58 Chapter 2. Automatic Inference of Fault Tree Models via Multi-Objective Evolutionary Algorithms a challenge for FTs with numerous BEs. A potential solution is to employ “guided” multi-objective evolutionary algorithms, which enhance the optimisation process by incorporating additional knowledge. One approach involves identifying patterns in the failure dataset to assemble parts of the FT (e.g., Waghen and Ouali, 2021). Another involves guiding the application of genetic operators by targeting FT components that likely require modification, potentially achieved through Bayesian optimisation. Alternatively, deep learning-based approaches, such as the one proposed by Cranmer, Sanchez-Gonzalez, Battaglia, et al., 2020, could be explored to derive symbolic rules from Graph Neural Networks. Incorporating Minimal Cut Sets (MCSs) into the multi-objective optimisation function significantly improves the process. However, the FT-MOEA algorithm computes MCSs using Disjunctive Normal Form, which is computationally expensive for large FTs. Additionally, MCSs cannot be computed in noisy data (see Appendix B.7 for preliminary results on noise e!ects). Therefore, exploring alternatives to address these issues is crucial. Finally, several challenges deserve further investigation: - Obtaining noise-free, balanced, and complete failure datasets for complex engineering systems is nearly impossible. Thus, further evaluation of our algorithm’s performance with incomplete, noisy, and unbalanced datasets is necessary. - Real-world problems often contain symmetries, such as fully exchangeable basic events. Leveraging these symmetries could reduce the solution space and accelerate convergence, requiring research in this direction. - Exploring methods to infer more sophisticated gates (e.g., VoT gates) is key for obtaining more compact and e"cient FT structures. - The methodology used in this chapter could be extended to infer other reliability models, such as Reliability Block Diagrams and Boolean circuits. - Further research is needed to understand and quantify the complexity in FT model inference. Developing guidelines and metrics to assess the practical capabilities of FT inference algorithms remains an open challenge. Overall, our novel algorithm, FT-MOEA, outperforms its predecessor, FT-EA, by converging faster, inferring more compact FT structures, achieving lower error levels, better removing superfluous variables, and maintaining consistency. 2.9 References Bakeli, T., A. A. Hafidi, et al. (2020). “COVID-19 infection risk management during construction activities: An approach based on Fault Tree Analysis (FTA)”. In: Journal of Emergency Management 18.7, pp. 161–176. doi: 10.5055/jem.0539. Cranmer, M., A. Sanchez-Gonzalez, P. Battaglia, R. Xu, K. Cranmer, D. Spergel, and S. Ho (2020). Discovering Symbolic Models from Deep Learning with Inductive Biases. doi: 10.48550/arXiv.2006.11287. arXiv: 2006.11287 [cs.LG]. Deb, K., A. Pratap, S. Agarwal, and T. Meyarivan (2002). “A fast and elitist multiobjective genetic algorithm: NSGA-II”. In: IEEE Transactions on Evolutionary Computation 6 (2), pp. 182–197. doi: 10.1109/4235.996017.
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