Finding Robust Solutions for Many-Objective Optimization Using NSGA-III

The primary task of evolutionary multi-objective optimization (EMO) is to find the globally best Pareto-optimal front. However, often decision makers (DMs) are not interested in obtaining the global frontier. Instead, they prefer a set of solutions for which there is no significant change in objective values within a small neighborhood of each decision variable vector, resulting in a set of robust solutions. The corresponding objective vectors are said to lie on the robust front. In practical applications, such as in engineering designs, designers are interested in robust designs which are less sensitive to the perturbation in the design variables and parameters, caused by the manufacturing process tolerances, material non-uniformity, uncertainties in supply-chain process, and by many other practical matters. An earlier robust EMO study proposed two different robustness measures and used the elitist non-dominated sorting genetic algorithms (NSGA-II) to find respective robust fronts. However, the limitation of NSGA-II in generating well-distributed and diverse set solutions for many-objective optimization, the robust optimization concept must be extended with evolutionary many-objective optimization (EMaO) algorithms to investigate the efficacy in more than three-objective problems. This study proposes an extension of test problems for robust many-objective optimization tasks and demonstrates the performance of updated NSGA-III procedure to two to eight-objective test and real-world problems.

I. Introduction

EVOLUTIONARY multi-objective optimization (EMO) algorithms have been primarily focused on obtaining a well-distributed and diverse set of Pareto-optimal (PO) solutions [1], [2]. Although, these non-dominated solutions are globally the best solutions from a theoretical optimization point of view, the solutions can be very sensitive to small perturbations in the neighborhood of decision variable vectors for one or more PO solutions. Practitioners usually do not like to adopt sensitive solutions, despite them being optimal, due to the uncertainties involved in implementing and deploying sensitive solutions in their desired forms. If an intended solution gets implemented slightly differently to a different solution, the respective objective vector would be different from the intended objective vector. In the context of multi- or many-objective optimization, the perturbed solution can now become dominated, infeasible, better or stay non-dominated. For these reasons, usually, practitioners are interested in finding out a set of robust solutions that are less sensitive to perturbations in the neighborhood of solutions.