# An Extension of the Non-Inferior Set Estimation Algorithm for Many Objectives

arXiv: https://arxiv.org/abs/1709.00797 · HTML: https://mlsanity.com/paper/1709.00797/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2017.

## Built on by (most cited first, 2 of 2)

- [Exploring the Trade-off Between Model Performance and Explanation Plausibility of Text Classifiers Using Human Rationales](https://mlsanity.com/paper/2404.03098/) (2024)
- [Interactive Pareto navigation for deep multi-task learning](https://mlsanity.com/paper/2606.19521/) (2026)

## Abstract (arXiv)

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.