Fig 7.

(Left) Number of restarts out of 20 that converged within a vicinity (percent) of the best-computed optimum for the NLP approach and the shooting method. For the NLP approach, these 20 restarts were performed with the 3rd-order Radau IIA method followed by refinement using the 9th-order method. The best achieved optimum was 660.39 with the 3rd-order method and 644.14 after the 9th-order refinement. For the shooting method we used the software INCA, and the best achieved optimum was 646.34. (Right) Results from 100 restarts for the genome-scale Synechocystis example. Using the NLP approach, most optimizations started from a random initial point converge to within 10% of the best-computed optimal solution, and a large fraction within 2%. This highlights the robustness of the NLP approach for inst-MFA applications.