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.