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The basic hierarchical overlapping coordination method is briefly reviewed. Three generalizations to this method with respect to convergence, problem formulation, and multiple objectives are presented. It is explained how a potential convergence problem in the basic scheme can be overcome by additional optimizations with respect to some interaction variables. In the problem formulation extension, the different decompositions are allowed to have different variables. Classical hierarchical methods are used for the overlapping coordination scheme resulting in a three-level structure. The single-objective hierarchical overlapping scheme is extended to multiple objectives using the Surrogate Worth Trade-off (SWT) method. Overlapping coordination and the Dantzig-Wolfe algorithm are compared. A simple example is used to articulate the respective attributes. Finally, the concept of hierarchical holographic modeling, obtained as an extension of the concept of hierarchical overlapping coordination, is presented with some preliminary mathematical results and illuminating examples.

This paper investigates large-scale multiobjective systems in the context of hierarchical generating methods which consider the problem of how to find the set of all noninferior solutions by decomposition and coordination. A hierarchical generating method with feasible decomposition is developed for a general class of multiobjective systems with nonconvex objectives, nonlinear subsystems, and nonseparable interaction among subsystems. A multilevel scheme is proposed based on a feasible decomposition theorem, and the decomposition is attained by fixing the output vectors of the subsystems. Lower-dimensioned multiobjective sub problems are solved at the lower level by the e-constraint approach. A way to map the noninferior frontiers of subsystems into the noninferior frontier of the overall system is established by using trade-off information in subsystems. At the upper level, coordination is accomplished by using the envelope approach in order to identify all noninferior solutions of the primal problem.

This paper treats three familiar characterizations of noninferior solutions of a vector optimization problem in terms of solutions of: (i) the e-constraint problem, (ii) the weighting problem, and (iii) the Lagrangian problem. The emphasis is to display interrelationships among the above characterizations by presenting a unified treatment of various known results found in literature. In addition to existing results, we also propose a necessary and sufficient condition for proper noriinferiority expressed in terms of the positivity of optimal Lagrange multipliers of the e-constraint problem.

Decomposition methods for multicriteria dynamic (discrete time) problems are derived. In these methods, the original problem is reduced to a series of multicriteria subproblems related to individual stages. Hence, the dimensionality of decision-variables in each subproblem is smaller than in the original problem. In a general case where the objectives may change in time, also the number of objectives in a subproblem may be smaller than that of the overall problem. The following decomposition procedures are developed: 1) a dynamic programming method, 2) a two point boundary value problem method, 3) multilevel methods, and 4) temporal hierarchy is formulated. For completeness, methods for multicriteria dynamic problems that, at the outset, transform the problem into a series of single-objective problems are reviewed. A method (called gradient method) belonging to this class is developed. Applicability and properties of various methods with respect to several factors are indicated (discrete or continuous time problem, change of objectives in time, type of constraints and functions, availability of the decision-maker). The correspondence of the methods to the single-objective dynamic methods is indicated.

Large-scale systems are often characterized by hierarchical structure, and they usually have multiple objectives that are noncommensurable. Two well-known approaches to the analysis of systems--hierarchical system theory and multiobjective optimization--have been developed to deal with these two aspects of large-scale systems. The past decade has seen an increasing concern with the integration of these two approaches into a unified framework for large scale systems, leading to the emergence of a new field known as hierarchical multiobjective analysis. This paper provides a systematic survey of the literature associated with the modeling and optimization of large scale systems, focusing on research based on the hierarchical multiobjective approach, the overlapping decomposition approach, and the multimodel approach. A large number of recently published papers that fall within these areas are reviewed.

The management of risk -- a measure of the probability and severity of adverse effects -- is addressed in this paper within the broad hierarchical-multi objective framework. Such a framework incorporates the hierarchical nature of the decision making process; the multiple decision makers at the various levels of the system's hierarchy; the multi objective nature of large scale systems, where multiple, non commensurate, and conflicting objectives characterize such systems; and the quantitative/empirical and the qualitative/normative/judgmental aspects, which are the driving force that ultimately influences the decision making process. Three major topics dominate the methodological components of the paper: hierarchical-multi objective coordination, risk of extreme events, and impact analysis. Applications from the areas of the maintenance of infrastructure and flood warning and evacuation systems are used as a vehicle to communicate the methodological framework with the readers.

This paper advances the premise that models and concepts from the fields of multiple-criteria decision-making, risk assessment and management, and impact analysis can prove to be formidable tools in the process of international conflict resolution through negotiation. In particular, the paper presents a framework whereby impact analysis can be incorporated into the hierarchical multiobjective decision-making process.

An iterative negotiation procedure for multiple decision makers, who have their own multiple objectives and who are depended on each other via common resources or physical connections, is proposed. The scheme includes two repe ated basic steps : the decision makers' independent multicriteria optimizations of their subsystems and a convenient step for trade-off between the decision makers. Assumptions guaranteeing the convergence of the negotiation scheme are addressed, among these, one assumption concerning independence of subsystems, is essential. The negotiation scheme can also be applied by a single decision maker to decompose a problem into simpler decision problems. Ariver planning example is included.