This work proposes a novel many objective optimization approach that globally finds a set of efficient solutions, also known as Pareto-optimal solutions, by automatically formulating and solving a sequence of weighted 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. Looking for theoretical support, we demonstrate that being a solution of the weighted problem is a necessary condition, and it will also be a sufficient condition at the convex hull of the feasible set. The proposal is conceived to operate in more than two dimensions, thus properly supporting many objectives. Moreover, specifically deal with two objectives, some nice additional properties are portrayed for the estimated non-inferior set. Experimental results are used to validate the proposal and have indicated that MONISE is competitive both in terms of computational cost and considering the overall quality of the non-inferior set, measured by the hypervolume.