An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach

TLDR

The precursor paper introduced NSGA‑III, a many‑objective optimization method based on NSGA‑II, and applied it to unconstrained test and practical problems with only box constraints. This paper extends NSGA‑III to handle generic constrained many‑objective optimization problems. The authors introduce three scalable constrained test problem types, extend MOEA/D for constrained problems, and make NSGA‑III adaptive by dynamically updating reference points. Constrained NSGA‑III outperforms constrained MOEA/D, especially on many‑objective problems, and its adaptive variant yields a denser Pareto front at equal cost, demonstrating a viable algorithm for both constrained and unconstrained scenarios and encouraging further research.

Abstract

In the precursor paper, a many-objective optimization method (NSGA-III), based on the NSGA-II framework, was suggested and applied to a number of unconstrained test and practical problems with box constraints alone. In this paper, we extend NSGA-III to solve generic constrained many-objective optimization problems. In the process, we also suggest three types of constrained test problems that are scalable to any number of objectives and provide different types of challenges to a many-objective optimizer. A previously suggested MOEA/D algorithm is also extended to solve constrained problems. Results using constrained NSGA-III and constrained MOEA/D show an edge of the former, particularly in solving problems with a large number of objectives. Furthermore, the NSGA-III algorithm is made adaptive in updating and including new reference points on the fly. The resulting adaptive NSGA-III is shown to provide a denser representation of the Pareto-optimal front, compared to the original NSGA-III with an identical computational effort. This, and the original NSGA-III paper, together suggest and amply test a viable evolutionary many-objective optimization algorithm for handling constrained and unconstrained problems. These studies should encourage researchers to use and pay further attention in evolutionary many-objective optimization.