Table 2.

Parameter estimation with eSS (AMIGO implementation): settings and results

Model ID	B1	B2	B3	B4	B5	B6
p U	5·p nom	$10·p_{\mathit{\text{nom}}}^{\left(\mathit{\text{ex}}\right)}$	$10·p_{\mathit{\text{nom}}}^{\left(\mathit{\text{ex}}\right)}$	5·p nom	varying	varying
p L	0.2·p nom	$0.1·p_{\mathit{\text{nom}}}^{\left(\mathit{\text{ex}}\right)}$	$0.1·p_{\mathit{\text{nom}}}^{\left(\mathit{\text{ex}}\right)}$	0.2·p nom	varying	varying
Local method	DHC	FMINCON	none	FMINCON	DHC	FMINCON
CPU time	≈170 hours	≈3 hours	≈336 hours	≈1 hour	≈16 hours	≈24 hours
Evaluations	6.9678·105	9.0728·104	7.2193·106	1.6193·105	8.8393·104	2.0751·106
J 0	5.8819·109	3.1136·104	4.6930·1016	6.6034·108	3.1485·104	8.5769·105
J f	1.3753·104	2.3390·102	3.7029·10−1	4.5718·101	3.0725·103	1.0833·105
J nom	1.0846·106	−	0	3.9068·101	4.2737·103	−
$\sum {\mathit{\text{NRMSE}}}_0$	3.5834·101	8.5995·10−2	3.5457·101	4.8005·101	4.0434·101	2.3808·102
$\sum {\mathit{\text{NRMSE}}}_f$	5.7558	2.4921	2.9298·10−1	2.8010	2.7430·101	1.6212·102
$\sum {\mathit{\text{NRMSE}}}_{\mathit{\text{nom}}}$	3.8203	−	0	2.8273	3.0114·101	−

Optimization settings and results obtained for each of the benchmarks with the eSS method, using the implementation provided in the AMIGO toolbox. In some cases the lower (p ^L) and upper (p ^U) bounds in the parameters are specified as a function of the nominal parameter vector, p _nom. There may be exceptions to these bounds, in cases where it makes sense biologically to have a different range of values (e.g. Hill coefficients in the range of 1–12). Cases with exceptions are marked by ^(ex). In other cases all the parameters have specific bounds; this is marked as “varying”. The initial objective function value, J ₀, corresponds to the parameter vector p ₀ used as initial guess in the optimizations, which is randomly selected between the bounds p ^L and p ^U. The only exception is benchmark B2, where p ₀ is the parameter vector reported in the original publication. The final value achieved in the optimizations is J _f, and the value obtained with the nominal parameter vector is J _nom. More details about the definition of the objective functions J are given in section “Problem statement”. $\sum$NRMSE is the cumulative normalized root-mean-square error as defined in eq. (12); the subscripts (₀, _f, _nom) have the same meaning as in the objective functions J. Results obtained on a computer with Intel Xeon Quadcore processor, 2.50 GHz, using Matlab 7.9.0.529 (R2009b) 32-bit.