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J. Axerio‐Cilies, G. Iaccarino
Asymmetries in the wake structure of a F1 tire
G. Petrone, G. Iaccarino, D. Quagliarella
Robustness criteria in optimization under uncertainty
C. Poloni, L. Padowan, L. Parussini, S. Pieri, V. Pediroda
Robust design of aircraft components: a multi‐objective optimization problem
K. Deb, Himanshu Gupta (2006)
Introducing Robustness in Multi-Objective OptimizationEvolutionary Computation, 14
E. Issakhanian, C. Elkins, K. Lo, J. Eaton (2010)
An Experimental Study of the Flow Around a Formula One Racing Car TireJournal of Fluids Engineering-transactions of The Asme, 132
E. Hughes (2001)
Evolutionary Multi-objective Ranking with Uncertainty and Noise
M. Basseur, E. Zitzler (2006)
Handling Uncertainty in Indicator-Based Multiobjective OptimizationInternational Journal of Computational Intelligence Research, 2
John Axerio-Cilies, E. Issakhanian, J. Jiménez, G. Iaccarino (2012)
An Aerodynamic Investigation of an Isolated Stationary Formula 1 Wheel AssemblyJournal of Fluids Engineering-transactions of The Asme, 134
K. Deb, K. Sindhya, T. Okabe
Self‐adaptive SBX for real‐parameter optimization
C. Mattson, A. Messac (2005)
Pareto Frontier Based Concept Selection Under Uncertainty, with VisualizationOptimization and Engineering, 6
J. Witteveen, G. Iaccarino
Simplex elements stochastic collocation in higher‐dimensional probability spaces
G. Petrone, J. Witteveen, J. Axerio‐Cilies, G. Iaccarino, C. de Nicola, D. Quagliarella
Wind turbine optimization under uncertainty with high performance computing
Jiang-feng Wang, J. Périaux (2001)
Multi-point optimization using GAs and Nash/Stackelberg games for high lift multi-airfoil design in aerodynamicsProceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546), 1
E. Issakhanian, C. Elkins, K. Lo, J. Eaton
An experimental study of the flow around a F1 racing car tire
Zhili Tang, J. Périaux, G. Bugeda, E. Oñate (2009)
Lift maximization with uncertainties for the optimization of high lift devices using Multi-Criterion Evolutionary Algorithms2009 IEEE Congress on Evolutionary Computation
K. Deb, S. Gupta, David Daum, J. Branke, A. Mall, D. Padmanabhan (2009)
Reliability-Based Optimization Using Evolutionary AlgorithmsIEEE Transactions on Evolutionary Computation, 13
G. Petrone, C. de Nicola, D. Quagliarella, J. Witteveen, G. Iaccarino
Wind turbine performance analysis under uncertainty
R. Coelho, P. Bouillard (2011)
Multi-Objective Reliability-Based Optimization with Stochastic MetamodelsEvolutionary Computation, 19
J. Axerio‐Cilies, G. Petrone, V. Sellappan, G. Iaccarino
Extreme ensemble computation for optimization under uncertainty
C. Fonseca, P. Fleming (1995)
Multiobjective genetic algorithms made easy: selection sharing and mating restriction
J. Teich (2001)
Pareto-Front Exploration with Uncertain Objectives
J. Witteveen, G. Iaccarino
Simplex elements stochastic collocation for uncertainty propagation in robust design optimization
K. Deb, S. Agrawal, Amrit Pratap, T. Meyarivan (2002)
A fast and elitist multiobjective genetic algorithm: NSGA-IIIEEE Trans. Evol. Comput., 6
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.
Engineering Computations: International Journal for Computer-Aided Engineering and Software – Emerald Publishing
Published: Nov 8, 2013
Keywords: Robust optimization; Uncertainty quantification; CDF; CFD; Formula 1; Pareto front
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