Design Space Reduction for Multi-Objective Optimization and Robust Design Optimization Problems

2004 ◽  
Author(s):  
G. Gary Wang ◽  
Songqing Shan
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Design Space ◽  
Optimization Problems ◽  
Robust Design Optimization ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Space Reduction

Multi-objective approach for robust design optimization problems

2007 ◽  
Vol 15 (1) ◽  
pp. 47-59 ◽  
Author(s):  
Igor N. Egorov ◽  
Gennadiy V. Kretinin ◽  
Igor A. Leshchenko ◽  
Sergey V. Kuptzov
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Optimization Problems ◽  
Robust Design Optimization ◽  
Multi Objective

Time-Dependent Reliability-Based Robust Design Optimization via Extreme Value Moment Method

2018 ◽  
Author(s):  
Shui Yu ◽  
Zhonglai Wang
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Robust Design ◽  
Moment Method ◽  
Time Dependent ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Multi Objective Optimization ◽  
Integrated Framework ◽  
Multi Objective

During the product design and development stage, design engineers often encounter reliability and robustness of dynamic uncertain structures. Meanwhile, time-varying and high nonlinear performance are the basic characteristics of reliability analysis and design. Hence, the time-dependent reliability analysis and integrating reliability-based design with robust design become a primary challenge in reliability-based robust design optimization. This paper proposes a multi-objective integrated framework for time-dependent reliability-based robust design optimization and the corresponding algorithms. The multi-objective integrated framework, which minimizes the mean value and coefficient of variation for the objective function at the same time subject to time-dependent probabilistic constraints, is first established. The time-dependent probabilistic constraints are then converted into deterministic constraints using a combination of moment method and the sparse grid based stochastic collocation method. The evolutionary multi-objective optimization algorithm is finally employed for the deterministic multi-objective optimization problem. Several examples are investigated to demonstrate the effectiveness of the proposed method.

Reliability-Based Robust Design Optimization in Consideration of Manufacturing Tolerance by Multi-Objective Evolutionary Optimization with Repair Algorithm

2021 ◽  
pp. 2150005
Author(s):  
Gang Li ◽  
Ye Liu ◽  
Gang Zhao ◽  
Yan Zeng
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Robust Design Optimization ◽  
Manufacturing Cost ◽  
Multi Objective Optimization ◽  
Random Design ◽  
Multi Objective ◽  
Design Variables ◽  
Objective Robustness ◽  
Repair Operator

There are inherently various uncertainties in practical engineering, and reliability-based design optimization (RBDO) and robust design optimization (RDO) are two well-established methodologies when considering the uncertainties. Naturally, reliability-based robust design optimization (RBRDO) is a methodology developed recently by combining RBDO and RDO, in which the tolerances of random design variables are always assumed as constants. However, the tolerance of random design variables is a key factor for the objective robustness and manufacturing cost, and the tolerance allocation is the core problem in mechanical manufacturing. Inspired by the cost–tolerance relationship in mechanical manufacturing, this paper presents an integrated framework to simultaneously find the optimal design variable and the corresponding tolerance in the multi-objective RBRDO, with the trade-off between objective robustness and manufacturing cost. The failure mechanism of the constraint handling strategy of the constrained reference vector-guided evolutionary algorithm (C-RVEA) is discussed to solve the multi-objective optimization formulation. Then the robust repair operator and reliability-based repair operator are proposed to transform unfeasible solutions to the feasible ones under reliability constraints. Numerical results reveal that the proposed repair algorithm is effective. By solving the integrated multi-objective optimization problem, the Pareto front with the compromised solutions between the objective robustness and manufacturing cost could be obtained, from which decision makers can select the satisfying solution conveniently according to the preferred requirements.

A Robust Design Optimization Method Considering Correlated Intervals

2019 ◽  
Vol 17 (10) ◽  
pp. 1950079
Author(s):  
Qiong Wang
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Optimization Model ◽  
Optimization Method ◽  
Robust Design Optimization ◽  
System Response ◽  
Multi Objective Optimization ◽  
Convex Model ◽  
Interval Model ◽  
Multi Objective

In the robust design, correlations of uncertain parameters exist widely and have an influence on the results in most cases. It is essential to develop a robust design optimization method considering parametric correlation to future improve the analysis accuracy and engineering applicability. In this paper, a robust design optimization method based on multidimensional parallelepiped convex model is presented. Considering the effects of the interval uncertainties and their correlations, a robust design optimization model considering correlated intervals is established. In the established model, the average performance and robustness of the system response of concern are taken as the design optimization objectives, and the correlations among interval parameters are quantified by integrating the multidimensional parallelepiped convex model. And then, through an independence transforming procedure it can be converted into an independent interval model, which is ultimately converted into a deterministic multi-objective optimization model by using the interval possibility degree to cope with the uncertain constraints. Finally, the deterministic multi-objective optimization model is treated by coupling an efficient micro multi-objective genetic algorithm with the first order Taylor expansion. The feasibility and practicability of the proposed method are demonstrated by the numerical and engineering examples.

Time-Dependent Reliability-Based Robust Design Optimization Using Evolutionary Algorithm

2019 ◽  
Vol 5 (2) ◽  
Author(s):  
Shui Yu ◽  
Zhonglai Wang ◽  
Zhihua Wang
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Dynamic Properties ◽  
Time Dependent ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Multi Objective Optimization ◽  
Engineering Structures ◽  
Integrated Framework ◽  
Multi Objective

Due to the uncertain and dynamic parameters from design, manufacturing, and working conditions, many engineering structures usually show uncertain and dynamic properties. During the product design and development stages, designers often encounter reliability and robustness measures of dynamic uncertain structures. Time-varying and high nonlinear performance brings a new challenge for the reliability-based robust design optimization. This paper proposes a multi-objective integrated framework for time-dependent reliability-based robust design optimization and the corresponding algorithms. The integrated framework is first established by minimizing the mean value and coefficient of variation of the objective performance at the same time subject to time-dependent probabilistic constraints. The time-dependent probabilistic constraints are then converted into deterministic constraints using the dimension reduction method. The evolutionary multi-objective optimization algorithm is finally employed for the deterministic multi-objective optimization problem. Several examples are investigated to demonstrate the effectiveness of the proposed method.

Expected-Improvement-Based Methods for Adaptive Sampling in Multi-Objective Optimization Problems

2016 ◽  
Author(s):  
Jesper Kristensen ◽  
You Ling ◽  
Isaac Asher ◽  
Liping Wang
Keyword(s):  
Convex Hull ◽  
Design Optimization ◽  
Adaptive Sampling ◽  
Pareto Front ◽  
Performance Metrics ◽  
Sampling Methods ◽  
Optimization Problems ◽  
Expected Improvement ◽  
Multi Objective Optimization ◽  
Multi Objective

Adaptive sampling methods have been used to build accurate meta-models across large design spaces from which engineers can explore data trends, investigate optimal designs, study the sensitivity of objectives on the modeling design features, etc. For global design optimization applications, adaptive sampling methods need to be extended to sample more efficiently near the optimal domains of the design space (i.e., the Pareto front/frontier in multi-objective optimization). Expected Improvement (EI) methods have been shown to be efficient to solve design optimization problems using meta-models by incorporating prediction uncertainty. In this paper, a set of state-of-the-art methods (hypervolume EI method and centroid EI method) are presented and implemented for selecting sampling points for multi-objective optimizations. The classical hypervolume EI method uses hyperrectangles to represent the Pareto front, which shows undesirable behavior at the tails of the Pareto front. This issue is addressed utilizing the concepts from physical programming to shape the Pareto front. The modified hypervolume EI method can be extended to increase local Pareto front accuracy in any area identified by an engineer, and this method can be applied to Pareto frontiers of any shape. A novel hypervolume EI method is also developed that does not rely on the assumption of hyperrectangles, but instead assumes the Pareto frontier can be represented by a convex hull. The method exploits fast methods for convex hull construction and numerical integration, and results in a Pareto front shape that is desired in many practical applications. Various performance metrics are defined in order to quantitatively compare and discuss all methods applied to a particular 2D optimization problem from the literature. The modified hypervolume EI methods lead to dramatic resource savings while improving the predictive capabilities near the optimal objective values.

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