Optimization Problems with Interval Uncertainty: Branch and Bound Method

Optimization natural gas pumping units operation by the economic criterion in the conditions of uncertainty

“…Since the first term in expression 10is an additive function of the quantities xG,i, Ep,i, and which have a Gaussian membership function [4], then R1 will also have a Gaussian membership function [6]…”

Properties of the Linear Unconditional Problem of Combinatorial Optimization on Arrangements Under Probabilistic Uncertainty

“…Since inequalities(8) hold, according to Corollary 1 of Theorem 1, point m( ) * X is the unique minimal of problem(14). Therefore, for any solutionX of problem (10) conditions (13) are satisfied.…”

“…However, wide bibliography is devoted to solving optimization problems with regard for various types of uncertainty, including probabilistic one [8][9][10][11][12][13]. These trends are combined, for example, in [14][15][16][17], where the solution of combinatorial optimization problems with interval or fuzzy uncertainty is considered.…”

“…For interval and fuzzy optimization problems an approach was proposed based on introducing the order relation [14,15]. In the present paper, we will consider the solution of one class of optimization problems with combinatorial constraints and probabilistic uncertainty, whose statement is based on introducing an order on the set of discrete random variables.…”

“…Let us show the existence of point X ¢ for which conditions C X m(~) X is the minimal in problem(14). Then according to Theorem 1, for all w J s Î the condition is satisfied: ( (~) M X q w ,..., M X q w an element of the set of permutations from elements of the multiset { ( ), ...note that indices q w are such that c q w = ...…”