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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.