Generating pareto-optimal alternatives by a nonfeasible hierarchical method

A hierarchical algorithm for generating Pareto-optimal alternatives for convex multicriteria problems is derived. At the upper level, values for Lagrange multipliers of the coupling constraints are first given. Then at the subsystems, Pareto-optimal values are determined for the subsystem objectives, whereby an additional term or an additional objective is included due to the Lagrange multipliers. In the subsystem optimizations, the coupling equations between the subsystems are not satisfied; therefore, the method is called nonfeasible. Finally, the upper level checks which of the subsystem solutions satisfy the coupling constraints; these solutions are Pareto-optimal solutions for the overall system.