Run and result

Just as described in above section 4.4, you run the program and rest for a while and then return back to have a check. It's lucky that the program has finished. It gives a bestindividual shown in Table 6.

Unfortunately, there're no true set of parameters as those nominal values used in above section 4.4. And also the bestindividual is very different from those produced by DYNAFIT $^{\mbox{\scriptsize\citep{DYNAFIT1996}}}$ and GEPASI $^{\mbox{\scriptsize\citep{GEPASI1998}}}$. So it's hard to say if it's the optimum.

Figure 17: Convergence curve of exhiv

But there are still some ways to examine the results. The fitness value and consumed time are compared with those of DYNAFIT $^{\mbox{\scriptsize\citep{DYNAFIT1996}}}$ and GEPASI $^{\mbox{\scriptsize\citep{GEPASI1998}}}$. The convergence curve drawn with the statistical information the program output indicates that libSRES can find the better individual using less time. Seen from Figure 17, the program has found one solution after three hours, running on the same platform described in Table 4. Just as mentioned above, it might not find the optimum as that in ThreeStep model, partly because there exist measurement errors. They are real experiments!

Figure 18: Fit curve of exhiv

Finally, the fit curve is drawn in Figure 18, where smooth curves represent simulated data using the optimized best individual and noisy curves represent the experimental data for the five experiments. The curves fit quite well. It's hard to judge if it's the optimum, but it fits.

Compared with other methods tested in previous work by Mendes and Kell $^{\mbox{\scriptsize\citep{GEPASI1998}}}$, SRES showed an advantage in global optimization. Table 8 listed performance of some methods: best results and corresponding number of simulations needed. The best result were found by SRES with rather less simulations (i.e., less time consumed). In contrast, some other methods converged to local solutions not far from the best solution, especially the methods of Levenberg-Marquardt and Hooke and Jeeves. These results also indicated the advantage (better performance) of SRES method.

Table 8: Performance comparison on HIV model

Methods	J	Ns		J	Ns
Simulated annealing	0.0211024	3131135	VS. SRES	0.021096	1034250
Levenberg-Marquardt	0.0213425	4475		0.021336	969500
Hooke and Jeeves (direct search)	0.0253683	43715		0.025339	556500
Genetic algorithm	0.226773	1020255		0.226124	192500
L-BFGS-B	1.92704	18690		1.795279	52500
Steepest descent	4.05282	1270		3.509421	29750
Random search	5.57454	1000155		4.654254	15750
				0.019999	1939000