A Methodology for Trading-Off Performance and Robustness Under Uncertainty

2005 ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Jinghong Liang
Keyword(s):  
Design Optimization ◽  
Pareto Frontier ◽  
Mathematical Optimization ◽  
Optimization Method ◽  
Mean Value ◽  
Preference Aggregation ◽  
Efficient Design ◽  
Multi Objective ◽  
Reliability Based Design ◽  
Reliability And Robustness

Mathematical optimization plays an important role in engineering design, leading to greatly improved performance. Deterministic optimization however, may result in undesired choices because it neglects uncertainty. Reliability-based design optimization (RBDO) and robust design can improve optimization by considering uncertainty. This paper proposes an efficient design optimization method under uncertainty, which simultaneously considers reliability and robustness. A mean performance is traded-off against robustness for a given reliability level of all performance targets. This results in a probabilistic multi-objective optimization problem. Variation is expressed in terms of a percentile difference, which is efficiently computed using the Advanced Mean Value (AMV) method. A preference aggregation method converts the multi-objective problem to a single-objective problem, which is then solved using an RBDO approach. Indifference points are used to select the best solution without calculating the entire Pareto frontier. Examples illustrate the concepts and demonstrate their applicability.

A Methodology for Trading-Off Performance and Robustness Under Uncertainty

2005 ◽  
Vol 128 (4) ◽  
pp. 856-863 ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Jinghong Liang
Keyword(s):  
Design Optimization ◽  
Pareto Frontier ◽  
Mathematical Optimization ◽  
Optimization Method ◽  
Mean Value ◽  
Preference Aggregation ◽  
Efficient Design ◽  
Reliability Based Design ◽  
Advanced Mean Value ◽  
Reliability And Robustness

Mathematical optimization plays an important role in engineering design, leading to greatly improved performance. Deterministic optimization, however, may result in undesired choices because it neglects uncertainty. Reliability-based design optimization (RBDO) and robust design can improve optimization by considering uncertainty. This paper proposes an efficient design optimization method under uncertainty, which simultaneously considers reliability and robustness. A mean performance is traded-off against robustness for a given reliability level of all performance targets. This results in a probabilistic multiobjective optimization problem. Variation is expressed in terms of a percentile difference, which is efficiently computed using the advanced mean value method. A preference aggregation method converts the multiobjective problem to a single-objective problem, which is then solved using an RBDO approach. Indifference points are used to select the best solution without calculating the entire Pareto frontier. Examples illustrate the concepts and demonstrate their applicability.

Reliability-Based Multi-Objective Optimization Methodology for Engineering Systems

2006 ◽  
Author(s):  
Kaushik Sinha
Keyword(s):  
Design Optimization ◽  
Optimization Method ◽  
Performance Measure ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Automotive Body ◽  
Reliability Based Design ◽  
Pareto Optimal Set ◽  
Optimization Methodology

This paper presents a methodology for reliability-based multi-objective design optimization (RBMODO) of automotive body components under impact scenario. Conflicting design requirements arise as one tries, for example, to minimize structural mass while maximizing energy absorption of an automotive rail section under structural and occupant safety related performance measure constraints. Because deterministic optimum designs obtained without taking uncertainty into account could lead to unreliable designs, a reliability-based approach to design optimization is preferable using a Reliability-based design optimization method. Uncertainty quantification is performed using two methods: reliability based approach and robustness based approach. The technique employed here treats multiple objective functions separately without combining them in any form. A decision-making criterion is subsequently invoked to select the “best” subset of solutions from the obtained non-dominated Pareto optimal solutions. The pareto optimal set obtained in case are compared and contrasted and observations made comparing reliability based approach vis-a`-vis robustness based approach. Deterministic, reliability-based and robustness based multi-objective optimization solutions are compared.

scholarly journals A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 149
Author(s):  
Yaohui Li ◽  
Jingfang Shen ◽  
Ziliang Cai ◽  
Yizhong Wu ◽  
Shuting Wang
Keyword(s):  
Global Optimization ◽  
Pareto Frontier ◽  
Kriging Model ◽  
Optimization Method ◽  
Function Evaluation ◽  
Sampling Point ◽  
Constrained Global Optimization ◽  
Multi Objective ◽  
Sample Data ◽  
Sampling Points

The kriging optimization method that can only obtain one sampling point per cycle has encountered a bottleneck in practical engineering applications. How to find a suitable optimization method to generate multiple sampling points at a time while improving the accuracy of convergence and reducing the number of expensive evaluations has been a wide concern. For this reason, a kriging-assisted multi-objective constrained global optimization (KMCGO) method has been proposed. The sample data obtained from the expensive function evaluation is first used to construct or update the kriging model in each cycle. Then, kriging-based estimated target, RMSE (root mean square error), and feasibility probability are used to form three objectives, which are optimized to generate the Pareto frontier set through multi-objective optimization. Finally, the sample data from the Pareto frontier set is further screened to obtain more promising and valuable sampling points. The test results of five benchmark functions, four design problems, and a fuel economy simulation optimization prove the effectiveness of the proposed algorithm.

scholarly journals Optimizing the 3D Distributed Climate inside Greenhouses Using Multi-Objective Optimization Algorithms and Computer Fluid Dynamics

Energies ◽  
2019 ◽  
Vol 12 (15) ◽  
pp. 2873 ◽  
Author(s):  
Kangji Li ◽  
Wenping Xue ◽  
Hanping Mao ◽  
Xu Chen ◽  
Hui Jiang ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Field Experiments ◽  
Climate Model ◽  
Pareto Frontier ◽  
Environmental Parameters ◽  
Optimization Method ◽  
Crop Growth ◽  
Control Variables ◽  
Greenhouse Production ◽  
Multi Objective

As one of the major production facilities in agriculture, a greenhouse has many spatial distributed factors influencing crop growth and energy consumption, such as temperature field, air flow pattern, CO 2 concentration distribution, etc. By introducing a hybrid computational fluid dynamics–evolutionary algorithm (CFD-EA) method, this paper constructs a micro-climate model of greenhouse with main environmental parameters optimized. Considering environmental factors’ spatial influences together with energy usage simultaneously, the optimal solutions of control variables for crop growth are calculated. A commercial greenhouse located in east China is chosen for the method validation. Field experiments using temperature/velocity sensor matrix are carried out for CFD accuracy investigation. On this basis, the proposed optimization method is employed to search for the optimal control variables and parameters corresponding to the environmental Pareto frontier. By the proposed multi-objective scheme, we believe the method can provide set point basis for the design and regulation of large/medium-sized greenhouse production with high spatial resolution.

Sign in / Sign up

Export Citation Format

Share Document