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

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.