B.3. Example of inferred Fault Trees 207 B.2.2 Crowding-Distance This process is based on the Crowding-Distance (di) which makes that individuals with a large di wins, the latter to avoid solutions to be similar (i.e., to maintain diversity). This metric estimates the density of a particular solution in the nondominated front based on the neighbour solutions. We provide below a summary of the steps necessary to compute di. For details, we suggest the reader to consult Deb, 2005. • Step 1: For each solution in the non-dominated set (F) assign di =0. • Step 2: for all the objective functions m=1,2, ..., M, sort the set in worse order of fm and obtain the sorted index vector as I m=sort(fm, >). • Step 3: For all the objective functions, assign a large distance to the boundary solutions (i.e., dIm 1 =dIm|F| =△), and for the rest of the solutions j =2 to (|F| →1) , assign dImj =dImj + f Imj+1 m →f Imj↑1 m fmax m →f min m (B.1) Here Ij denotes the solution index of the j-th member sorted in the vector. • Step 4: Pass the solution with the largest di, then the solution with the second largest di, until the maximum population size is met. B.3 Example of inferred Fault Trees Here we provide as an example a pair of FTs obtained with the FT-MOEA. Figure B.2 shows the inferred FT associated with the Mono-propellant Propulsion System (MPPS) case study, the example that was used several times to exemplify our results. Here the right branch of the FT (i.e., the one associated with the intermediate event IE2), both sets of BEs and IEs coincide with the ground truth FT. In contrast, the intermediate events of the left branch were inferred by FT-MOEA (red boxes), to which we gave an interpretation. Similarly, in Figure B.3 we present the inferred FT of the COVID-19 infection risk. This FT originally has 33 elements, but after applying FT-MOEA, most of the intermediate events were replaced by more e"cient logics, resulting in an FT with 13 elements. Again, we provide an interpretation to the intermediate events found by the FT-MOEA (red boxes). First, it is interesting to see that all transmission modes were clustered under an OR-gate (IE3). We interpret the other two intermediate as Transmissibility of COVID-19 pathogen (AND-gate, IE2) and Existence of COVID-19 (OR-gate, IE1).
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