90 Chapter 4. Fault Tree inference using Multi-Objective Evolutionary Algorithms and Confusion Matrix-based metrics Table 4.6: Convergence time in minutes taken per algorithm across all the case studies (evaluated 5 times) in Part I of this dissertation. |BEs| is the number of Basic Events; |F| is the FT size; |CD| is the number of MCSs in the ground truth problem. Q1, Q2, and Q3 are respectively the 25%, 50%, and 75% quantiles. Case |BEs||F| |CD| FT-EA FT-MOEA SymLearn FT-MOEA-CM Q1 Q2 Q3 Q1 Q2 Q3 Q1 Q2 Q3 Q1 Q2 Q3 CSD(a) 6 10 3 6.5 27.5 42.1 4.6 5.0 5.0 - - - 9.7 10.8 12.1 PT(b) 6 11 5 0.1 0.1 4.0 2.0 2.8 3.0 - - - 6.5 6.8 7.2 COVID-19(c) 9 13 6 37.8 39.0 42.9 13.2 22.3 24.1 - - - 12.6 14.4 15.3 ddFT(d) 8 13 6 26.8 37.7 40.9 10.9 23.0 56.3 - - - 21.7 23.1 25.7 MPPS(e) 8 23 7 19.0 46.6 55.3 26.2 29.9 33.9 - - - 16.6 16.9 18.0 SMS(f) 13 25 13 0.1‡ 0.1‡ 0.1‡ 214.0 218.8 219.0 - - - 215.3 216.4 216.5 gpt12(g1) 12 25 13 - - - 95.0 102.9 136.3 - - - 91.7 115.7 132.2 gpt15(g2) 15 27 10 - - - 254.2 254.2 308.5 - - - 399.5 402.8 432.8 SS(h1) 10 23 8 - - - 131.5 142.9 146.9 0.0 0.0 0.0 - - - SC(h2) 6 11 4 - - - 33.8 34.6 35.8 0.0 0.0 0.0 - - - TS1(i1) 10 34† 16 - - - 163.8 214.7 273.3 211.0 211.9 224.9 42.2 47.9 53.4 TS2(i2) 24 25† 26 - - - 51.7 112.2 127.1 0.7 0.7 0.7 - - - TS3(i3) 20 63† 18 - - - 89.4 91.4 92.8 2.1 2.2 2.2 - - - † Fault Trees associated to truss systems (Jimenez-Roa, Volk, and Stoelinga, 2022). (a)CSD: Container Seal Design (NASA, 2002); (b)PT: Pressure Tank (NASA, 2002); (c)COVID-19: COVID-19 FT (Jimenez-Roa, Heskes, Tinga, et al., 2023); (d)ddFT: Data-driven FT (Lazarova-Molnar, Niloofar, and Barta, 2020); (e)MPPS: Mono-propellant propulsion system (NASA, 2002); (f)SMS: Spread Monitoring System (Mentes and Helvacioglu, 2011); (g1)gpt12: GPT generated FT with 12 BEs (Jimenez-Roa, Rusnac, Volk, et al., 2024); (g2)gpt15: GPT generated FT with 15 BEs (Jimenez-Roa, Rusnac, Volk, et al., 2024); (h1)SS: symmetric toy-example (Jimenez-Roa, Volk, and Stoelinga, 2022); (h2)SC: symmetric toy-example (Jimenez-Roa, Volk, and Stoelinga, 2022); (h3)SC: Truss system case TS1 (Jimenez-Roa, Volk, and Stoelinga, 2022); (h4)SC: Truss system case TS2 (Jimenez-Roa, Volk, and Stoelinga, 2022); (h5)SC: Truss system case TS3 (Jimenez-Roa, Volk, and Stoelinga, 2022) We compared FT-MOEA-CM (this chapter), FT-MOEA (Chapter 2), SymLearn (Chapter 3), and FT-EA (Linard, Bucur, and Stoelinga, 2019) across 9 case studies, and the results suggest that FT-MOEA-CM is more robust, consistently achieving the global optima across all case studies, unlike the other implementations, and producing similar FT structures. In terms of scalability, FT-MOEA-CM appears superior to the alternatives, being capable of handling larger problems. Additionally, FT-MOEA-CM demonstrated a higher convergence speed, evaluated by both convergence time and convergence profile. FT-MOEA-CM’s features, caching and parallelisation, proved to improve convergence speed, with potential benefits to infer larger FTs. Future research. Possible directions for future work include: - Addressing the scalability issue in computing the algorithm’s confusion matrix metrics for exponentially growing datasets by using approximate evaluations with subsets of the failure dataset during initial algorithm generations. - Exploring methods to facilitate convergence to Directed Acyclic Graphs (DAGs) instead of trees, using tree decomposition and Tree Width metrics to measure a graph’s resemblance to a tree, applicable to specific DAG instances.
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