“…Numerous optimizations with each method, as shown in Figure 6, are needed to test their performances as the optimizations estimate probabilistic phenomena and both the GA and complex algorithm are probabilistic methods. Popular measures of the accuracy and robustness are therefore mean values and standard deviations of the objective function values of the optimal points received from the optimizations (Tenne, 2015). Several performance measures for the efficiency of an optimization algorithm have been proposed (Schutte & Haftka, 2005;Krus & Ö lvander, 2013), but for this comparison the measure that is presented by Persson and Ö lvander (2013), h, is used.…”
Section: Proposed Comparison Methodsmentioning
confidence: 99%
“…Numerous optimizations with each method, as shown in Figure 6, are needed to test their performances as the optimizations estimate probabilistic phenomena and both the GA and complex algorithm are probabilistic methods. Popular measures of the accuracy and robustness are therefore mean values and standard deviations of the objective function values of the optimal points received from the optimizations (Tenne, 2015). Fig.…”
This paper proposes a method to compare the performances of different methods for robust design optimization of computationally demanding models. Its intended usage is to help the engineer to choose the optimization approach when faced with a robust optimization problem. This paper demonstrates the usage of the method to find the most appropriate robust design optimization method to solve an engineering problem. Five robust design optimization methods, including a novel method, are compared in the demonstration of the comparison method. Four of the five compared methods involve surrogate models to reduce the computational cost of performing robust design optimization. The five methods are used to optimize several mathematical functions that should be similar to the engineering problem. The methods are then used to optimize the engineering problem to confirm that the most suitable optimization method was identified. The performance metrics used are the mean value and standard deviation of the robust optimum as well as an index that combines the required number of simulations of the original model with the accuracy of the obtained solution. These measures represent the accuracy, robustness, and efficiency of the compared methods. The results of the comparison show that sequential robust optimization is the method with the best balance between accuracy and number of function evaluations. This is confirmed by the optimizations of the engineering problem. The comparison also shows that the novel method is better than its predecessor is.
“…Numerous optimizations with each method, as shown in Figure 6, are needed to test their performances as the optimizations estimate probabilistic phenomena and both the GA and complex algorithm are probabilistic methods. Popular measures of the accuracy and robustness are therefore mean values and standard deviations of the objective function values of the optimal points received from the optimizations (Tenne, 2015). Several performance measures for the efficiency of an optimization algorithm have been proposed (Schutte & Haftka, 2005;Krus & Ö lvander, 2013), but for this comparison the measure that is presented by Persson and Ö lvander (2013), h, is used.…”
Section: Proposed Comparison Methodsmentioning
confidence: 99%
“…Numerous optimizations with each method, as shown in Figure 6, are needed to test their performances as the optimizations estimate probabilistic phenomena and both the GA and complex algorithm are probabilistic methods. Popular measures of the accuracy and robustness are therefore mean values and standard deviations of the objective function values of the optimal points received from the optimizations (Tenne, 2015). Fig.…”
This paper proposes a method to compare the performances of different methods for robust design optimization of computationally demanding models. Its intended usage is to help the engineer to choose the optimization approach when faced with a robust optimization problem. This paper demonstrates the usage of the method to find the most appropriate robust design optimization method to solve an engineering problem. Five robust design optimization methods, including a novel method, are compared in the demonstration of the comparison method. Four of the five compared methods involve surrogate models to reduce the computational cost of performing robust design optimization. The five methods are used to optimize several mathematical functions that should be similar to the engineering problem. The methods are then used to optimize the engineering problem to confirm that the most suitable optimization method was identified. The performance metrics used are the mean value and standard deviation of the robust optimum as well as an index that combines the required number of simulations of the original model with the accuracy of the obtained solution. These measures represent the accuracy, robustness, and efficiency of the compared methods. The results of the comparison show that sequential robust optimization is the method with the best balance between accuracy and number of function evaluations. This is confirmed by the optimizations of the engineering problem. The comparison also shows that the novel method is better than its predecessor is.
“…Metamodel-assisted EAs have been used extensively in problems ranging from drug formulation to aircraft design [1]. Extensions ensembles of multiple metamodels [5] and [6] for incorporation of machine learning techniques.…”
RBF metamodels, which are commonly used in expensive optimization problems, rely on a hyperparameter which affects their prediction. The optimal hyperparameter value is typically unknown and hence needs to be estimated by additional procedures. As such this study examines if this overhead is justified from an overall search effectiveness perspective, namely, if changes in the hyperparameter yield significant performance differences. Analysis based on extensive numerical experiments shows that changes are significant in functions with low to moderate multimodality but are less significant in functions with highly multimodality.
“…Lift and drag coefficients were obtained with the Xfoil analysis code [19] and each airfoil evaluation Ack:Ackley, Gri:Griewank, Ras:Rastrigin Ros:Rosenbrock, Sch:Schwefel 3.12, Wei:Weierstrass required 10-30 seconds on a desktop computer. Airfoils were defined by the Hicks-Henne method [20] which combines a baseline airfoil shape with shape functions [21] b i (x) = sin πx…”
Computer simulations are being extensively used as a partial substitute for real-world experiments. Such simulations are often computationally intensive and hence metamodels are used to approximate them and to yield estimated output values more economically. While this setup can work well in low dimensional problems it can struggle in high-dimensional ones due to poor metamodel prediction accuracy. As such this study examines the application of dimensionality-reduction procedures during the search so that a simplified problems is formulated which is easier to solve and which could yield a better solution of the original one. An extensive performance analysis with both mathematical test functions and an engineering application shows the effectiveness of the proposed approach.
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