56 Chapter 2. Automatic Inference of Fault Tree Models via Multi-Objective Evolutionary Algorithms c d dc sc sd sdc m.o.f. 0 25 50 75 100 125 150 175 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 c d dc sc sd sdc m.o.f. c d dc sc sd sdc m.o.f. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 COVID-19 MPPS ddFT c d dc sc sd sdc m.o.f. 0 50 100 150 200 250 300 Conv. Time (min) (a) (b) (c) (d) d s c Figure 2.8: Comparison of m.o.f. performance for case studies: COVID-19, MPPS, and ddFT (see Table 2.5), with ps =400, ng =100, and uc =20: (a) εd, (b) εc, (c) εs, and (d) convergence time in minutes. Figure 2.8(a) shows the error based on the failure dataset (ωd). Di!erent objective functions exhibit varied behaviours. The m.o.f. dc achieves the exact solution for all cases, whereas the other m.o.f.s fail to find the global optimum in at least one case. Similarly, Figure 2.8(b) shows the error based on MCSs (ωc). As expected, the m.o.f. dc achieves ωc =0.0 for all cases. However, note that a low ωd does not necessarily imply an optimal FT; for instance, compare ωd and ωc for the MPPS case using m.o.f.s d and sd. Errors ωd and ωc, particularly for the ddFT case study, tend to increase when ωs is minimised (i.e., m.o.f.s sc, sd, and sdc), suggesting that FT-MOEA may converge to an FT with a slightly larger error but smaller size. Figure 2.8(c) shows the sizes of the inferred FTs (ωs). The influence of minimising ωs is evident; when considered, ωs in most cases is equal to or smaller than the ground truth, as indicated by the horizontal lines for di!erent case studies (see Appendix B.3 for examples and details). When not considered, ωs may exceed the ground truth in some cases.
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