Robust Optimization With NURBS HyPerModels

2008 ◽  
Author(s):  
Abiola M. Ajetunmobi ◽  
Cameron J. Turner ◽  
Richard H. Crawford
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Control Point ◽  
Optimization Methods ◽  
Design System ◽  
Optimization Approach ◽  
Engineering Systems ◽  
Parameter Uncertainties ◽  
Real Time System ◽  
Practical Engineering

Engineering systems are generally susceptible to parameter uncertainties that influence real-time system performance and long-term system reliability. However, designers and engineers must design system solutions that are both optimal and dependable. Robust design techniques and robust optimization methods in particular, have emerged as promising methodologies to address the problem of dealing with parameter uncertainties. This research advances a robust optimization approach that exploits gradient information embedded in proximate NURBs control point clusters that are inherent in NURBs metamodel design space representations. The proximate control point clusters embody the target sensitivity profile and therefore include robust optimal solutions, thus enabling selective optimization within regions associated with the clusters. This robust optimization framework has been implemented and is demonstrated on unconstrained robust optimization problems from two test functions and a constrained robust optimization problem from a practical engineering design problem.

Identification of the Optimal Product Configuration and Parameters for Improving Manufacturability

1996 ◽  
Author(s):  
Deyi Xue
Keyword(s):  
Global Optimization ◽  
Optimization Methods ◽  
Product Configuration ◽  
Design System ◽  
Optimization Approach ◽  
Continuous Variables ◽  
Integer Variables ◽  
System A ◽  
Global Optimization Methods

Abstract A global optimization approach for identifying the optimal product configuration and parameters is proposed to improve manufacturability measures including feasibility, cost, and time of production. Different product configurations, including alternative design candidates and production processes, are represented by an AND/OR graph. Product parameters are described by variables including continuous variables, integer variables, Boolean variables, and discrete variables. Two global optimization methods, genetic algorithm and simulated annealing, are employed for identifying the optimal product configuration and parameters. The introduced approach serves as a key component in an integrated concurrent design system. A case study example is given to show how the proposed method is used for solving the engineering problems.

Robust Optimization With Mixed Interval and Probabilistic Parameter Uncertainties, Model Uncertainty, and Metamodeling Uncertainty

2019 ◽  
Author(s):  
Yanjun Zhang ◽  
Tingting Xia ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Real World ◽  
Parameter Uncertainty ◽  
Model Uncertainty ◽  
Optimization Problems ◽  
Probability Distributions ◽  
Parameter Uncertainties ◽  
True Value ◽  
Uncertainty Model ◽  
The Difference

Abstract Various types of uncertainties, such as parameter uncertainty, model uncertainty, metamodeling uncertainty may lead to low robustness. Parameter uncertainty can be either epistemic or aleatory in physical systems, which have been widely represented by intervals and probability distributions respectively. Model uncertainty is formally defined as the difference between the true value of the real-world process and the code output of the simulation model at the same value of inputs. Additionally, metamodeling uncertainty is introduced due to the usage of metamodels. To reduce the effects of uncertainties, robust optimization (RO) algorithms have been developed to obtain solutions being not only optimal but also less sensitive to uncertainties. Based on how parameter uncertainty is modeled, there are two categories of RO approaches: interval-based and probability-based. In real-world engineering problems, both interval and probabilistic parameter uncertainties are likely to exist simultaneously in a single problem. However, few works have considered mixed interval and probabilistic parameter uncertainties together with other types of uncertainties. In this work, a general RO framework is proposed to deal with mixed interval and probabilistic parameter uncertainties, model uncertainty, and metamodeling uncertainty simultaneously in design optimization problems using the intervals-of-statistics approaches. The consideration of multiple types of uncertainties will improve the robustness of optimal designs and reduce the risk of inappropriate decision-making, low robustness and low reliability in engineering design. Two test examples are utilized to demonstrate the applicability and effectiveness of the proposed RO approach.

Feasibility Robust Optimization via Scenario Generation and Reduction

2018 ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case ◽  
Robust Solution

Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains without any known probability distributions. The proposed approach integrates a new sampling-based scenario generation scheme with a new scenario reduction approach in order to solve feasibility robust optimization problems. An analysis of the computational cost of the proposed approach was performed to provide worst case bounds on its computational cost. The new proposed approach was applied to three test problems and compared against other scenario-based robust optimization approaches. A test was conducted on one of the test problems to demonstrate that the computational cost of the proposed approach does not significantly increase as additional uncertain parameters are introduced. The results show that the proposed approach converges to a robust solution faster than conventional robust optimization approaches that discretize the uncertain parameters.

Isogeometric shape optimization for design dependent loads

2021 ◽  
pp. 1-13
Author(s):  
Arkaprabho Pal ◽  
Sourav Rakshit
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Minimum Weight ◽  
Control Point ◽  
Optimization Approach ◽  
Shape Sensitivity ◽  
Body Forces ◽  
Design Variables ◽  
Design Dependent Loads ◽  
Material Layout

Abstract This paper presents a new isogeometric formulation for shape optimization of structures subjected to design dependent loads. This work considers two types of design dependent loads, namely surface loads like pressure where the direction and/or magnitude of force changes with the variation of boundary shape, and body forces that depend on the material layout. These problems have been mostly solved by topology optimization methods which are prone to difficulties in determination of the loading surface for pressure loads and problems associated with non-monotonous behaviour of compliance and low density regions for body forces. This work uses an isogeometric shape optimization approach where the geometry is defined using NURBS and the control point coordinates and control weights of the boundary are chosen as design variables. This approach accommodates the design dependent loads easily, in addition to its other advantages like exact geometry representation, local control, fewer design variables, excellent shape sensitivity, efficient mesh refinement strategies, and smooth results that can be integrated with CAD. Two classes of optimization problems have been discussed, they are minimum compliance problems subject to volume constraint and minimum weight problems subjected to local stress constraints. These problems are solved using convex optimization programs. Hence, expressions for full sensitivities are derived which is new for structural shape optimization problems with design dependent loads. Some representative engineering examples are solved and compared with existing literature to demonstrate the application of the proposed method.

scholarly journals A Novel Hybrid Bat Algorithm with Harmony Search for Global Numerical Optimization

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Gaige Wang ◽  
Lihong Guo
Keyword(s):  
Numerical Optimization ◽  
Optimization Problems ◽  
Harmony Search ◽  
Bat Algorithm ◽  
Optimization Methods ◽  
Population Based ◽  
Optimization Approach ◽  
Global Numerical Optimization ◽  
Hybrid Metaheuristic ◽  
Real World Applications

A novel robust hybrid metaheuristic optimization approach, which can be considered as an improvement of the recently developed bat algorithm, is proposed to solve global numerical optimization problems. The improvement includes the addition of pitch adjustment operation in HS serving as a mutation operator during the process of the bat updating with the aim of speeding up convergence, thus making the approach more feasible for a wider range of real-world applications. The detailed implementation procedure for this improved metaheuristic method is also described. Fourteen standard benchmark functions are applied to verify the effects of these improvements, and it is demonstrated that, in most situations, the performance of this hybrid metaheuristic method (HS/BA) is superior to, or at least highly competitive with, the standard BA and other population-based optimization methods, such as ACO, BA, BBO, DE, ES, GA, HS, PSO, and SGA. The effect of the HS/BA parameters is also analyzed.

scholarly journals Non-Convex Feasibility Robust Optimization Via Scenario Generation and Local Refinement

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case

Abstract Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains. The proposed approach is based on an integration of two techniques: (i) a sampling-based scenario generation scheme and (ii) a local robust optimization approach. An analysis of the computational cost of this integrated approach is performed to provide worst-case bounds on its computational cost. The proposed approach is applied to several non-convex engineering test problems and compared against two existing robust optimization approaches. The results show that the proposed approach can efficiently find a robust optimal solution across the test problems, even when existing methods for non-convex robust optimization are unable to find a robust optimal solution. A scalable test problem is solved by the approach, demonstrating that its computational cost scales with problem size as predicted by an analysis of the worst-case computational cost bounds.

scholarly journals Conic reformulations for Kullback-Leibler divergence constrained distributionally robust optimization and applications

2021 ◽  
Vol 11 (2) ◽  
pp. 139-151
Author(s):  
Burak Kocuk
Keyword(s):  
Robust Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Empirical Distribution ◽  
Computational Study ◽  
Facility Location Problem ◽  
Optimization Approach ◽  
Distributionally Robust Optimization ◽  
Leibler Divergence ◽  
Distributionally Robust

In this paper, we consider a Kullback-Leibler divergence constrained distributionally robust optimization model. This model considers an ambiguity set that consists of all distributions whose Kullback-Leibler divergence to an empirical distribution is bounded. Utilizing the fact that this divergence measure has an exponential cone representation, we obtain the robust counterpart of the Kullback-Leibler divergence constrained distributionally robust optimization problem as a dual exponential cone constrained program under mild assumptions on the underlying optimization problem. The resulting conic reformulation of the original optimization problem can be directly solved by a commercial conic programming solver. We specialize our generic formulation to two classical optimization problems, namely, the Newsvendor Problem and the Uncapacitated Facility Location Problem. Our computational study in an out-of-sample analysis shows that the solutions obtained via the distributionally robust optimization approach yield significantly better performance in terms of the dispersion of the cost realizations while the central tendency deteriorates only slightly compared to the solutions obtained by stochastic programming.

Multifidelity and Multiscale Bayesian Framework for High-Dimensional Engineering Design and Calibration

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Soumalya Sarkar ◽  
Sudeepta Mondal ◽  
Michael Joly ◽  
Matthew E. Lynch ◽  
Shaunak D. Bopardikar ◽  
...  
Keyword(s):  
Machine Learning ◽  
Learning Strategies ◽  
Optimization Problems ◽  
Bayesian Optimization ◽  
High Dimensional ◽  
Optimization Approach ◽  
Information Theoretic ◽  
Compressor Rotor ◽  
Practical Engineering ◽  
Microstructure Prediction

AbstractThis paper proposes a machine learning–based multifidelity modeling (MFM) and information-theoretic Bayesian optimization approach where the associated models can have complex discrepancies among each other. Advantages of MFM-based optimization over a single-fidelity surrogate, specifically under complex constraints, are discussed with benchmark optimization problems involving noisy data. The MFM framework, based on modeling of the varied fidelity information sources via Gaussian processes, is augmented with information-theoretic active learning strategies that involve sequential selection of optimal points in a multiscale architecture. This framework is demonstrated to exhibit improved efficiency on practical engineering problems like high-dimensional design optimization of compressor rotor via implementing its multiscale architecture and calibration of expensive microstructure prediction model. From the perspective of the machine learning–assisted design of multiphysics systems, advantages of the proposed framework have been presented with respect to accelerating the search of optimal design conditions under budget constraints.

A multi-objective robust optimization approach for engineering design under interval uncertainty

2018 ◽  
Vol 35 (2) ◽  
pp. 580-603 ◽  
Author(s):  
Qi Zhou ◽  
Xinyu Shao ◽  
Ping Jiang ◽  
Tingli Xie ◽  
Jiexiang Hu ◽  
...  
Keyword(s):  
Robust Optimization ◽  
Engineering Design ◽  
Optimization Problems ◽  
Interval Uncertainty ◽  
Optimization Approach ◽  
Content Type ◽  
Computational Burden ◽  
Multi Objective ◽  
Design Alternatives ◽  
Kriging Metamodel

Purpose Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty. Design/methodology/approach In K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process. Findings Five numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost. Practical implications The proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties. Originality/value A K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.

Robust Design of UOE Forming Process Based on Support Vector Machine

2015 ◽  
Vol 817 ◽  
pp. 523-530
Author(s):  
Tian Xia Zou ◽  
Guang Han Wu ◽  
Da Yong Li ◽  
Qiang Ren ◽  
Ying Hong Peng
Keyword(s):  
Support Vector Machine ◽  
Robust Optimization ◽  
Robust Design ◽  
Pipeline Steel ◽  
Optimization Methods ◽  
Material Behavior ◽  
Support Vector ◽  
Optimization Approach ◽  
Forming Process ◽  
Noise Factors

Fluctuations in material properties of the incoming steel for UOE forming process are widespread. According to the statistics, the fluctuation range of the yield strength of the same grade pipeline steel is around 80MPa. Robust optimization methods have been widely applied in sheet metal forming area. In this paper, experiments were conducted to investigate how a stochastic material behavior of noise factors affected UOE forming quality. Robust design models integrated with response surface method for UOE forming process were established to minimize impact of the variations and improve the qualified rate of UOE pipe ovality. Support vector machine in both classification and regression was adopted to map the relation between input process parameters and forming qualities. The deterministic and robust optimization results are presented and compared, demonstrating increased process robustness and decreased number of product rejects by application of the robust optimization approach.

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