### Abstract

In the scope of a NIMR (Netherlands Institute for Metals Research) project called Optimisation of
Forming Processes, an efficient algorithm has been developed to solve optimisation problems for
metal forming processes using time consuming FEM (Finite Element Method) simulations. The
developed Sequential Approximate Optimisation algorithm (SAO) uses both Response Surface
Methodology and Design and Analysis of Computer Experiments. The efficiency of this algorithm
decreases with increasing number of design variables because of the high number of FEM
simulations required.
To overcome such a problem two solutions have been investigated in the present research. The first
one is to use an Evolutionary Strategy (ES), which is good to find global optimum and is able to deal
with a higher numbers of design variables. Unfortunately, it requires many function evaluations.
Behind this idea was to create an algorithm called ESAO, which is an Evolutionary version of the
SAO, to keep the benefit of the ES while using the metamodels of the SAO to avoid too many
function evaluations.
The second solution consists in comparing different Design Of Experiments (DOE) for a fixed
number of design variables of the SAO. The DOE used are: full factorial design, fractional factorial
design or latin hypercube design.
This paper investigates the sensitivity of the three algorithms, SAO (with different DOE’s), ES and
ESAO, to an increasing number of design variables taken into account in optimisation problems.
Even if this comparison has not yet been applied to a real industrial study, it can be concluded that
the SAO algorithm outperforms both the ES and the ESAO algorithm, i.e. it gives more accurate
results for less iterations. It is especially emphasized that when the number of design variables is
larger than five, then the choice of the DOE becomes crucial. Indeed, it is shown that for a given
number of points, the use of corner points decreases the accuracy of the metamodel inside the
domain. The comparison of the DOE’s shows that the SAO associated with a fractional factorial
design is the most efficient method.

Original language | English |
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Publisher | University of Twente |

Number of pages | 16 |

Publication status | Published - 2006 |

### Keywords

- IR-59578

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## Cite this

Trichon, S. (2006).

*Stay at University of Twente: Faculty of Engineering Technology, Applied Mechanics Group*. University of Twente.