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

TL;DR

This paper introduces MONISE, an extension of the NISE algorithm, capable of efficiently approximating Pareto fronts in many-objective problems using mixed-integer linear programming and scalarization techniques.

Contribution

It extends the NISE algorithm to handle three or more objectives with a mixed-integer linear programming formulation and demonstrates its effectiveness in convex and non-convex problems.

Findings

MONISE effectively approximates Pareto fronts in many-objective problems.

The method is competitive in terms of computational cost and solution quality.

Experimental results show MONISE's robustness in convex and non-convex scenarios.

Abstract

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.