2 2.6. Inferring Fault Trees via Multi-Objective Evolutionary Algorithms (FT-MOEA) 49 inaccurate MCSs or high computational costs could extend convergence time (discussed in Appendix B.7). The extraction of MCSs from a failure dataset follows Lazarova-Molnar, Niloofar, and Barta, 2020: Step 1: Identify all BE combinations resulting in class 1 (TE=1). Step 2: Select the combination with the minimal order (fewest true BE) and add it to the MCSs matrix (MD). Step 3: Remove any remaining combinations in the sub-set containing the identified MCS. Step 4: Repeat Steps 2 and 3 until the sub-set is empty. The resulting MD can be used to compute accuracy based on MCSs (ωc) (see Eq. 2.3). Table 2.3 shows an example of MD for the failure dataset in Table 2.2 associated to Figure 2.2. Table 2.3: Example of MCS matrix (MD) computed from the failure dataset described in Table 2.2 associated with the example in Figure 2.2. MCS BE1 BE2 BE3 BE4 BE5 BE6 BE7 1 1 1 0 0 0 0 0 2 0 0 1 1 1 0 1 3 0 0 1 0 1 1 1 4 0 0 1 1 0 1 1 2.6.3 Step 2 - Parent Fault Trees The parent Fault Trees serve as the basis from which the o!spring population is generated using genetic operators (Section 2.6.4). The choice of parent FT(s) is crucial as it influences the initial distance from the global optimum in the optimisation process. In Linard, Bucur, and Stoelinga, 2019, two parent FTs are used: one connects the set of BE to a single OR gate, and the other to a single ANDgate. 2.6.4 Step 3 - Genetic operators The genetic operators are mathematical functions designed to alter the structure of an FT. We employ the seven operators proposed by Linard, Bucur, and Stoelinga, 2019, which also provides their formal definitions. A brief overview is given next. Let G=V\BE be the set of gates in the FT: (i) G-create: Randomly creates an ANDor OR gate under an existing gate in the set Gfor a given FT. (ii) G-mutate: Randomly selects a gate in the set Gand changes its type (i.e., OR↑ANDor AND↑OR). (iii) G-delete: Selects a gate in the set Gof a given FT and deletes it along with its children.
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