On the Generating of Pareto Optimal Alternatives in Large Scale Systems

Abstract

Basic issues concerning Pareto optimal (noninferior) alternatives in large scale decomposable systems are considered. The mathematical models are supposed to consist of interconnected subsystems with multiple objectives in each. The overall objectives are functions of the subsystem objectives. Three different cases with respect to the number of decision makers are covered: (1) one decision maker for the overall objectives and one decision maker for each subsystem, (2) one decision maker interested in overall objectives, (3) conflicting decision makers in subsystems only. Firstly, basic properties concerning the correspondence between the Pareto optimality of different objective vectors in these cases are derived. Secondly mathematical methods of generating noninferior alternatives which exploit the structure of a decomposable system are discussed. These include well known hierarchical optimization methods. In addition, a non-iterative organisational method is proposed for systems with few coupling variables. The key point of this procedure is a condition which checks whether Pareto optimal alternatives of the subsystems constitute a noninferior solution for the whole system.