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Table 5 Case 1 - Results Monte Carlo simulations (N=1000) in case of three uniformly distributed uncertain parameters k 1,k 2 and k 3 for robustified terminal constraint 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

PCE2 Uniform

α=1.96

      

\(\bar {J}\)

11.913

13.477

13.618

13.847

13.601

13.591

σ J

0.5470

0.9601

0.9942

1.0000

0.9835

0.9790

\(\bar {c_{t}}\)

0.88917

1.4768

1.5273

1.5533

1.5347

1.5261

\(\sigma _{c_{t}}\)

0.1818

0.3015

0.3110

0.3132

0.3137

0.3118

c t violation

516 (51.6 %)

4 (0.4 %)

1 (0.1 %)

0 (0.0 %)

1 (0.1 %)

2 (0.2 %)

α=1.65

      

\(\bar {J}\)

11.913

13.066

13.143

13.347

13.155

13.330

σ J

0.5470

0.8489

0.8730

0.6813

0.8750

0.8881

\(\bar {c_{t}}\)

0.88917

1.3384

1.3792

1.3940

1.3809

1.3660

\(\sigma _{c_{t}}\)

0.1818

0.2740

0.2820

0.2808

0.2819

0.2754

c t violation

516 (51.6 %)

35 (3.5 %)

22 (2.2 %)

11 (1.1 %)

22 (2.2 %)

22 (2.2 %)