PSI - Issue 37

Alexandru Vasile et al. / Procedia Structural Integrity 37 (2022) 857–864 Vasile et al./ Structural Integrity Procedia 00 (2019) 000 – 000

864

8

Table 3. Table with results from running the algorithms on 10 different initial configurations.

No of tests that converged to a local maximum

No of tests that converged to a global maximum

Mean estimated time [s]

Symbol

Greedy Algorithm

10

0

78

Simulated Annealing (with acc_prob compared to a random number ∈ [0;1)) Simulated Annealing (with acc_prob compared to an imposed value of 0.5)

7

3

331

4

6

684

5. Conclusions We can conclude that in order to assess the accuracy of other types of optimization algorithms it is necessary to have all the possible distributions of materials available. We were able to gather indications about the precision of our algorithms using a brute force approach. It is important to mention that the brute force program created using the PyAnsys software that uses the Ansys solver was faster than the same program written using the MAPDL software in Ansys by an estimated 11%. We can reiterate the issue of the Greedy algorithm of not being able to accept worse solutions, drawback which can be avoided if we implement a few simulated annealing elements to the optimization program, as to avoid being blocked on a local maximum. The simulated annealing program provided better results than the Greedy algorithm in all analyzed cases, but it does not always converge to a global optimum. A way to improve the accuracy of the procedure could be to modify the parameters used, for example, the acceptance probability and temperature, because their expression greatly influences the obtained results. One disadvantage is that the simulated annealing program takes a longer time to compile than for the Greedy algorithm. However, its speed can be modified with the parameters defined, depending on how thorough we need it to be in its analysis. 6. Future work To improve the current performance of the algorithms we intend to look for other formulations for the objective function, which is the most important parameter that influences our designs, check the behavior of the algorithms on wider domains, develop for a method that does not involve choosing a new random distribution when we need to cross the local minimum and to find other formulations for the temperature and acceptance probability parameters. Acknowledgements This work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CCCDI - UEFISCDI, project number ERANET-M-RIPE4TEC-1, within PNCDI III. References Gu, G.X., Dimas, L, Qin, Z., Buehler, M.J., 2016. Optimization of Composite Fracture Properties: Method, Validation, and Applications, Journal of Applied Mechanics, Transactions ASME 83, 1 – 7, doi: 10.1115/1.4033381. Kaszynski, A., Williams, D., Xavier, J., Kreuter, D., Capodiferro, M., 2021. pyansys/pymapdl: PyMAPDL 0.59.5 Release Notes. https://github.com/pyansys/pymapdl/releases , accessed September 22, 2021. Kato, J., 2010. Material Optimization for Fiber Reinforced Composites Applying a Damage Formulation, PhD Thesis, Universität Stuttgart. Nikolaev, A.G., Jacobson, S.H., 2010. Simulated Annealing, in “ Handbook of Metaheuristics ” , International Series in Operations Research & Management Science 146. In: M. Gendreau, J.-Y. Potvin (eds.), doi: 10.1007/978-1-4419-1665-5_1, Springer Science+Business Media, New York, pp. 1 – 39.