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Table 7 Case 2 - Results Monte Carlo simulations (N=1000) in case of three normally distributed uncertain parameters (K m , λ and k cat) for robustified terminal constraint and objective function with the number of constraint violations, mean values and variances on the objective function and terminal constraint, respectively

From: Dynamic optimization of biological networks under parametric uncertainty

  Nominal case Linearization Sigma points PCE1 PCE2
α=1.96      
\(\bar {J}\) 6.5268 12.996 12.549 8.7702 9.1358
σ J 0.57543 1.1893 1.15230 0.78540 0.82107
\(\bar {c_{t}}\) 0.69319 1.0106 1.0106 1.1406 1.2099
\(\sigma _{c_{t}}\) 0.18291 0.17462 0.17752 0.27117 0.28089
c t violation 477 (47.7 %) 15 (1.5 %) 18 (1.8 %) 23 (2.3 %) 13 (1.3 %)
α=1.65      
\(\bar {J}\) 6.5268 10.04 9.6011 8.2477 8.5514
σ J 0.57543 0.88430 0.83741 0.73621 0.76632
\(\bar {c_{t}}\) 0.69319 1.0143 1.0157 1.0339 1.0933
\(\sigma _{c_{t}}\) 0.18291 0.20620 0.21414 0.25176 0.26120
c t violation 477 (47.7 %) 31 (3.1 %) 39 (3.9 %) 53 (5.3 %) 34 (3.4 %)