Coordination of Hierarchical Multiobjective Systems: Theory and Methodology

Abstract
A static deterministic hierarchical system consisting of subsystems with multiple objectives is considered here; this system's overall multiple objectives are functions of its subsystems' objectives. Two powerful and well-developed approaches-the hierarchical multilevel and the multiobjective multiattribute approaches-are integrated into a unified hierarchical multiobjective framework. Theoretical and methodological grounding for this framework are developed. Two basic schemes-the feasible and the nonfeasible-are derived. The feasible scheme extends existing algorithms with respect to the possibility of several objectives in each subsystem. The nonfeasible scheme constitutes a new contribution to the hierarchical multiobjective framework. Lower dimensional multiobjective subproblems are formulated in terms of trade-offs. Algorithms for coordinating the subproblems are derived. Mainly systems having a single decisionmaker are considered. Thus the first-hand benefit of decomposition accrues to the analyst dealing with lower dimensional subsystems; a possible benefit for the decisionmaker lies in the decreased number of interactions. The presence of multiple decisionmakers is dealt with briefly, using the Stackelberg strategy and negotiations about trade-offs. A numerical example illustrating the basic concepts is presented.