A comparison between optimisation algorithms for metal forming processes: With application to forging

During the last decades, Finite Element (FEM) simulations of metal forming processes have become important tools for designing feasible production processes. In more recent years, several authors recognised the potential of coupling FEM simulations to mathematical opti- misation algorithms to design optimal metal forming processes instead of only feasible ones. The aim of this report is to compare two potentially powerful optimisation algorithms for optimising metal forming processes to each other: the Metamodel Assisted Evolutionary Strategy (MAES) developed at CEMEF and the Sequential Approximate Optimisation (SAO) algorithm developed at the University of Twente. For SAO, special attention was given to sequential improvement strategies. Four strategies have been developed, implemented and investigated: 1. SAO without zooming (SAO) 2. SAO with Zooming and Resampling (Z+R) 3. SAO with improvement by Minimising a Merit Function (SAO-MMF) 4. SAO with improvement by Maximising Expected Improvement (SAO-MEI) (Z+R) gave bad results for analytical test functions and was excluded from further research. SAO, SAO-MMF and SAO-MEI were compared to MAES by applying them to two forging processes: the Triaxe and the Engrenage. Next to the three SAO variants and MAES, an iterative BFGS algorithm and reference situations were also taken into account in the comparison. It can be concluded that: ² All optimisation algorithms yield better results than the reference situations ² SAO and MAES both outperform the iterative BFGS algorithm ² SAO-MMF and SAO-MEI yield better results than SAO without zooming ² SAO-MMF, SAO-MEI and MAES perform comparably well for both forging applica- tions. Although the di®erences are negligible, SAO-MEI proved to be slightly more superior than the other two algorithms for both the Triaxe and the Engrenag