Decomposition for Solutions of Large-Scale Multicriteria Problems

The problem of constructing a set of effective vector estimates for a large number of partial effectiveness criteria has been demonstrated. The definition implies that the sets of effective (Xe) and weakly effective (X0) solutions from the feasible set (X) satisfy where w(Xe), w(X0), and w(X) are the sets of effective, weakly effective, and feasible vectors (vector estimates), respectively. The degree of branching N(m)rapidly grows as the number m of criteria increases, which leads to considerable computational difficulties in the solution of large-scale multicriteria problems. Assume that there are only two levels of hierarchy, and let the decision makers at the upper and lower hierarchy levels be referred to as managers and subordinates, respectively. The computational resources can be used more efficiently in the solution of large-scale multicriteria problems.