Coordination of Hierarchical Multiobjective Systems: Theory and Methodology

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.