An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints

TLDR

There is a growing need for evolutionary multiobjective optimization algorithms capable of handling many‑objective problems, and this paper presents results on unconstrained cases while a sequel will address constraints. The paper reviews recent work and proposes a reference‑point‑based many‑objective evolutionary algorithm (NSGA‑III) to address many‑objective optimization. NSGA‑III extends the NSGA‑II framework by selecting nondominated individuals near supplied reference points and is evaluated on many‑objective test problems with 3–15 objectives against two MOEA/D variants. NSGA‑III yields satisfactory results across all tested problems, while the two MOEA/D variants excel on different problem classes.

Abstract

Having developed multiobjective optimization algorithms using evolutionary optimization methods and demonstrated their niche on various practical problems involving mostly two and three objectives, there is now a growing need for developing evolutionary multiobjective optimization (EMO) algorithms for handling many-objective (having four or more objectives) optimization problems. In this paper, we recognize a few recent efforts and discuss a number of viable directions for developing a potential EMO algorithm for solving many-objective optimization problems. Thereafter, we suggest a reference-point-based many-objective evolutionary algorithm following NSGA-II framework (we call it NSGA-III) that emphasizes population members that are nondominated, yet close to a set of supplied reference points. The proposed NSGA-III is applied to a number of many-objective test problems with three to 15 objectives and compared with two versions of a recently suggested EMO algorithm (MOEA/D). While each of the two MOEA/D methods works well on different classes of problems, the proposed NSGA-III is found to produce satisfactory results on all problems considered in this paper. This paper presents results on unconstrained problems, and the sequel paper considers constrained and other specialties in handling many-objective optimization problems.