Decomposition of the problem of approximating the Edgeworth–Pareto hull

For nonlinear block separable multicriteria optimization (MCO) problems, a decomposition method is proposed that simplifies the approximation of the Edgeworth–Pareto hull (EPH), i.e., the maximum (by inclusion) set having the same Pareto frontier as the set of feasible criteria vectors in the MCO problem. A two-level system is considered that consists of an upper coordinating level and lower-level subsystems interacting via the upper level. It is assumed that the criteria are related to the upper-level variables. According to the method, preliminarily constructed approximations to block EPHs are used to obtain an EPH approximation for the whole MCO problem. As an example, the EPH for an MCO problem arising in estimating the potential possibilities of water resource management for a cascade of reservoirs is constructed.