Performance analysis of parameter estimation using numerical optimization methods.

<p>(<b>a</b>) A two dimensional parameter estimation problem <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074335#pone.0074335-Himmelblau1" target="_blank">[15]</a> bearing multiple optima (global: A; local: B,C,D) is displayed for illustrative purposes. Traces in parameter space of two hypothetical methods with high (blue) and low performance (red) are displayed. 50 independent runs with each method are displayed; the circles indicate the results of the estimation. (<b>b</b>) The visualization of optimization performance by sorting objective function values increasingly is also possible for high dimensional problems. It reveals that the performance of the red method is low, i.e. results are unreliable, whereas the performance of the blue method is high, i.e. results are reproducible and reliable. (<b>c,d</b>) Visualization of performance using 100 independent optimization runs with each of the considered algorithms for both quantitative dynamic models. For illustrative reasons, the global optimum was centered to one. For stochastic optimization (gray), 12 different algorithms <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074335#pone.0074335-Kronfeld1" target="_blank">[18]</a> were used (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074335#pone-0074335-g011" target="_blank">Figure 11</a> for details). For deterministic optimization, two different approaches for the calculation of derivatives were compared: (i) finite difference approximation (red) and (ii) analytically derived sensitivity equations (orange and blue). Initial guesses for the parameters were generated by Latin hypercube sampling <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074335#pone.0074335-Owen1" target="_blank">[17]</a>. All algorithms are described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074335#pone-0074335-t001" target="_blank">Table 1</a>.