Metamodel Assisted Robust Optimization under Interval Uncertainly Based on Reverse Model

Abstract

Previous deterministic robust optimization approaches based on sensitivity region information usually involve nested optimization, leading to a significant burden in computational time. In this paper, a strategy to improve the computational efficiency of the robust approach based on reverse model, metamodel assisted robust optimization, in which the nested optimization structure is reduced into a single loop optimization structure, is studied. A numerical example is used to demonstrate the applicability of the proposed metamodel assisted robust optimization.

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) √ √ …”

“…Operation imprecision and seen from this figure, robust optimization methods can be divided into two types of probabilistic and non-probabilistic approaches (Cao et al, 2015). In probabilistic or stochastic robust optimization methods, the designer performs the problem by employing the probability distribution of variables, particularly the mean and variation of uncertain or noise variables.…”

“…This types of methods attempt to find robustness and optimum solution by recording different uncertainty sets in objective and constraint space. The main gap for these methods are that when uncertainties change in their variation region and previous results miss their validation, so it needs to designer evaluate problem again (Cao et al, 2015). To be more familiar with these types of methods see (Ben-Tal et al, 2009;Bertsimas et al, 2011;Ehrgott et al, 2014;Ide & Schobel, 2016;Salomon et al, 2014).…”

“…There are number of indexes to evaluate metamodel accuracy, see (Cao et al, 2015;Jin et al, 2003;Wang & Shan, 2007). Table 4.…”

Confidence-based robust optimisation using multi-objective meta-heuristics

“…In fact, this method can be considered as a meta-modal (surrogateassisted model) which suffers from the drawbacks mentioned above. Another similar interpolation-based meta-models were proposed in [39,40,41,42].…”