Branch and Bound Method for Optimization Problems on Fuzzy Sets

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

“…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.…”

“…, where indices h i (i J r Î ) satisfy(15), n i are multiplicities of elements of the basis of multiset { ( ), ..., ( )} H G H G 1 h arranged in lexicographic order. As above, we assume that s is determined from the condition h s + > 1 k , the set G i are equal to each other, from condition(12) it follows that for the minimal X * of problem (…”