Multiobjective Collaborative Robust Optimization (McRO) With Interval Uncertainty and Interdisciplinary Uncertainty Propagation

2007 ◽  
Author(s):  
Mian Li ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Optimization Problems ◽  
Uncertainty Propagation ◽  
Multiple Objectives ◽  
Interval Uncertainty ◽  
Optimization Approach ◽  
Collaborative Robust Optimization ◽  
Fully Coupled

Real-world engineering design optimization problems often involve systems that have coupled disciplines with uncontrollable variations in their parameters. No approach has yet been reported for the solution of these problems when there are multiple objectives in each discipline, mixed continuous-discrete variables, and when there is a need to account for uncertainty and also uncertainty propagation across disciplines. We present a Multiobjective collaborative Robust Optimization (McRO) approach for this class of problems that have interval uncertainty in their parameters. McRO obtains Multidisciplinary Design Optimization (MDO) solutions which are as best as possible in a multiobjective and multidisciplinary sense. For McRO solutions, the sensitivity of objective and/or constraint functions is kept within an acceptable range. McRO involves a technique for interdisciplinary uncertainty propagation. The approach can be used for robust optimization of MDO problems with multiple objectives, or constraints, or both together at system and subsystem levels. Results from an application of the approach to a numerical and an engineering example are presented. It is concluded that the McRO approach can solve fully coupled MDO problems with interval uncertainty and can obtain solutions that are comparable to an all-at-once robust optimization approach.

Multiobjective Collaborative Robust Optimization With Interval Uncertainty and Interdisciplinary Uncertainty Propagation

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
M. Li ◽  
S. Azarm
Keyword(s):  
Robust Optimization ◽  
Probability Distributions ◽  
Uncertainty Propagation ◽  
Multiple Objectives ◽  
Interval Uncertainty ◽  
Optimization Approach ◽  
Solution Approach ◽  
Time In Literature ◽  
Collaborative Robust Optimization ◽  
First Time

We present a new solution approach for multidisciplinary design optimization (MDO) problems that, for the first time in literature, has all of the following characteristics: Each discipline has multiple objectives and constraints with mixed continuous-discrete variables; uncertainty exists in parameters and as a result, uncertainty propagation exists within and across disciplines; probability distributions of uncertain parameters are not available but their interval of uncertainty is known; and disciplines can be fully (two-way) coupled. The proposed multiobjective collaborative robust optimization (McRO) approach uses a multiobjective genetic algorithm as an optimizer. McRO obtains solutions that are as best as possible in a multiobjective and multidisciplinary sense. Moreover, for McRO solutions, the variation of objective and/or constraint functions can be kept within an acceptable range. McRO includes a technique for interdisciplinary uncertainty propagation. The approach can be used for robust optimization of MDO problems with multiple objectives, or constraints, or both together at system and subsystem levels. Results from an application of McRO to a numerical and an engineering example are presented. It is concluded that McRO can solve fully coupled MDO problems with interval uncertainty and obtain solutions that are comparable to a single-disciplinary robust optimization approach.

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.

An on-line Kriging metamodel assisted robust optimization approach under interval uncertainty

2017 ◽  
Vol 34 (2) ◽  
pp. 420-446 ◽  
Author(s):  
Qi Zhou ◽  
Ping Jiang ◽  
Xinyu Shao ◽  
Hui Zhou ◽  
Jiexiang Hu
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Interval Uncertainty ◽  
Optimization Approach ◽  
Content Type ◽  
Computational Burden ◽  
Design Alternative ◽  
Kriging Metamodel ◽  
On Line

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.

A New Sequential Robust Approach for MDO Problems Under Mixed Interval and Probabilistic Uncertainties

2018 ◽  
Author(s):  
Tingting Xia ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Optimization Problems ◽  
Early Stage ◽  
Optimization Process ◽  
Multidisciplinary Design ◽  
Worst Case ◽  
Interval Uncertainties ◽  
Mixed Uncertainties

In the design process of complex multidisciplinary systems, uncertainties in parameters or variables cannot be ignored. Robust multidisciplinary design optimization methods (RMDOs) can treat uncertainties as specified probabilistic distributions when enough statistical information is available. RMDOs need to assign intervals for nondeterministic variables since some design quantities may not have enough information to obtain statistical distributions, especially in the early stage of a design optimization process. Both types of uncertainties are very likely to appear simultaneously. In order to obtain robust solutions for multidisciplinary design optimization problems under mixed interval and probabilistic uncertainties, this work proposed a new sequential robust MDO approach, mixed SR-MDO. First, the robust optimization problem in a single discipline under mixed uncertainties is formulated and solved. Then, following the SR-MDO framework in our early work, MDO problems under mixed uncertainties are solved by handling probabilistic and interval uncertainties sequentially in decomposed subsystem problems. Interval uncertainties are handled by using the worst-case sensitivity analysis and fixing probabilistic uncertainties at their mean first, and then the influence of probabilistic uncertainties in objectives, constraints as well as in discipline analysis models is characterized by corresponding mean and variance. The applied SR-MDO framework allows subsystems in its full autonomy robust optimization and sequential robust optimization stages to run independently in parallel. This makes mixed SR-MDO be efficient for independent disciplines to work simultaneously and be more time-saving. Computational complexity of the proposed approach mainly relates to the double-loop optimization process in the worst-case interval uncertainties analysis. Examples are presented to demonstrate the applicability and efficiency of the mixed SR-MDO approach.

A Sequential Robust Optimization Approach for Multidisciplinary Design Optimization With Uncertainty

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Tingting Xia ◽  
Mian Li ◽  
Jianhua Zhou
Keyword(s):  
Robust Optimization ◽  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Optimization Procedure ◽  
Multidisciplinary Design ◽  
Sequential Optimization ◽  
Optimization Approach ◽  
Time Saving ◽  
Robust Solution ◽  
Optimization Stage

One real challenge for multidisciplinary design optimization (MDO) problems to gain a robust solution is the propagation of uncertainty from one discipline to another. Most existing methods only consider an MDO problem in the deterministic manner or find a solution which is robust for a single-disciplinary optimization problem. These rare methods for solving MDO problems under uncertainty are usually computationally expensive. This paper proposes a robust sequential MDO (RS-MDO) approach based on a sequential MDO (S-MDO) framework. First, a robust solution is obtained by giving each discipline full autonomy to perform optimization without considering other disciplines. A tolerance range is specified for each coupling variable to take care of uncertainty propagation in the coupled system. Then the obtained robust extreme points of global variables and coupling variables are dispatched into subsystems to perform robust optimization (RO) sequentially. Additional constraints are added in each subsystem to keep the consistency and to guarantee a robust solution. To find a solution with such strict constraints, genetic algorithm (GA) is used as a solver in each optimization stage. The proposed RS-MDO can save significant amount of computational efforts by using the sequential optimization procedure. Since all iterations in the sequential optimization stage can be processed in parallel, this robust MDO approach can be more time-saving. Numerical and engineering examples are provided to demonstrate the availability and effectiveness of the proposed approach.

scholarly journals Multi-Objective Multidisciplinary Design Optimization of a Robotic Fish System

2021 ◽  
Vol 9 (5) ◽  
pp. 478
Author(s):  
Hao Chen ◽  
Weikun Li ◽  
Weicheng Cui ◽  
Ping Yang ◽  
Linke Chen
Keyword(s):  
Design Optimization ◽  
Optimization Algorithm ◽  
Multidisciplinary Design Optimization ◽  
Robotic Fish ◽  
Multidisciplinary Design ◽  
Optimization Approach ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Cfd Method ◽  
The Individual

Biomimetic robotic fish systems have attracted huge attention due to the advantages of flexibility and adaptability. They are typically complex systems that involve many disciplines. The design of robotic fish is a multi-objective multidisciplinary design optimization problem. However, the research on the design optimization of robotic fish is rare. In this paper, by combining an efficient multidisciplinary design optimization approach and a novel multi-objective optimization algorithm, a multi-objective multidisciplinary design optimization (MMDO) strategy named IDF-DMOEOA is proposed for the conceptual design of a three-joint robotic fish system. In the proposed IDF-DMOEOA strategy, the individual discipline feasible (IDF) approach is adopted. A novel multi-objective optimization algorithm, disruption-based multi-objective equilibrium optimization algorithm (DMOEOA), is utilized as the optimizer. The proposed MMDO strategy is first applied to the design optimization of the robotic fish system, and the robotic fish system is decomposed into four disciplines: hydrodynamics, propulsion, weight and equilibrium, and energy. The computational fluid dynamics (CFD) method is employed to predict the robotic fish’s hydrodynamics characteristics, and the backpropagation neural network is adopted as the surrogate model to reduce the CFD method’s computational expense. The optimization results indicate that the optimized robotic fish shows better performance than the initial design, proving the proposed IDF-DMOEOA strategy’s effectiveness.

Multidisciplinary Design Optimization of a Lunar Lander’s Soft-Landing Gear

2010 ◽  
Vol 42 ◽  
pp. 118-121
Author(s):  
Yun Tong Lu ◽  
Chun Jie Wang ◽  
Ang Li ◽  
Han Wang
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Rapid Development ◽  
Fem Analysis ◽  
Landing Gear ◽  
Collaborative Optimization ◽  
Multidisciplinary Design ◽  
Optimization Approach ◽  
Soft Landing ◽  
Multi Body

The rapid development of Multidisciplinary Design Optimization (MDO) approach can simultaneously guarantee the cut of cost on design and optimal performance of spacecraft. Based on the theory of Collaborative Optimization approach (CO) of MDO, present paper proposes the method of CO by integrating Pro/E(3D modeling), Patran/Nastran(FEM analysis) and ADAMS(multi-body dynamic analysis) with the Isight software. In the analysis of the soft-landing gear of Lunar Lander, this method can optimize the mass of the landing gear and meanwhile ensures the reliability of structure statics, structure dynamics and multi-body dynamics. Thus the feasibility, applied value and guideline significance of this method in spacecraft structural design are proven.

Multi-objective collaborative multidisciplinary design optimization using particle swarm techniques and fuzzy decision making

2012 ◽  
Vol 226 (9) ◽  
pp. 2281-2295 ◽  
Author(s):  
Mohammad Reza Farmani ◽  
Jafar Roshanian ◽  
Meisam Babaie ◽  
Parviz M Zadeh
Keyword(s):  
Particle Swarm Optimization ◽  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Collaborative Optimization ◽  
Multidisciplinary Design ◽  
Fuzzy Decision ◽  
Swarm Optimization ◽  
Multi Objective

This article focuses on the efficient multi-objective particle swarm optimization algorithm to solve multidisciplinary design optimization problems. The objective is to extend the formulation of collaborative optimization which has been widely used to solve single-objective optimization problems. To examine the proposed structure, racecar design problem is taken as an example of application for three objective functions. In addition, a fuzzy decision maker is applied to select the best solution along the pareto front based on the defined criteria. The results are compared to the traditional optimization, and collaborative optimization formulations that do not use multi-objective particle swarm optimization. It is shown that the integration of multi-objective particle swarm optimization into collaborative optimization provides an efficient framework for design and analysis of hierarchical multidisciplinary design optimization problems.

A Regularized Inexact Penalty Decomposition Algorithm for Multidisciplinary Design Optimization Problems With Complementarity Constraints

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Shen Lu ◽  
Harrison M. Kim
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Original Problem ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Decomposition Algorithm ◽  
Multidisciplinary Design ◽  
Stationary Points ◽  
Complementarity Constraints ◽  
Regularization Technique

Economic and physical considerations often lead to equilibrium problems in multidisciplinary design optimization (MDO), which can be captured by MDO problems with complementarity constraints (MDO-CC)—a newly emerging class of problem. Due to the ill-posedness associated with the complementarity constraints, many existing MDO methods may have numerical difficulties solving this class of problem. In this paper, we propose a new decomposition algorithm for the MDO-CC based on the regularization technique and inexact penalty decomposition. The algorithm is presented such that existing proofs can be extended, under certain assumptions, to show that it converges to stationary points of the original problem and that it converges locally at a superlinear rate. Numerical computation with an engineering design example and several analytical example problems shows promising results with convergence to the all-in-one solution.

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.

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