2 2.7. Experimental evaluation 51 Here, tr(.) represents the trace, and ωc ranges from 0 to 1, where 0 denotes perfect correlation between MD and M F . The RV-coe"cient is utilised due to the consistent number of unique BEs across all problems, despite the di!ering numbers of MCSs in FTs relative to those in the failure dataset (p ⇑ =q). Setups of the multi-objective functions Table 2.4: Di!erent setups of the m.o.f. m.o.f. ωs ωd ωc sdc ↭ ↭ ↭ dc ↭ ↭ sc ↭ ↭ sd ↭ ↭ c ↭ d ↭ Given that our multi-objective function (m.o.f.) has three arguments, we can explore various configurations to evaluate their impact (see Section 2.7.4 for parametric analysis results). For instance, to minimise only the error based on MCSs (ωc), we can deactivate ωs and ωd by setting them to constants (e.g., ωs =ωd =1). To distinguish between di!erent m.o.f. configurations, we adopt the nomenclature in Table 2.4, where ‘↭’ indicates whether a metric is considered (or active). 2.6.6 Step 5 - Convergence criteria Our convergence criterion is defined by two initial parameters: the max. number of generations (ng) and the max. generations with unchanged best candidate (see Section 2.6.1). The convergence process is also terminated if ωc =0 or ωd =0 when the minimisation of the FT size is deactivated, specifically for the m.o.f.’s cd, c, or d. 2.7 Experimental evaluation For our experimental evaluation, we selected six case studies from the literature (Section 2.7.2) and implemented our FT-MOEA algorithm in Python; the source code and data are available at zenodo.org/record/5536431. We evaluated the algorithm using synthetic failure datasets (Section 2.7.1). Section 2.7.3 compares FT-MOEA with FT-EA and provides details on convergence, while Section 2.7.4 presents our parametric analysis. 2.7.1 The Monte Carlo method We use the Monte Carlo method to generate synthetic failure datasets based on the case studies in Section 2.7.2, maintaining the properties of the input dataset described in Section 2.5. To generate the synthetic dataset, we: (i) randomly generate (N) data points by drawing the BE independently from a binomial distribution with a success probability of pi (where i represents a basic event), and (ii) compute the corresponding TE using the logical rules of the given FT (e.g., case studies in Section 2.7.2). To ensure the failure dataset is complete (see Section 2.5), we draw su"cient data points from the Monte Carlo simulation
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