Approximation Assisted Multiobjective Optimization With Combined Global and Local Metamodeling

2012 ◽  
Author(s):  
W. Hu ◽  
K. H. Saleh ◽  
S. Azarm
Keyword(s):  
Multiobjective Optimization ◽  
Engineering Design ◽  
Design Space ◽  
Pareto Optimum ◽  
Optimization Approach ◽  
Design Problems ◽  
Engineering Design Problems ◽  
Computationally Intensive ◽  
Global And Local ◽  
Global Metamodeling

Approximation Assisted Optimization (AAO) is widely used in engineering design problems to replace computationally intensive simulations with metamodeling. Traditional AAO approaches employ global metamodeling for exploring an entire design space. Recent research works in AAO report on using local metamodeling to focus on promising regions of the design space. However, very limited works have been reported that combine local and global metamodeling within AAO. In this paper, a new approximation assisted multiobjective optimization approach is developed. In the proposed approach, both global and local metamodels for objective and constraint functions are used. The approach starts with global metamodels for objective and constraint functions and using them it selects the most promising points from a large number of randomly generated points. These selected points are then “observed”, which means their actual objective/constraint function values are computed. Based on these values, the “best” points are grouped in multiple clustered regions in the design space and then local metamodels of objective/constraint functions are constructed in each region. All observed points are also used to iteratively update the metamodels. In this way, the predictive capabilities of the metamodels are progressively improved as the optimizer approaches the Pareto optimum frontier. An advantage of the proposed approach is that the most promising points are observed and that there is no need to verify the final solutions separately. Several numerical examples are used to compare the proposed approach with previous approaches in the literature. Additionally, the proposed approach is applied to a CFD-based engineering design example. It is found that the proposed approach is able to estimate Pareto optimum points reasonably well while significantly reducing the number of function evaluations.

On combinatorial design spaces for the configuration design of product families

2001 ◽  
Vol 15 (2) ◽  
pp. 91-108 ◽  
Author(s):  
ZAHED SIDDIQUE ◽  
DAVID W. ROSEN
Keyword(s):  
Engineering Design ◽  
Design Space ◽  
Optimization Problems ◽  
Product Family ◽  
Product Variety ◽  
Combinatorial Design ◽  
Configuration Design ◽  
Design Problems ◽  
Engineering Design Problems ◽  
Space Modeling

For typical optimization problems, the design space of interest is well defined: It is a subset of Rn, where n is the number of (continuous) variables. Constraints are often introduced to eliminate infeasible regions of this space from consideration. Many engineering design problems can be formulated as search in such a design space. For configuration design problems, however, the design space is much more difficult to define precisely, particularly when constraints are present. Configuration design spaces are discrete and combinatorial in nature, but not necessarily purely combinatorial, as certain combinations represent infeasible designs. One of our primary design objectives is to drastically reduce the effort to explore large combinatorial design spaces. We believe it is imperative to develop methods for mathematically defining design spaces for configuration design. The purpose of this paper is to outline our approach to defining configuration design spaces for engineering design, with an emphasis on the mathematics of the spaces and their combinations into larger spaces that more completely capture design requirements. Specifically, we introduce design spaces that model physical connectivity, functionality, and assemblability considerations for a representative product family, a class of coffeemakers. Then, we show how these spaces can be combined into a “common” product variety design space. We demonstrate how constraints can be defined and applied to these spaces so that feasible design regions can be directly modeled. Additionally, we explore the topological and combinatorial properties of these spaces. The application of this design space modeling methodology is illustrated using the coffeemaker product family.

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.

Preferences and Correlated Uncertainties in Engineering Design

2003 ◽  
Author(s):  
Tomonori Honda ◽  
Erik K. Antonsson
Keyword(s):  
Engineering Design ◽  
Design Variable ◽  
Design Space ◽  
Design Method ◽  
Design Problems ◽  
Performance Variables ◽  
Design Variables ◽  
Engineering Design Problems ◽  
Engineering Problems ◽  
And Performance

The Method of Imprecision (MOI) is a multi-objective design method that maximizes the overall degree of both design and performance preferences. Sets of design variables are iteratively selected, and the corresponding performances are approximately computed. The designer’s judgment (expressed as preferences) are combined (aggregated) with the customer’s preferences, to determine the overall preference for sets of points in the design space. In addition to degrees of preference for values of the design and performance variables, engineering design problems also typically include uncertainties caused by uncontrolled variations, for example, measuring and fabrication limitations. This paper illustrates the computation of expected preference for cases where the uncertainties are uncorrelated, and also where the uncertainties are correlated. The result is a “best” set of design variable values for engineering problems, where the overall aggregated preference is maximized. As is illustrated by the examples shown here, where both preferences and uncontrolled variations are present, the presence of uncertainties can have an important effect on the choice of the overall best set of design variable values.

Standards, Codes of Practice and Expert Systems

1988 ◽  
Vol 21 (1) ◽  
pp. 5-9 ◽  
Author(s):  
E G McCluskey ◽  
S Thompson ◽  
D M G McSherry
Keyword(s):  
Expert System ◽  
Expert Systems ◽  
Engineering Design ◽  
Performance Criteria ◽  
Design Problems ◽  
Codes Of Practice ◽  
Engineering Design Problems ◽  
And Performance

Many engineering design problems require reference to standards or codes of practice to ensure that acceptable safety and performance criteria are met. Extracting relevant data from such documents can, however, be a problem for the unfamiliar user. The use of expert systems to guide the retrieval of information from standards and codes of practice is proposed as a means of alleviating this problem. Following a brief introduction to expert system techniques, a tool developed by the authors for building expert system guides to standards and codes of practice is described. The steps involved in encoding the knowledge contained in an arbitrarily chosen standard are illustrated. Finally, a typical consultation illustrates the use of the expert system guide to the standard.

A Robust Error-Pursuing Sequential Sampling Approach for Global Metamodeling Based on Voronoi Diagram and Cross Validation

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
Shengli Xu ◽  
Haitao Liu ◽  
Xiaofang Wang ◽  
Xiaomo Jiang
Keyword(s):  
Engineering Design ◽  
Voronoi Diagram ◽  
Cross Validation ◽  
Sequential Sampling ◽  
Voronoi Cell ◽  
Sensitive Region ◽  
Engineering Design Problems ◽  
Simulation Based ◽  
Global Metamodeling ◽  
Sampling Approach

Surrogate models are widely used in simulation-based engineering design and optimization to save the computing cost. The choice of sampling approach has a great impact on the metamodel accuracy. This article presents a robust error-pursuing sequential sampling approach called cross-validation (CV)-Voronoi for global metamodeling. During the sampling process, CV-Voronoi uses Voronoi diagram to partition the design space into a set of Voronoi cells according to existing points. The error behavior of each cell is estimated by leave-one-out (LOO) cross-validation approach. Large prediction error indicates that the constructed metamodel in this Voronoi cell has not been fitted well and, thus, new points should be sampled in this cell. In order to rapidly improve the metamodel accuracy, the proposed approach samples a Voronoi cell with the largest error value, which is marked as a sensitive region. The sampling approach exploits locally by the identification of sensitive region and explores globally with the shift of sensitive region. Comparative results with several sequential sampling approaches have demonstrated that the proposed approach is simple, robust, and achieves the desired metamodel accuracy with fewer samples, that is needed in simulation-based engineering design problems.

Biologically Inspired Design: A Macrocognitive Account

2010 ◽  
Author(s):  
Swaroop S. Vattam ◽  
Michael Helms ◽  
Ashok K. Goel
Keyword(s):  
Biological Sciences ◽  
Information Processing ◽  
Engineering Design ◽  
Design Patterns ◽  
Information Processing Model ◽  
Biologically Inspired ◽  
Design Problems ◽  
Engineering Design Problems ◽  
Other Information ◽  
Biologically Inspired Design

Biologically inspired engineering design is an approach to design that espouses the adaptation of functions and mechanisms in biological sciences to solve engineering design problems. We have conducted an in situ study of designers engaged in biologically inspired design. Based on this study we develop here a macrocognitive information-processing model of biologically inspired design. We also compare and contrast the model with other information-processing models of analogical design such as TRIZ, case-based design, and design patterns.

scholarly journals Lévy-Flight Moth-Flame Algorithm for Function Optimization and Engineering Design Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-22 ◽  
Author(s):  
Zhiming Li ◽  
Yongquan Zhou ◽  
Sen Zhang ◽  
Junmin Song
Keyword(s):  
Engineering Design ◽  
Function Optimization ◽  
Superior Performance ◽  
Local Optimum ◽  
Lévy Flight ◽  
Design Problems ◽  
Levy Flight ◽  
Spiral Path ◽  
Straight Line ◽  
Engineering Design Problems

The moth-flame optimization (MFO) algorithm is a novel nature-inspired heuristic paradigm. The main inspiration of this algorithm is the navigation method of moths in nature called transverse orientation. Moths fly in night by maintaining a fixed angle with respect to the moon, a very effective mechanism for travelling in a straight line for long distances. However, these fancy insects are trapped in a spiral path around artificial lights. Aiming at the phenomenon that MFO algorithm has slow convergence and low precision, an improved version of MFO algorithm based on Lévy-flight strategy, which is named as LMFO, is proposed. Lévy-flight can increase the diversity of the population against premature convergence and make the algorithm jump out of local optimum more effectively. This approach is helpful to obtain a better trade-off between exploration and exploitation ability of MFO, thus, which can make LMFO faster and more robust than MFO. And a comparison with ABC, BA, GGSA, DA, PSOGSA, and MFO on 19 unconstrained benchmark functions and 2 constrained engineering design problems is tested. These results demonstrate the superior performance of LMFO.

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