New Approximation Assisted Multi-objective collaborative Robust Optimization (new AA-McRO) under interval uncertainty

2012 ◽  
Vol 47 (1) ◽  
pp. 19-35 ◽  
Author(s):  
Weiwei Hu ◽  
Shapour Azarm ◽  
Ali Almansoori
Keyword(s):  
Robust Optimization ◽  
Interval Uncertainty ◽  
Multi Objective ◽  
Collaborative Robust Optimization

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.

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.

A New Hybrid Algorithm for Multi-Objective Robust Optimization With Interval Uncertainty

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Shuo Cheng ◽  
Jianhua Zhou ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Hybrid Approach ◽  
Interval Uncertainty ◽  
Engineering Optimization ◽  
Objective Functions ◽  
Robust Solutions ◽  
Multi Objective ◽  
And Performance

Uncertainty is a very critical but inevitable issue in design optimization. Compared to single-objective optimization problems, the situation becomes more difficult for multi-objective engineering optimization problems under uncertainty. Multi-objective robust optimization (MORO) approaches have been developed to find Pareto robust solutions. While the literature reports on many techniques in MORO, few papers focus on using multi-objective differential evolution (MODE) for robust optimization (RO) and performance improvement of its solutions. In this article, MODE is first modified and developed for RO problems with interval uncertainty, formulating a new MODE-RO algorithm. To improve the solutions’ quality of MODE-RO, a new hybrid (MODE-sequential quadratic programming (SQP)-RO) algorithm is proposed further, where SQP is incorporated into the procedure to enhance the local search. The proposed hybrid approach takes the advantage of MODE for its capability of handling not-well behaved robust constraint functions and SQP for its fast local convergence. Two numerical and one engineering examples, with two or three objective functions, are tested to demonstrate the applicability and performance of the proposed algorithms. The results show that MODE-RO is effective in solving MORO problems while, on the average, MODE-SQP-RO improves the quality of robust solutions obtained by MODE-RO with comparable numbers of function evaluations.

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.

Multiobjective Collaborative Robust Optimization (McRO) With Interval Uncertainty and Interdisciplinary Uncertainty Propagation

2007 ◽  
Author(s):  
Mian Li ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Optimization Problems ◽  
Uncertainty Propagation ◽  
Multiple Objectives ◽  
Interval Uncertainty ◽  
Optimization Approach ◽  
Collaborative Robust Optimization ◽  
Fully Coupled

Real-world engineering design optimization problems often involve systems that have coupled disciplines with uncontrollable variations in their parameters. No approach has yet been reported for the solution of these problems when there are multiple objectives in each discipline, mixed continuous-discrete variables, and when there is a need to account for uncertainty and also uncertainty propagation across disciplines. We present a Multiobjective collaborative Robust Optimization (McRO) approach for this class of problems that have interval uncertainty in their parameters. McRO obtains Multidisciplinary Design Optimization (MDO) solutions which are as best as possible in a multiobjective and multidisciplinary sense. For McRO solutions, the sensitivity of objective and/or constraint functions is kept within an acceptable range. McRO involves 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 the approach to a numerical and an engineering example are presented. It is concluded that the McRO approach can solve fully coupled MDO problems with interval uncertainty and can obtain solutions that are comparable to an all-at-once robust optimization approach.

Integrated multi-objective robust optimization and sensitivity analysis with irreducible and reducible interval uncertainty

2009 ◽  
Vol 41 (10) ◽  
pp. 889-908 ◽  
Author(s):  
M. Li ◽  
S. Azarm ◽  
N. Williams ◽  
S. Al Hashimi ◽  
A. Almansoori ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Robust Optimization ◽  
Interval Uncertainty ◽  
Multi Objective

Improving Multi-Objective Robust Optimization Under Interval Uncertainty Using Worst Possible Point Constraint Cuts

2009 ◽  
Author(s):  
W. Hu ◽  
M. Li ◽  
S. Azarm ◽  
S. Al Hashimi ◽  
A. Almansoori ◽  
...  
Keyword(s):  
Robust Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Computational Effort ◽  
Interval Uncertainty ◽  
Master Problem ◽  
Multi Objective ◽  
Acceptable Range ◽  
Function Calls ◽  
Order Of Magnitude

Many real-world engineering design optimization problems are multi-objective and have uncertainty in their parameters. For such problems it is useful to obtain design solutions that are both multi-objectively optimum and robust. A robust design is one whose objective and constraint function variations under uncertainty are within an acceptable range. While the literature reports on many techniques in robust optimization for single objective optimization problems, very few papers report on methods in robust optimization for multi-objective optimization problems. The Multi-Objective Robust Optimization (MORO) technique with interval uncertainty proposed in this paper is a significant improvement, with respect to computational effort, over a previously reported MORO technique. In the proposed technique, a master problem solves a relaxed optimization problem whose feasible domain is iteratively confined by constraint cuts determined by the solutions from a sub-problem. The proposed approach and the synergy between the master problem and sub-problem are demonstrated by three examples. The results obtained show a general agreement between the solutions from the proposed MORO and the previous MORO technique. Moreover, the number of function calls for obtaining solutions from the proposed technique is an order of magnitude less than that from the previous MORO technique.

Multi-Objective Robust Optimization for Planning of Mineral Processing under Uncertainty

2021 ◽  
Author(s):  
Quan Xu ◽  
Kesheng Zhang ◽  
Mingyu Li ◽  
Yangang Chu ◽  
Danwei Zhang
Keyword(s):  
Robust Optimization ◽  
Mineral Processing ◽  
Multi Objective
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