Six-Sigma Robust Design Optimization Using a Many-Objective Decomposition-Based 
Evolutionary Algorithm

Abstract

Robust design optimization aims to find solutions that are competent and reliable 
under given uncertainties. While such uncertainties can emerge from a number of 
sources (imprecise variable values, errors in performance estimates, varying environmental 
conditions, etc.), this paper focuses on problems where uncertainties emanate from design 
variables. In commercial designs, being reliable is often of more practical value than 
being globally best (but unreliable). Robust optimization poses three key challenges: 1) 
appropriate formulation of the problem; 2) accurate estimation of the "robustness" measure; 
and 3) efficient means to identify the set of tradeoff robust solutions with an affordable 
computational cost. In this paper, four different problem formulations for robust optimization 
are presented and analyzed. The proposed formulations offer a set of tradeoff solutions with 
robustness from two perspectives-feasibility robustness, i.e., robustness against failure 
and performance robustness, i.e., robustness assuring good performance. The approach also 
provides means to identify critical constraints or performance functions that affect the 
overall robustness. The problem is posed as a many-objective optimization problem and a 
decomposition-based evolutionary approach is used for solving it. The performance of the 
proposed approach and the consequences of using different formulations are illustrated 
using two numerical examples and four engineering problems.