Statistical Methods for Convergence Detection of Multi-Objective Evolutionary Algorithms

In this paper, two approaches for estimating the generation in which a multi-objective evolutionary algorithm (MOEA) shows statistically significant signs of convergence are introduced. A set-based perspective is taken where convergence is measured by performance indicators. The proposed techniques fulfill the requirements of proper statistical assessment on the one hand and efficient optimisation for real-world problems on the other hand. The first approach accounts for the stochastic nature of the MOEA by repeating the optimisation runs for increasing generation numbers and analysing the performance indicators using statistical tools. This technique results in a very robust offline procedure. Moreover, an online convergence detection method is introduced as well. This method automatically stops the MOEA when either the variance of the performance indicators falls below a specified threshold or a stagnation of their overall trend is detected. Both methods are analysed and compared for two MOEA and on different classes of benchmark functions. It is shown that the methods successfully operate on all stated problems needing less function evaluations while preserving good approximation duality at the same time.Article / Letter to editorLeiden Inst. Advanced Computer Science

Statistical Methods for Convergence Detection of Multi-Objective Evolutionary Algorithms

In this paper, two approaches for estimating the generation in which a multi-objective evolutionary algorithm (MOEA) shows statistically significant signs of convergence are introduced. A set-based perspective is taken where convergence is measured by performance indicators. The proposed techniques fulfill the requirements of proper statistical assessment on the one hand and efficient optimisation for real-world problems on the other hand. The first approach accounts for the stochastic nature of the MOEA by repeating the optimisation runs for increasing generation numbers and analysing the performance indicators using statistical tools. This technique results in a very robust offline procedure. Moreover, an online convergence detection method is introduced as well. This method automatically stops the MOEA when either the variance of the performance indicators falls below a specified threshold or a stagnation of their overall trend is detected. Both methods are analysed and compared for two MOEA and on different classes of benchmark functions. It is shown that the methods successfully operate on all stated problems needing less function evaluations while preserving good approximation duality at the same time.FWN – Publicaties zonder aanstelling Universiteit Leide

Distributions of deposits and hydrogen on the upper and lower TDUs3 target elements of Wendelstein 7-X

Distributions of deposits and hydrogen (H) on the graphite divertor target elements TM4h4 and TM3v5 in the test divertor units 3 (TDUs3) of Wendelstein 7-X (W7-X) are studied. The TM4h4 and TM3v5 are located at the magnetically symmetric positions in the upper and lower divertor. The microstructure of the deposition layer is characterized by a transmission electron microscope (TEM) combined with a focused ion beam (FIB). Metallic deposits such as iron (Fe), molybdenum (Mo), chromium (Cr) are detected in the deposition layer by energy-dispersive x-ray spectroscopy (EDS). The depth-resolved distribution patterns of boron (B) and metallic deposits on upper and lower horizontal (h) divertor target elements TDUs3-TM4h4 as well as upper and lower vertical (v) divertor target elements TDUs3-TM3v5 are clarified by glow discharge optical emission spectrometry (GDOES). Results for both TDUs3-TM4h4 and TDUs3-TM3v5 show that the B deposition regions exhibit higher H retention due to the co-deposition with deposits. On the other hand, up-down asymmetries in B deposition caused by particle drift exist on both TDUs3-TM4h4 and TDUs3-TM3v5. The B deposition amount on upper TDUs3-TM4h4 is 40% smaller than that on lower TDUs3-TM4h4. While for the vertical target elements, the B deposition amount on upper TDUs3-TM3v5 is 35% larger than that on lower TDUs3-TM3v5. Meanwhile, a shift of around 3 cm in B deposition peaks is observed on upper and lower TDUs3-TM4h4 and TDUs3-TM3v5. Results of numerical simulation of carbon deposition/erosion profiles on the target elements using ERO2.0 code and power flux measured by infrared cameras are shown and compared with the above mentioned B profiles