Robust Design via NSGA-II with Latin Hypercube Sampling
Applied to Structural Beams
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Full Text |
Pdf |
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Author |
Jaymar Soriano, Laurent Dumas
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ISSN |
2079-8407 |
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On Pages
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259-264
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Volume No. |
5
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Issue No. |
3
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Issue Date |
April 1, 2014 |
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Publishing Date |
April 1, 2014 |
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Keywords |
evolutionary algorithms, NSGA-II, optimization, robust design
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Abstract
In structural beam design, the cross-sectional area is minimized not only to minimize the cost of production but also the weight of the beam. This is subject to constraints on maximum bending stress, maximum beam deflection, and bounds on the dimensions of the beam. Furthermore, the beam design also considers uncertainties in the manufacturing of the beams that may be caused by factors such as measurement precision errors. This is a case of robust optimization problem – solutions are sampled around the neighborhood of a normal solution and the mean and variance of this sample are taken as objective functions. In this study, robust optimization is presented using an elitist Non dominated Sorting Genetic Algorithm (NSGA-II), which does not involve a-priori weights on the objective functions as commonly done in practice. The solutions are evaluated using a penalized function of the cross-sectional area – constraint violation is penalized via static exterior penalty method. On the other hand, the uncertainties are generated using Latin Hypercube sampling instead of the usual Monte Carlo method. The robust solution is then taken from the optimum Pareto front of solutions based on the design priority of the manufacturer. It is found that the solution to the structural beam design without uncertainties tends to yield maximum bending stress. Thus, taking uncertainties into account penalizes the cross-sectional area of the solution leading to large values of average penalized objective function. Robust design on all three beams considered yields an increase of around 10 cm2 in their cross-sectional area but with reduced bending stress values. Remarkably, the robust design with Latin Hypercube sampling requires fewer samples in obtaining robust optimum than with Monte Carlo method.
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