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Strategy Single Iteration vs. Sequential

The two strategies for the calculation of global metamodels Single Iteration and Sequential are investigated.

Some applications of LS-OPT, like sensitivity analysis or multi-objective optimization (Pareto optimal solutions), require a global metamodel. There are two strategies available to calculate global metamodels, Single Iteration and Sequential. The strategies are compared by means of an application example.

The Crashworthiness Optimization example is used to compare the strategie Single Iteration and Sequential. The strategies and the number of simulation points are adapted.

  • For Single Iteration the number of sampling points is set to 30.
  • For Sequential 5 sampling points per iteration per case are calculated, and the maximal number of iterations is set to 6 iterations, hence 30 points are calculated in total.


Comparison of the results of the strategies Single Iteration and Sequential

Single Stage



Scatter Plots in 2D for the design variables

The distribution of the points is similar for both strategies.




Since the distribution of the points within the design space is a little bit different, the metamodels are also not exactly the same, but the tendencies are comparable.

single_06.png   sequential_06.png


Also the accuracy of the metamodels is similar. For the responses HIC and Disp2, the strategy Sequential leads to a little better results, whereas for the responses Mass and Disp1, the Singel Iteration results are a little bit more accurate.

single_05.png   sequential_05.png
Errors of each response Single Stage Sequential
RMS[%] SPRESS[%] Rsq RMS[%] SPRESS[%] Rsq
HIC 16.6 22.1 0.878 6.96 17.1 0.982
Mass 0.00641 0.00722 1 0.00702 0.00774 1
Disp2 0.294 0.59 0.996 0.238 0.373 0.997
Disp1 0.789 1.83 0.904 1.88 2.24 0.497

Global Sensitivities

The Global Sensitivity results are comparable and the variable ranking is the same for all responses.

single_10.png   sequential_10.png
Global Sensitivities of each response Single Stage Sequential
thood tbumper thood tbumper
HIC 0.8772 0.1713 0.8878 0.1724
Mass 0.9365 0.06658 0.9365 0.06658
Disp2 0.9752 0.03312 0.9743 0.03519
Disp1 0.7049 0.4837 0.7839 0.2812

 For the same total number of simulation points, the results of the strategies Single Iteration and Sequential are comparable.

Advantage of Sequential Strategy

The Sequential strategy is more flexible than the Single Iteration strategy. An advantage of Sequential methods is that one can set stopping tolerances. These allow the accuracy of the design model to be maximized if sufficient computing resources are available.

We can observe the progress of the metamodel quality, the sensitivity measures, ... after each iteration. In case there is no improvement, the process could be stopped, and continued otherwise.

SPRESS[%] errors  of each


Iteration number 
1 2 3 4 5 6
HIC 91.5 39.5 28.8 20.9 17.7 17.1
Mass 5.63e-06 0.00769 0.00662 0.00682 0.00755 0.00774
Disp2 2.62 1.45 0.443 0.507 0.435 0.373
Disp1 4.19 2.14 2.22 2.39 2.37 2.24

 If a Single Iteration strategy is selected, there is no information if additional simulation points could still improve the results, or even less points could have led to a similar accuracy.