Nonfeasible Hierarchical Multicriteria Methods

Abstract

General nonfeasible (price-coordination, interaction balance) hierarchical optimization algorithms for large-scale systems with multiple objectives are considered. The systems studied consist of connected subsystems with multiple objectives (subgoals, indicators); the overall objectives are functions of the subsystem objectives. It is shown that, unlike in the single objective case, there is no general transformation, modification, of the objective vectors of the subsystems (cf. the additional price term in the single objective case). However, a series of transformed subproblems can be defined such that the limit solution can be taken as the subsystem solution. That is, in the general case where the way the decision-maker expresses his preference is free, an additional iteration is needed in each subproblem. A multicriteria duality theory is reviewed. Based on this theory a nonfeasible algorithm is rederived, where the subproblems are solved by multicriteria methods using explicit trade-offs (such as the SWT and Geoffrion's method). The derivation using the duality theory conveniently gives us a coordination algorithm, sufficient convexity properties, and a new suboptimal stopping rule.