2 2.6. Inferring Fault Trees via Multi-Objective Evolutionary Algorithms (FT-MOEA) 47 Table 2.2: Example of failure dataset associated to the example in Figure 2.2. Ob. BE1 BE2 BE3 BE4 BE5 BE6 BE7 TE Count 10000000 01,968 20000001 02,039 .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . 240010111 11,976 .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . 1281111111 11,947 p ↑ 0.50 0.50 0.50 0.50 0.50 0.50 0.50 N= 250,000 2.6 Inferring Fault Trees via Multi-Objective Evolutionary Algorithms (FT-MOEA) The algorithm takes as input the failure dataset (Section 2.5) and the initial MOEA parameters (Section 2.6.1). It outputs a string describing the inferred FT structure (AND- and OR-gates) and relevant error metrics between the inferred FT and the failure dataset, as detailed in Section 2.6.5. Figure 2.4 outlines our approach, comprising five steps: 1. Initialise the algorithm by loading the failure dataset (Section 2.5) and initial parameters (Section 2.6.1). Optionally, extract MCSs from the failure dataset (Section 2.6.2) if the objective function uses MCSs-based metrics. 2. Initialise the population with parent fault tree(s) (Section 2.6.3) and apply genetic operators to reach the desired population size. 3. Apply genetic operators (Section 2.6.4) to modify the FTs structure, repeating until the desired population size is achieved. 4. Calculate the optimisation metrics for each FT in the o!spring population (Section 2.6.5). Determine the next generation’s FTs using NSGA-II and Crowding-Distance (Section 2.3). 5. Evaluate convergence criteria (Section 2.6.6). If they are not met, repeat Steps 3 to 5 until a criterion is satisfied, resulting in a Pareto set of inferred FTs. Select the best individual with the smallest size and error(s) from the first Pareto set. 2.6.1 Step 1 - Initialisation We have the following initial parameters: - Population size (ps): Corresponds to the number of FTs within a generation. Only the best ps FTs can pass to the next generation. - Selection strategy: For the NSGA-II algorithm we only use the elitist selection strategy.
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