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 study 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 (a) appropriate formulation of the problem, (b) accurate estimation of the 'robustness' measure and (c) 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 perspectivesfeasibility 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.

An overview on robust design hybrid metamodeling: Advanced methodology in process optimization under uncertainty

“…This gap has also existed in optimization models as well as another field of engineering (Ehrgott et al, 2014;Gabrel et al, 2014;Goerigk & Schöbel, 2015;Wang & Shan, 2007). (Ghodratnama et al, 2015) √ √ √ √ √ √ 16 (Pishvaee & Fazli Khalaf, 2016 (Gul & Zoubir, 2017) √ √ √ 33 (Goerigk & Schöbel, 2015) √ √ √ √ √ 34 (Gorissen, 2015) √ √ √ √ √ √ 35 (Liu et al, 2015) √ √ √ √ 36 (Sun et al, 2015) √ √ √ 37 √ √ √ √ 38 (Wu , 2015) √ √ √ √ √ 39 (Khan et al, 2015) √ √ √ 40 (Park, 2016) √ √ √ 41 (Goberna et al, 2015) √ √ √ √ 42 √ √ √ 43 (Wang & Pedrycz, 2015) √ √ √ √ √ 44 (Yu & Zeng, 2015) √ √ √ 45 (Asafuddoula et al, 2015) √ √ √ √ √ √ 46 (Dellino et al, 2015) √ √ √ √ √ √ √ √ √ 47 (Auzins et al, 2015) √ √ √ √ √ √ 48 (Cao et al, 2015) √ √ √ √ √ √ 49 (Ng et al, 2015) √ √ √ √ √ √ √ 50 (Allahverdi, 2015) √ √ …”

Discretization Analysis Method of Hybrid Reliability Based on Evidence Theory

“…As shown in Figure 4(a), within the distribution range of , select the mean value = as the center, truncated radius is , and then the six-sigma rule is applied to truncate the continuous random variables [40]; hence the identification interval [ , ] = [ − , + ] is obtained. It is clear that the larger the truncated parameter , the higher the calculation accuracy.…”

A Robust Technique Without Additional Computational Cost in Evolutionary Antenna Optimization

“…It is a hot topic in evolutionary computation. Some previously published methods on robust evolutionary optimization have been presented in [18][19][20][21][22][23][24][25]. In [18], the method of adopting the average fitness value of an individual's neighbors instead of the fitness value of that individual.…”

“…In paper [23], the random solutions were generated using the Latin Hyper Sphere (LHS), it also did not solve the problem of reducing additional computational cost. Authors proposed robust optimization, which considered an efficient means to identify the set of tradeoff robust solutions with an affordable computational cost in [24]. However, reduced computational cost is a less important factor to consider.…”