A Multi-Objective Robust Optimization Approach Under Interval Uncertainty Based on Kriging and Support Vector Machine

2018 ◽  
Author(s):  
Tingli Xie ◽  
Ping Jiang ◽  
Qi Zhou ◽  
Leshi Shu ◽  
Yang Yang
Keyword(s):  
Support Vector Machine ◽  
Robust Optimization ◽  
Kriging Model ◽  
Interval Uncertainty ◽  
Support Vector ◽  
Optimization Approach ◽  
Multi Objective ◽  
Large Numbers ◽  
Design Alternatives ◽  
Engineering Design Problems

Interval uncertainty can cause uncontrollable variations in the objective and constraint values, which could seriously deteriorate the performance or even change the feasibility of the optimal solutions. Robust optimization is to obtain solutions that are optimal and minimally sensitive to uncertainty. Because large numbers of complex engineering design problems depend on time-consuming simulations, the robust optimization approaches might become computationally intractable. To address this issue, a multi-objective robust optimization approach based on Kriging and support vector machine (MORO-KS) is proposed in this paper. Firstly, the feasible domain of main problem in MORO-KS is iteratively restricted by constraint cuts formed in the subproblem. Secondly, each objective function is approximated by a Kriging model to predict the response value. Thirdly, a Support Vector Machine (SVM) model is constructed to replace all constraint functions classifying design alternatives into two categories: feasible and infeasible. A numerical example and the design optimization of a microaerial vehicle fuselage are adopted to test the proposed MORO-KS approach. Compared with the results obtained from the MORO approach based on Constraint Cuts (MORO-CC), the effectiveness and efficiency of the proposed MORO-KS approach are illustrated.

Advanced Multi-Objective Robust Optimization Under Interval Uncertainty Using Kriging Model and Support Vector Machine

2018 ◽  
Vol 18 (4) ◽  
Author(s):  
Tingli Xie ◽  
Ping Jiang ◽  
Qi Zhou ◽  
Leshi Shu ◽  
Yahui Zhang ◽  
...  
Keyword(s):  
Support Vector Machine ◽  
Robust Optimization ◽  
Engineering Design ◽  
Kriging Model ◽  
Support Vector ◽  
Svm Classifier ◽  
Optimization Approach ◽  
Design Problems ◽  
Multi Objective ◽  
Engineering Design Problems

There are a large number of real-world engineering design problems that are multi-objective and multiconstrained, having uncertainty in their inputs. Robust optimization is developed to obtain solutions that are optimal and less sensitive to uncertainty. Since most of complex engineering design problems rely on time-consuming simulations, the robust optimization approaches may become computationally intractable. To address this issue, an advanced multi-objective robust optimization approach based on Kriging model and support vector machine (MORO-KS) is proposed in this work. First, the main problem in MORO-KS is iteratively restricted by constraint cuts formed in the subproblem. Second, each objective function is approximated by a Kriging model to predict the response value. Third, a support vector machine (SVM) classifier is constructed to replace all constraint functions classifying design alternatives into two categories: feasible and infeasible. The proposed MORO-KS approach is tested on two numerical examples and the design optimization of a micro-aerial vehicle (MAV) fuselage. Compared with the results obtained from other MORO approaches, the effectiveness and efficiency of the proposed MORO-KS approach are illustrated.

A multi-objective robust optimization approach for engineering design under interval uncertainty

2018 ◽  
Vol 35 (2) ◽  
pp. 580-603 ◽  
Author(s):  
Qi Zhou ◽  
Xinyu Shao ◽  
Ping Jiang ◽  
Tingli Xie ◽  
Jiexiang Hu ◽  
...  
Keyword(s):  
Robust Optimization ◽  
Engineering Design ◽  
Optimization Problems ◽  
Interval Uncertainty ◽  
Optimization Approach ◽  
Content Type ◽  
Computational Burden ◽  
Multi Objective ◽  
Design Alternatives ◽  
Kriging Metamodel

Purpose Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty. Design/methodology/approach In K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process. Findings Five numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost. Practical implications The proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties. Originality/value A K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.

Robust Design of UOE Forming Process Based on Support Vector Machine

2015 ◽  
Vol 817 ◽  
pp. 523-530
Author(s):  
Tian Xia Zou ◽  
Guang Han Wu ◽  
Da Yong Li ◽  
Qiang Ren ◽  
Ying Hong Peng
Keyword(s):  
Support Vector Machine ◽  
Robust Optimization ◽  
Robust Design ◽  
Pipeline Steel ◽  
Optimization Methods ◽  
Material Behavior ◽  
Support Vector ◽  
Optimization Approach ◽  
Forming Process ◽  
Noise Factors

Fluctuations in material properties of the incoming steel for UOE forming process are widespread. According to the statistics, the fluctuation range of the yield strength of the same grade pipeline steel is around 80MPa. Robust optimization methods have been widely applied in sheet metal forming area. In this paper, experiments were conducted to investigate how a stochastic material behavior of noise factors affected UOE forming quality. Robust design models integrated with response surface method for UOE forming process were established to minimize impact of the variations and improve the qualified rate of UOE pipe ovality. Support vector machine in both classification and regression was adopted to map the relation between input process parameters and forming qualities. The deterministic and robust optimization results are presented and compared, demonstrating increased process robustness and decreased number of product rejects by application of the robust optimization approach.

Advanced Robust Optimization Approach for Design Optimization With Interval Uncertainty Using Sequential Quadratic Programming

2013 ◽  
Author(s):  
Jianhua Zhou ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Linear Equations ◽  
Variable Parameter ◽  
Optimal Solution ◽  
Interval Uncertainty ◽  
Computational Time ◽  
Optimization Approach ◽  
Engineering Optimization ◽  
Loop Optimization ◽  
New Approach

Uncertainty is inevitable in real world. It has to be taken into consideration, especially in engineering optimization; otherwise the obtained optimal solution may become infeasible. Robust optimization (RO) approaches have been proposed to deal with this issue. Most existing RO algorithms use double-looped structures in which a large amount of computational efforts have been spent in the inner loop optimization to determine the robustness of candidate solutions. In this paper, an advanced approach is presented where no optimization run is required to be performed for robustness evaluations in the inner loop. Instead, a concept of Utopian point is proposed and the corresponding maximum variable/parameter variation will be obtained by just solving a set of linear equations. The obtained robust optimal solution from the new approach may be conservative, but the deviation from the true robust optimal solution is very small given the significant improvement in the computational efficiency. Six numerical and engineering examples are tested to show the applicability and efficiency of the proposed approach, whose solutions and computational time are compared with those from a similar but double-looped approach, SQP-RO, proposed previously.

Multiobjective Collaborative Robust Optimization With Interval Uncertainty and Interdisciplinary Uncertainty Propagation

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
M. Li ◽  
S. Azarm
Keyword(s):  
Robust Optimization ◽  
Probability Distributions ◽  
Uncertainty Propagation ◽  
Multiple Objectives ◽  
Interval Uncertainty ◽  
Optimization Approach ◽  
Solution Approach ◽  
Time In Literature ◽  
Collaborative Robust Optimization ◽  
First Time

We present a new solution approach for multidisciplinary design optimization (MDO) problems that, for the first time in literature, has all of the following characteristics: Each discipline has multiple objectives and constraints with mixed continuous-discrete variables; uncertainty exists in parameters and as a result, uncertainty propagation exists within and across disciplines; probability distributions of uncertain parameters are not available but their interval of uncertainty is known; and disciplines can be fully (two-way) coupled. The proposed multiobjective collaborative robust optimization (McRO) approach uses a multiobjective genetic algorithm as an optimizer. McRO obtains solutions that are as best as possible in a multiobjective and multidisciplinary sense. Moreover, for McRO solutions, the variation of objective and/or constraint functions can be kept within an acceptable range. McRO includes a technique for interdisciplinary uncertainty propagation. The approach can be used for robust optimization of MDO problems with multiple objectives, or constraints, or both together at system and subsystem levels. Results from an application of McRO to a numerical and an engineering example are presented. It is concluded that McRO can solve fully coupled MDO problems with interval uncertainty and obtain solutions that are comparable to a single-disciplinary robust optimization approach.

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