  This work proposes a novel multi-objective optimization approach that
globally finds a representative non-inferior set of solutions, also known as
Pareto-optimal solutions, by automatically formulating and solving a sequence
of weighted sum method scalarization problems. The approach is called MONISE
(Many-Objective NISE) because it represents an extension of the well-known
non-inferior set estimation (NISE) algorithm, which was originally conceived to
deal with two-dimensional objective spaces. The proposal is endowed with the
following characteristics: (1) uses a mixed-integer linear programming
formulation to operate in two or more dimensions, thus properly supporting many
(i.e., three or more) objectives; (2) relies on an external algorithm to solve
the weighted sum method scalarization problem to optimality; and (3) creates a
faithful representation of the Pareto frontier in the case of convex problems,
and a useful approximation of it in the non-convex case. Moreover, when dealing
specifically with two objectives, some additional properties are portrayed for
the estimated non-inferior set. Experimental results validate the proposal and
indicate that MONISE is competitive, in convex and non-convex (combinatorial)
problems, both in terms of computational cost and the overall quality of the
non-inferior set, measured by the acquired hypervolume.
