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Article
Publication date: 11 November 2013

Giovanni Petrone, John Axerio-Cilies, Domenico Quagliarella and Gianluca Iaccarino

A probabilistic non-dominated sorting genetic algorithm (P-NSGA) for multi-objective optimization under uncertainty is presented. The purpose of this algorithm is to…

Abstract

Purpose

A probabilistic non-dominated sorting genetic algorithm (P-NSGA) for multi-objective optimization under uncertainty is presented. The purpose of this algorithm is to create a tight coupling between the optimization and uncertainty procedures, use all of the possible probabilistic information to drive the optimizer, and leverage high-performance parallel computing.

Design/methodology/approach

This algorithm is a generalization of a classical genetic algorithm for multi-objective optimization (NSGA-II) by Deb et al. The proposed algorithm relies on the use of all possible information in the probabilistic domain summarized by the cumulative distribution functions (CDFs) of the objective functions. Several analytic test functions are used to benchmark this algorithm, but only the results of the Fonseca-Fleming test function are shown. An industrial application is presented to show that P-NSGA can be used for multi-objective shape optimization of a Formula 1 tire brake duct, taking into account the geometrical uncertainties associated with the rotating rubber tire and uncertain inflow conditions.

Findings

This algorithm is shown to have deterministic consistency (i.e. it turns back to the original NSGA-II) when the objective functions are deterministic. When the quality of the CDF is increased (either using more points or higher fidelity resolution), the convergence behavior improves. Since all the information regarding uncertainty quantification is preserved, all the different types of Pareto fronts that exist in the probabilistic framework (e.g. mean value Pareto, mean value penalty Pareto, etc.) are shown to be generated a posteriori. An adaptive sampling approach and parallel computing (in both the uncertainty and optimization algorithms) are shown to have several fold speed-up in selecting optimal solutions under uncertainty.

Originality/value

There are no existing algorithms that use the full probabilistic distribution to guide the optimizer. The method presented herein bases its sorting on real function evaluations, not merely measures (i.e. mean of the probabilistic distribution) that potentially do not exist.

Details

Engineering Computations, vol. 30 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 6 July 2015

Hyeong-Uk Park, Jae-Woo Lee, Joon Chung and Kamran Behdinan

The purpose of this paper is to study the consideration of uncertainty from analysis modules for aircraft conceptual design by implementing uncertainty-based design…

Abstract

Purpose

The purpose of this paper is to study the consideration of uncertainty from analysis modules for aircraft conceptual design by implementing uncertainty-based design optimization methods. Reliability-Based Design Optimization (RBDO), Possibility-Based Design Optimization (PBDO) and Robust Design Optimization (RDO) methods were developed to handle uncertainties of design optimization. The RBDO method is found suitable for uncertain parameters when sufficient information is available. On the other hand, the PBDO method is proposed when uncertain parameters have insufficient information. The RDO method can apply to both cases. The RBDO, PBDO and RDO methods were considered with the Multidisciplinary Design Optimization (MDO) method to generate conservative design results when low fidelity analysis tools are used.

Design/methodology/approach

Methods combining MDO with RBDO, PBDO and RDO were developed and have been applied to a numerical analysis and an aircraft conceptual design. This research evaluates and compares the characteristics of each method in both cases.

Findings

The RBDO result can be improved when the amount of data concerning uncertain parameters is increased. Conversely, increasing information regarding uncertain parameters does not improve the PBDO result. The PBDO provides a conservative result when less information about uncertain parameters is available.

Research limitations/implications

The formulation of RDO is more complex than other methods. If the uncertainty information is increased in aircraft conceptual design case, the accuracy of RBDO will be enhanced.

Practical implications

This research increases the probability of a feasible design when it considers the uncertainty. This result gives more practical optimization results on a conceptual design level for fabrication.

Originality/value

It is RBDO, PBDO and RDO methods combined with MDO that satisfy the target probability when the uncertainties of low fidelity analysis models are considered.

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Article
Publication date: 13 August 2019

Hui Lü, Kun Yang, Wen-bin Shangguan, Hui Yin and DJ Yu

The purpose of this paper is to propose a unified optimization design method and apply it to handle the brake squeal instability involving various uncertainties in a…

Abstract

Purpose

The purpose of this paper is to propose a unified optimization design method and apply it to handle the brake squeal instability involving various uncertainties in a unified framework.

Design/methodology/approach

Fuzzy random variables are taken as equivalent variables of conventional uncertain variables, and a unified response analysis method is first derived based on level-cut technique, Taylor expansion and central difference scheme. Next, a unified reliability analysis method is developed by integrating the unified response analysis and fuzzy possibility theory. Finally, based on the unified reliability analysis method, a unified reliability-based optimization model is established, which is capable of optimizing uncertain responses in a unified way for different uncertainty cases.

Findings

The proposed method is extended to perform squeal instability analysis and optimization involving various uncertainties. Numerical examples under eight uncertainty cases are provided and the results demonstrate the effectiveness of the proposed method.

Originality/value

Most of the existing methods of uncertainty analysis and optimization are merely effective in tackling one uncertainty case. The proposed method is able to handle the uncertain problems involving various types of uncertainties in a unified way.

Details

Engineering Computations, vol. 37 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 11 November 2013

Pietro Marco Congedo, Gianluca Geraci, Rémi Abgrall, Valentino Pediroda and Lucia Parussini

– This paper aims to deal with an efficient strategy for robust optimization when a large number of uncertainties are taken into account.

Abstract

Purpose

This paper aims to deal with an efficient strategy for robust optimization when a large number of uncertainties are taken into account.

Design/methodology/approach

ANOVA analysis is used in order to perform a variance-based decomposition and to reduce stochastic dimension based on an appropriate criterion. A massive use of metamodels allows reconstructing response surfaces for sensitivity indexes in the design variables plan. To validate the proposed approach, a simplified configuration, an inverse problem on a 1D nozzle flow, is solved and the performances compared to an exact Monte Carlo reference solution. Then, the same approach is applied to the robust optimization of a turbine cascade for thermodynamically complex flows.

Findings

First, when the stochastic dimension is reduced, the error on the variance between the reduced and the complete problem was found to be roughly estimated by the quantity (1− TSI )×100, where TSI is the summation of TSI concerning the variables respecting the TSI criterion. Second, the proposed strategy allowed obtaining a converged Pareto front with a strong reduction of computational cost by preserving the same accuracy.

Originality/value

Several articles exist in literature concerning robust optimization but very few dealing with a global approach for solving optimization problem affected by a large number of uncertainties. Here, a practical and efficient approach is proposed that could be applied also to realistic problems in engineering field.

Details

Engineering Computations, vol. 30 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 18 October 2018

Lei Wang, Haijun Xia, Yaowen Yang, Yiru Cai and Zhiping Qiu

The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval…

Abstract

Purpose

The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval uncertainties of load and material parameters based on the technology of 3D printing or additive manufacturing.

Design/methodology/approach

First, the uncertainty quantification analysis is accomplished by interval Taylor extension to determine boundary rules of concerned displacement responses. Based on the interval interference theory, a novel reliability index, named as the optimization feature distance, is then introduced to construct non-probabilistic reliability constraints. To circumvent convergence difficulties in solving large-scale variable optimization problems, the gradient-based method of moving asymptotes is also used, in which the sensitivity expressions of the present reliability measurements with respect to design variables are deduced by combination of the adjoint vector scheme and interval mathematics.

Findings

The main findings of this paper should lie in that new non-probabilistic reliability index, i.e. the optimization feature distance which is defined and further incorporated in continuum topology optimization issues. Besides, a novel concurrent design strategy under consideration of macro-micro integration is presented by using the developed RBTO methodology.

Originality/value

Uncertainty propagation analysis based on the interval Taylor extension method is conducted. Novel reliability index of the optimization feature distance is defined. Expressions of the adjoint vectors between interval bounds of displacement responses and the relative density are deduced. New NRBTO method subjected to continuum structures is developed and further solved by MMA algorithms.

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Article
Publication date: 16 April 2018

Qi Zhou, Xinyu Shao, Ping Jiang, Tingli Xie, Jiexiang Hu, Leshi Shu, Longchao Cao and Zhongmei Gao

Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might…

Abstract

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.

Details

Engineering Computations, vol. 35 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 18 April 2017

Qi Zhou, Ping Jiang, Xinyu Shao, Hui Zhou and Jiexiang Hu

Uncertainty is inevitable in real-world engineering optimization. With an outer-inner optimization structure, most previous robust optimization (RO) approaches under…

Abstract

Purpose

Uncertainty is inevitable in real-world engineering optimization. With an outer-inner optimization structure, most previous robust optimization (RO) approaches under interval uncertainty can become computationally intractable because the inner level must perform robust evaluation for each design alternative delivered from the outer level. This paper aims to propose an on-line Kriging metamodel-assisted variable adjustment robust optimization (OLK-VARO) to ease the computational burden of previous VARO approach.

Design/methodology/approach

In OLK-VARO, Kriging metamodels are constructed for replacing robust evaluations of the design alternative delivered from the outer level, reducing the nested optimization structure of previous VARO approach into a single loop optimization structure. An on-line updating mechanism is introduced in OLK-VARO to exploit the obtained data from previous iterations.

Findings

One nonlinear numerical example and two engineering cases have been used to demonstrate the applicability and efficiency of the proposed OLK-VARO approach. Results illustrate that OLK-VARO is able to obtain comparable robust optimums as to that obtained by previous VARO, while at the same time significantly reducing computational cost.

Practical implications

The proposed approach exhibits great capability for practical engineering design optimization problems under interval uncertainty.

Originality/value

The main contribution of this paper lies in the following: an OLK-VARO approach under interval uncertainty is proposed, which can significantly ease the computational burden of previous VARO approach.

Details

Engineering Computations, vol. 34 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

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Article
Publication date: 5 March 2018

Siyang Deng, Stéphane Brisset and Stephane Clénet

This paper compares six reliability-based design optimization (RBDO) approaches dealing with uncertainties for a simple mathematical model and a multidisciplinary…

Abstract

Purpose

This paper compares six reliability-based design optimization (RBDO) approaches dealing with uncertainties for a simple mathematical model and a multidisciplinary optimization problem of a safety transformer to highlight the most effective.

Design/methodology/approach

The RBDO and various approaches to calculate the probability of failure are is presented. They are compared in terms of precision and number of evaluations on mathematical and electromagnetic design problems.

Findings

The mathematical example shows that the six RBDO approaches have almost the same results except the approximate moment approach that is less accurate. The optimization of the safety transformer highlights that not all the methods can converge to the global solution. Performance measure approach, single-loop approach and sequential optimization and reliability assessment (SORA) method appear to be more stable. Considering both numerical examples, SORA is the most effective method among all RBDO approaches.

Originality/value

The comparison of six RBDO methods on the optimization problem of a safety transformer is achieved for the first time. The comparison in terms of precision and number of evaluations highlights the most effective ones.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 37 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 17 June 2020

Davood Darvishi, Sifeng Liu and Jeffrey Yi-Lin Forrest

The purpose of this paper is to survey and express the advantages and disadvantages of the existing approaches for solving grey linear programming in decision-making problems.

Abstract

Purpose

The purpose of this paper is to survey and express the advantages and disadvantages of the existing approaches for solving grey linear programming in decision-making problems.

Design/methodology/approach

After presenting the concepts of grey systems and grey numbers, this paper surveys existing approaches for solving grey linear programming problems and applications. Also, methods and approaches for solving grey linear programming are classified, and its advantages and disadvantages are expressed.

Findings

The progress of grey programming has been expressed from past to present. The main methods for solving the grey linear programming problem can be categorized as Best-Worst model, Confidence degree, Whitening parameters, Prediction model, Positioned solution, Genetic algorithm, Covered solution, Multi-objective, Simplex and dual theory methods. This survey investigates the developments of various solving grey programming methods and its applications.

Originality/value

Different methods for solving grey linear programming problems are presented, where each of them has disadvantages and advantages in providing results of grey linear programming problems. This study attempted to review papers published during 35 years (1985–2020) about grey linear programming solving and applications. The review also helps clarify the important advantages, disadvantages and distinctions between different approaches and algorithms such as weakness of solving linear programming with grey numbers in constraints, inappropriate results with the lower bound is greater than upper bound, out of feasible region solutions and so on.

Details

Grey Systems: Theory and Application, vol. 11 no. 1
Type: Research Article
ISSN: 2043-9377

Keywords

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Article
Publication date: 17 June 2008

Jerzy Józefczyk

In many decision‐making problems under parameter uncertainty, the most popular stochastic approach is not used because of its serious drawbacks. The purpose of this paper…

Abstract

Purpose

In many decision‐making problems under parameter uncertainty, the most popular stochastic approach is not used because of its serious drawbacks. The purpose of this paper is to present another approach, which copes with the uncertainty of parameters. It uses a precise criterion evaluating a decision with respect to uncertain parameters. This precision by the maximum operator is performed on a term based on the criterion and called the relative regret. The approach is applied to the allocation problems in a complex of operations.

Design/methodology/approach

The resource allocation problems in a complex of operations of independent and dependent structures to minimize a total execution time of all operations are investigated. Then, the results are extended for the problem of a task allocation in the complex of independent operations. The case is considered when the parameters in the functional models of the operations are uncertain, and their values belong to the intervals of known bounds. The solution algorithms for the uncertain problems are based on known solution algorithms for the corresponding deterministic problems. The solution algorithms for the latter problems are outlined in the paper.

Findings

The main contribution of the paper consists in presenting the property that it is possible for the uncertain problems considered to replace the solution of the uncertain allocation problems by solving a number of corresponding deterministic problems.

Research limitations/implications

The useful and interesting property of the solution algorithm for the allocation problems, in general, cannot be applied to the other decision‐making problems under uncertainty. As an example of such a problem, a simple routing‐scheduling problem is presented for which, however, a number of possible parameter scenarios can be substantially limited.

Practical implications

The allocation problems addressed in the paper have a variety of applications in computer systems and in manufacturing systems. Moreover, a lack of crisp values for the parameters in models of individual operations is rather common.

Originality/value

The paper extends previous results for the allocation problems in a complex of operations.

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