Towards a Better Understanding of Modeling Feasibility Robustness in Engineering Design

1999 ◽  
Vol 122 (4) ◽  
pp. 385-394 ◽  
Author(s):  
Xiaoping Du ◽  
Wei Chen
Keyword(s):  
Robust Design ◽  
Optimization Problems ◽  
Practical Significance ◽  
Engineering Practice ◽  
Probabilistic Optimization ◽  
Importance Sampling Method ◽  
Feasibility Evaluation ◽  
Feasibility Robustness ◽  
Computationally Intensive ◽  
Six Sigma Approach

In robust design, it is important not only to achieve robust design objectives but also to maintain the robustness of design feasibility under the effect of variations (or uncertainties). However, the evaluation of feasibility robustness is often a computationally intensive process. Simplified approaches in existing robust design applications may lead to either over-conservative or infeasible design solutions. In this paper, several feasibility-modeling techniques for robust optimization are examined. These methods are classified into two categories: methods that require probability and statistical analyses and methods that do not. Using illustrative examples, the effectiveness of each method is compared in terms of its efficiency and accuracy. Constructive recommendations are made to employ different techniques under different circumstances. Under the framework of probabilistic optimization, we propose to use a most probable point (MPP) based importance sampling method, a method rooted in the field of reliability analysis, for evaluating the feasibility robustness. The advantages of this approach are discussed. Though our discussions are centered on robust design, the principles presented are also applicable for general probabilistic optimization problems. The practical significance of this work also lies in the development of efficient feasibility evaluation methods that can support quality engineering practice, such as the Six Sigma approach that is being widely used in American industry. [S1050-0472(00)00904-1]

Towards a Better Understanding of Modeling Feasibility Robustness in Engineering Design

1999 ◽  
Author(s):  
Xiaoping Du ◽  
Wei Chen
Keyword(s):  
Robust Optimization ◽  
Robust Design ◽  
Optimization Problems ◽  
Statistical Analyses ◽  
Practical Significance ◽  
Worst Case Analysis ◽  
Engineering Practice ◽  
Worst Case ◽  
Feasibility Robustness ◽  
Six Sigma Approach

Abstract In robust design, it is important not only to achieve robust design objectives but also to maintain the robustness of design feasibility under the effect of variations (or uncertainties). However, the evaluation of feasibility robustness is often a computationally intensive process. Simplified approaches in existing robust design applications may lead to either over-conservative or infeasible design solutions. In this paper, several feasibility-modeling techniques for robust optimization are examined. These methods are classified into two categories: methods that require probability and statistical analyses (i.e., the probabilistic feasibility formulation and the moment matching method) and methods do not require probability and statistical analyses (i.e., the worst case analysis, the corner space evaluation, and the variation pattern method). Using illustrative examples, the effectiveness of each method is compared in terms of its efficiency and accuracy. Constructive recommendations are made to employ different techniques for modeling feasibility robustness under different circumstances. Under the framework of probabilistic robust optimization, we propose to use a most probable point (MPP) based importance sampling method, a method rooted in the field of reliability analysis, for evaluating the feasibility robustness. The advantages of this approach are discussed. Though our discussions are centered on robust design, the principles presented are also applicable for general probabilistic optimization problems. The practical significance of this work also lies in the development of efficient feasibility evaluation methods that can support quality engineering practice, such as the Six Sigma approach that is being widely used in American industry.

scholarly journals Novel Robust Design Method of Multilayer Optical Coatings

ISRN Optics ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Suyong Wu ◽  
Xingwu Long ◽  
Kaiyong Yang
Keyword(s):  
Robust Design ◽  
Optimization Design ◽  
Design Method ◽  
Analytical Calculation ◽  
Design Procedure ◽  
Deposition Process ◽  
Practical Significance ◽  
Optical Coatings ◽  
Optical Films ◽  
Robust Design Method

We present a novel fast robust design method of multilayer optical coatings. The sensitivity of optical films to production errors is controlled in the whole optimization design procedure. We derive an analytical calculation model for fast robust design of multilayer optical coatings. We demonstrate its effectiveness by successful application of the robust design method to a neutral beam splitter. It is showed that the novel robust design method owns an inherent fast computation characteristic and the designed film is insensitive to the monitoring thickness errors in deposition process. This method is especially of practical significance to improve the mass production yields and repetitive production of high-quality optical coatings.

A Culture-Based Particle Swarm Optimization Framework for Dynamic, Constrained Multi-Objective Optimization

2012 ◽  
Vol 3 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Ashwin A. Kadkol ◽  
Gary G. Yen
Keyword(s):  
Particle Swarm Optimization ◽  
Transfer Functions ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Parameter Tuning ◽  
Cultural Algorithms ◽  
Swarm Optimization ◽  
Objective Space ◽  
Computationally Intensive ◽  
Available Information

Real-world optimization problems are often dynamic, multiple objective in nature with various constraints and uncertainties. This work proposes solving such problems by systematic segmentation via heuristic information accumulated through Cultural Algorithms. The problem is tackled by maintaining 1) feasible and infeasible best solutions and their fitness and constraint violations in the Situational Space, 2) objective space bounds for the search in the Normative Space, 3) objective space crowding information in the Topographic Space, and 4) function sensitivity and relocation offsets (to reuse available information on optima upon change of environments) in the Historical Space of a cultural framework. The information is used to vary the flight parameters of the Particle Swarm Optimization, to generate newer individuals and to better track dynamic and multiple optima with constraints. The proposed algorithm is validated on three numerical optimization problems. As a practical application case study that is computationally intensive and complex, parameter tuning of a PID (Proportional–Integral–Derivative) controller for plants with transfer functions that vary with time and imposed with robust optimization criteria has been used to demonstrate the effectiveness and efficiency of the proposed design.

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

Sequential Quadratic Programming for Robust Optimization With Interval Uncertainty

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Jianhua Zhou ◽  
Shuo Cheng ◽  
Mian Li
Keyword(s):  
Quadratic Programming ◽  
Robust Optimization ◽  
Sequential Quadratic Programming ◽  
Optimization Problems ◽  
Critical Role ◽  
Interval Uncertainty ◽  
Design Solution ◽  
Novel Approach ◽  
Design Variables ◽  
Feasibility Robustness

Uncertainty plays a critical role in engineering design as even a small amount of uncertainty could make an optimal design solution infeasible. The goal of robust optimization is to find a solution that is both optimal and insensitive to uncertainty that may exist in parameters and design variables. In this paper, a novel approach, sequential quadratic programming for robust optimization (SQP-RO), is proposed to solve single-objective continuous nonlinear optimization problems with interval uncertainty in parameters and design variables. This new SQP-RO is developed based on a classic SQP procedure with additional calculations for constraints on objective robustness, feasibility robustness, or both. The obtained solution is locally optimal and robust. Eight numerical and engineering examples with different levels of complexity are utilized to demonstrate the applicability and efficiency of the proposed SQP-RO with the comparison to its deterministic SQP counterpart and RO approaches using genetic algorithms. The objective and/or feasibility robustness are verified via Monte Carlo simulations.

scholarly journals Educational Information System Optimization for Artificial Intelligence Teaching Strategies

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Taotang Liu ◽  
Zhongxin Gao ◽  
Honghai Guan
Keyword(s):  
Artificial Intelligence ◽  
Information System ◽  
Network Architecture ◽  
Optimization Problems ◽  
Optimization Methods ◽  
System Optimization ◽  
Engineering Problem ◽  
Engineering Practice ◽  
Local Optimum ◽  
Clustering Method

Under the background of the information age, scientific research and engineering practice have developed vigorously, resulting in many complex optimization problems that are difficult to solve. How to design more effective optimization methods has become the focus of urgent solutions in many academic fields. Under the guidance of such demand, intelligent optimization algorithms have emerged. This article analyzes and optimizes the modern artificial intelligence teaching information system in detail. On the basis of determining the network architecture, a detailed demand analysis was carried out, and the overall structure optimization of the network was given; the business process and data flow of the main modules of the website (resource center module and collaborative learning module) were optimized. In order to further enhance the local search ability of the algorithm, a multiclass interactive optimization algorithm is proposed in combination with the Euclidean distance-based clustering method, which changes the teaching mode from “one-person teaching” to “multiperson teaching.” This clustering method has lower complexity and is beneficial to enhance the utilization of neighborhood information. At the same time, in order to enhance the diversity of the population and strengthen the connection between the subgroups, after the teaching phase, the worst students in each subgroup are allowed to learn from the best teachers of the population, and after the learning phase, individuals in a random subgroup are allowed to learn from other subgroups. The algorithm was tested in the experimental environment of unconstrained, constrained, and an engineering problem. From the test results, it can be seen that the algorithm is not easy to fall into the local optimum. Compared with other algorithms, the solution accuracy is higher and the stability is better. And it performed well in engineering optimization problems, thus verifying the effectiveness of the strategy.

Local Approximation of the Efficient Frontier in Robust Design

1999 ◽  
Author(s):  
Jinhuan Zhang ◽  
Margaret M. Wiecek ◽  
Wei Chen
Keyword(s):  
Utility Function ◽  
Robust Design ◽  
Optimization Problems ◽  
Design Procedure ◽  
Efficient Frontier ◽  
Pareto Solution ◽  
Quadratic Utility ◽  
Weighted Sum Method ◽  
Quality Aspects ◽  
Design Solutions

Abstract The multiple quality aspects of robust design have brought more and more attention in the advancement of robust design methods. Neither the Taguchi’s signal-to-noise ratio nor the weighted-sum method is adequate in addressing designer’s preference in making tradeoffs between the mean and variance attributes. An interactive multiobjective robust design procedure that follows upon the developments on relating utility function optimization to a multiobjective programming method has been proposed by the authors. This paper is an extension of our previous work on this topic. It presents a formal procedure for deriving a quadratic utility function at a candidate solution as an approximation of the efficient frontier to explore alternative robust design solutions. The proposed procedure is investigated at different locations of candidate solutions, with different ranges of interest, and for efficient frontiers with both convex and nonconvex behaviors. This quadratic utility function provides a decision maker with new information regarding how to choose a most preferred Pareto solution. As an integral part of the interactive robust design procedure, the proposed method assists designers in adjusting the preference structure and exploring alternative efficient robust design solutions. It eliminates the needs of solving the original bi-objective optimization problem repeatedly using new preference structures, which is often a computationally expensive task for problems in a complex domain. Though demonstrated for robust design problems, the principle is also applicable to any bi-objective optimization problems.

Parameterized Design Optimization of a Magnetohydrodynamic Liquid Metal Active Cooling Concept

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Darren J. Hartl ◽  
Edgar Galvan ◽  
Richard J. Malak ◽  
Jeffrey W. Baur
Keyword(s):  
Liquid Metal ◽  
Design Optimization ◽  
Optimization Problems ◽  
Material Design ◽  
Element Model ◽  
Algebraic Model ◽  
Engineering Problem ◽  
Computationally Efficient ◽  
Design Selection ◽  
Computationally Intensive

The success of model-based multifunctional material design efforts relies on the proper development of multiphysical models and advanced optimization algorithms. This paper addresses both in the context of a structure that includes a liquid metal (LM) circuit for integrated cooling. We demonstrate for the first time on a complex engineering problem the use of a parameterized approach to design optimization that solves a family of optimization problems as a function of parameters exogenous to the subsystem of interest. This results in general knowledge about the capabilities of the subsystem rather than a restrictive point solution. We solve this specialized problem using the predictive parameterized Pareto genetic algorithm (P3GA) and show that it efficiently produces results that are accurate and useful for design exploration and reasoning. A “population seeding” approach allows an efficient multifidelity approach that combines a computationally efficient reduced-fidelity algebraic model with a computationally intensive finite-element model. Using data output from P3GA, we explore different design scenarios for the LM thermal management concept and demonstrate how engineers can make a final design selection once the exogenous parameters are resolved.

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