Robust optimization based on a polynomial expansion of chaos constructed with integration point rules

2008 ◽  
Vol 223 (5) ◽  
pp. 1263-1272 ◽  
Author(s):  
D L Wei ◽  
Z S Cui ◽  
J Chen
Keyword(s):  
Robust Optimization ◽  
Engineering Design ◽  
Uncertainty Propagation ◽  
Probabilistic Approach ◽  
Main Idea ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Computationally Efficient ◽  
Design Problems ◽  
Engineering Design Problems

Robust optimization is a probabilistic approach to engineering design under uncertainty. The main idea is to select designs insensitive to changes in given parameters. Robust optimization using numerical simulations for black-box problems has received increasing interest. However, when the simulation programmes are computationally expensive, robust optimization is difficult to implement due to the intensive computational demand of uncertainty propagation. Based on polynomial chaos expansion (PCE), an efficient robust optimization method is presented. The PCE is constructed with points of monomial cubature rules (MCRs) to approximate the original model. As the number of points of MCRs is small and all of the points are sampled, the robust optimization procedure is computationally efficient and stable. Two engineering design problems are employed to demonstrate the availability of the proposed method.

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.

Multi-Objective Optimal Design of Automotive Engine Using Genetic Algorithm

1998 ◽  
Author(s):  
Kikuo Fujita ◽  
Noriyasu Hirokawa ◽  
Shinsuke Akagi ◽  
Shinji Kitamura ◽  
Hideaki Yokohata
Keyword(s):  
Genetic Algorithm ◽  
Engineering Design ◽  
Design Problem ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Total Power ◽  
Design Problems ◽  
Automotive Engine ◽  
Multi Objective ◽  
Engineering Design Problems

Abstract A genetic algorithm based optimization method is proposed for a multi-objective design problem of an automotive engine, that includes several difficulties in practical engineering optimization problems. While various optimization techniques have been applied to engineering design problems, a class of realistic engineering design problems face on a mixture of different optimization difficulties, such as the rugged nature of system response, the numbers of design variables and objectives, etc. In order to overcome such a situation, this paper proposes a genetic algorithm based multi-objective optimization method, that introduces Pareto-optimality based fitness function, similarity based selection and direct real number crossover. This optimization method is also applied to the design problem of an automotive engine with the design criteria on a total power train. The computational examples show the ability of the proposed method for finding a relevant set of Pareto optima.

Reliability Optimization Involving Mixed Continuous-Discrete Uncertainties

2005 ◽  
Author(s):  
Subroto Gunawan ◽  
Panos Y. Papalambros
Keyword(s):  
Engineering Design ◽  
Optimization Method ◽  
Spatial Distance ◽  
Reliability Optimization ◽  
Discrete Variables ◽  
Design Problems ◽  
Engineering Design Problems

Engineering design problems frequently involve a mix of both continuous and discrete uncertainties. However, most methods in the literature deal with either continuous or discrete uncertainties, but not both. In particular, no method has yet addressed uncertainty for categorically discrete variables or parameters. This article develops an efficient optimization method for problems involving mixed continuous-discrete uncertainties. The method reduces the number of function evaluations performed by systematically filtering the discrete factorials used for estimating reliability based on their importance. This importance is assessed using the spatial distance from the feasible boundary and the probability of the discrete components. The method is demonstrated in examples and is shown to be very efficient with only small errors.

A Unified Approach to Solving Graph Based Design Problems

2007 ◽  
Author(s):  
Matthew I. Campbell ◽  
Sandeep Nair ◽  
Jay Patel
Keyword(s):  
Engineering Design ◽  
Graph Transformation ◽  
Electric Circuit ◽  
Optimization Method ◽  
Graph Grammar ◽  
Science Literature ◽  
Design Problems ◽  
Novel Approach ◽  
Engineering Design Problems ◽  
Graph Transformation Systems

This paper proposes a new perspective of using graph transformation systems as a way of organizing and solving engineering design problems. Using this novel technique the synthesis of optimal solutions in the form of graph topologies for design problems is made possible. Though the concept of graph grammars has existed for several decades in computer science literature, researchers in the field of design have now begun to realize the merit of using them to harness both the knowledge and heuristics of a particular problem domain. This paper examines the fundamental challenges in applying graph transformations in a design context. The paper also presents the first topology optimization method that has been developed specifically for domains representable by a graph grammar schema. This novel approach could also be used in several problems such as network problems (especially in determining the placement of hubs), electric circuit design, neural networks, sheet metal, and product architecture. The abstraction afforded by graphs also enables us to tackle multi-disciplinary problems found throughout engineering design. A few engineering examples are shown in this paper in order to illustrate the power of the approach in automating the design process.

A Flexible Optimization Procedure for Mechanical Component Design Based on Genetic Adaptive Search

1998 ◽  
Vol 120 (2) ◽  
pp. 162-164 ◽  
Author(s):  
K. Deb ◽  
M. Goyal
Keyword(s):  
Engineering Design ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Optimization Procedure ◽  
Continuous Variables ◽  
Design Problems ◽  
Component Design ◽  
Engineering Design Problems ◽  
Complex Engineering ◽  
Optimum Solution

A flexible algorithm for solving nonlinear engineering design optimization problems involving zero-one, discrete, and continuous variables is presented. The algorithm restricts its search only to the permissible values of the variables, thereby reducing the search effort in converging near the optimum solution. The efficiency and ease of application of the proposed method is demonstrated by solving four different mechanical design problems chosen from the optimization literature. These results are encouraging and suggest the use of the technique to other more complex engineering design problems.

Reliability Optimization With Mixed Continuous-Discrete Random Variables and Parameters

2006 ◽  
Vol 129 (2) ◽  
pp. 158-165 ◽  
Author(s):  
Subroto Gunawan ◽  
Panos Y. Papalambros
Keyword(s):  
Engineering Design ◽  
Random Variables ◽  
Optimization Method ◽  
Spatial Distance ◽  
Reliability Optimization ◽  
Design Problems ◽  
Discrete Random Variables ◽  
Engineering Design Problems ◽  
Random Components ◽  
Discrete Type

Engineering design problems frequently involve a mix of both continuous and discrete random variables and parameters. However, most methods in the literature deal with only the continuous or the discrete type, but not both. In particular, no method has yet addressed problems for which the random components (variables and∕or parameters) are categorically discrete. This paper develops an efficient optimization method for problems involving mixed continuous-discrete random variables and parameters. The method reduces the number of function evaluations performed by systematically filtering the discrete combinations used for estimating reliability based on their importance. This importance is assessed using the spatial distance from the feasible boundary and the probability of the discrete components. The method is demonstrated in examples and is shown to be very efficient with only small errors.

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