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### Reasonable Goals Method -- general case

To avoid complications related to non-convex sets of feasible goals, the Reasonable Goals Method (RGM) may be used instead of the FGM. In the RGM, the convex hull of the Feasible Set in Criterion Space, the FSCS, is constructed and displayed by the IDM technique. A non-linear mathematical model describing decision problems with infinite number of decision variants is used for stochastic approximation of the FSCS (see Multidimensional Images Given by Mappings): the set of feasible decisions is approximated by a large finite number of variants. Then the criterion values for these variants are computed. In this case, the convex hull of the set of feasible goals is stochastically approximated by the convex hull of a finite system of points in criterion space.

User has to explore decision maps, which look like the decision maps for convex problems. A goal is identified in the same way as in the Feasible Goals Method. As usually, the main problem is related to the fact that, in contrast to the FGM, the goal in the RGM may be not feasible. Fortunately, the goal belongs to the convex hull of the set of feasible goals, and therefore its points are linear combinations of feasible goals. This means that the goal is reasonable. Then, several variants that are close to it are selected.