K.SH. MAMMADOV, A.H. MAMMADOVA
METHOD OF NONLINEAR PENALTY AND ESTIMATION OF ERROR IN CONSTRUCTING SUBOPTIMISTIC AND SUBPESSIMISTIC SOLUTIONS FOR INTEGER PROGRAMMING PROBLEMS WITH INTERVAL DATA


The concepts of "optimistic", "pessimistic", "suboptimistic" and "subpessimistic" solutions are introduced. A "nonlinear penalty" method is developed for constructing suboptimistic and subpessimistic solutions. The error of the solutions found from the optimal solution is estimated. To this end, a Lagrange-type function is constructed, it is shown that the minimum value of this function is the upper limit of suboptimistic and subpessimistic values, respectively. Algorithms such as steep and subgradient descent are developed to minimize this function. Numerous computational experiments on random large-dimensional problems are carried out. These experiments once again show the high efficiency of the methods developed in this paper.

Keywords: interval integer programming problem, optimistic, pessimistic, suboptimistic and subpessimistic solutions, nonlinear penalty, Lagrange type function, upper bound, computational experiments
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