.It is therefore necessary to estimate the relative error of the found to estimate theerror of the suboptimistic and subpessimistic solutions from optimistic and pessimistic solutions appropriately. For this purpose Lagrange typemajoring function is constructed. It is proved, that the minimum value of this function is the upper bound of the optimistic and pessimisticvalues of the objective function appropriately. Minimization of this function is in the upper border of the suboptimistic and subpessimisticvalues of the performance function. Numerous computational experiments on the examples with different dimensions are provided.