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Table 4: T0335Results The results obtained with CPSA for T0335 are shown in Table 4. First of all, it can be observed that the execution time is significantly reduced in contrast with TSA. Notice that the quality solution is also increased with CPSAQ9 for al the target proteins tested. Additionally, in the previous experimentation a three reheats technique of CPSA is applied. However, to reduce the computational cost of CPSA algorithms, the number of reheats can be reduced to only one. Finally, in Table 5 the best implementation of the Cluster perturbation method is compared versus TSA and SMMP. A significant reduction in execution time by using CPSA with one reheat can be observed for all the instances tested in this work. We observed that whether the number of the reheat is risen the computational cost of CPSA is increased. CPSA overcomes TSA with an important reduction in execution time, and the best quality solution is obtained. SMMP with constant default values obtains good results for the worst and average cases; however, the computational time taken for hard proteins like T0335 is excessively large. This can be avoided by reducing the number of iterations that the SMMP algorithm performs, but the quality of the solution would be affected.

Table 4 T0335Results The results obtained with CPSA for T0335 are shown in Table 4. First of all, it can be observed that the execution time is significantly reduced in contrast with TSA. Notice that the quality solution is also increased with CPSAQ9 for al the target proteins tested. Additionally, in the previous experimentation a three reheats technique of CPSA is applied. However, to reduce the computational cost of CPSA algorithms, the number of reheats can be reduced to only one. Finally, in Table 5 the best implementation of the Cluster perturbation method is compared versus TSA and SMMP. A significant reduction in execution time by using CPSA with one reheat can be observed for all the instances tested in this work. We observed that whether the number of the reheat is risen the computational cost of CPSA is increased. CPSA overcomes TSA with an important reduction in execution time, and the best quality solution is obtained. SMMP with constant default values obtains good results for the worst and average cases; however, the computational time taken for hard proteins like T0335 is excessively large. This can be avoided by reducing the number of iterations that the SMMP algorithm performs, but the quality of the solution would be affected.

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Frausto-Solis J., Sanchez-Perez M., Linan-Garcia E., Sanchez-Hernandez J.P. ...
Frausto-Solis J., Sanchez-Perez M., Linan-Garcia E., Sanchez-Hernandez J.P. ...
Other parameters are also used in this analytical tuning method; one of them is the length of the Markov chain (L,) of the Metropolis cycle (or number of iterations) [Frausto-Solis et al., 2006]. SA can be adapted using constant or vari- able Markov Chains. The first approach is in general more easily implemented; however, the last one has shown to achieve a better performance than constant Markov chains [Frausto-Solis et al., 2007]. In order to adjust the variable Markov Chains, the analytical tuning method determines the length of the metropolis cycle. tion of the objective function (AZyax,AZwrn) and the associated acceptance probability from equation 2 and 3.
Other parameters are also used in this analytical tuning method; one of them is the length of the Markov chain (L,) of the Metropolis cycle (or number of iterations) [Frausto-Solis et al., 2006]. SA can be adapted using constant or vari- able Markov Chains. The first approach is in general more easily implemented; however, the last one has shown to achieve a better performance than constant Markov chains [Frausto-Solis et al., 2007]. In order to adjust the variable Markov Chains, the analytical tuning method determines the length of the metropolis cycle. tion of the objective function (AZyax,AZwrn) and the associated acceptance probability from equation 2 and 3.
Figure 1: Cooling Behavior of SA with Reheat Frausto-Solis J., Sanchez-Perez M., Linan-Garcia E., Sanchez-Hernandez J.P. ...
Figure 1: Cooling Behavior of SA with Reheat Frausto-Solis J., Sanchez-Perez M., Linan-Garcia E., Sanchez-Hernandez J.P. ...
Figure 2: Behavior of Different values of a in the range of 0.7 < a < 0.99 In this work, a high a value of 0.95 was experimentally determined, consid- ering a trade-off between execution time and quality solution.
Figure 2: Behavior of Different values of a in the range of 0.7 < a < 0.99 In this work, a high a value of 0.95 was experimentally determined, consid- ering a trade-off between execution time and quality solution.
Table 1: Protein Folding Instances The algorithms TSA, CPSA, and their variants were executed thirty times. The runtime values and minimum and maximum values of energy were obtained for the purpose of comparing the target proteins, and the results are discussed in the next section.
Table 1: Protein Folding Instances The algorithms TSA, CPSA, and their variants were executed thirty times. The runtime values and minimum and maximum values of energy were obtained for the purpose of comparing the target proteins, and the results are discussed in the next section.
Table 2: Met°® — enkephaline Results Table 2 shows the best, worst and average solution for that CPSA, SMMP and TSA. For the best solution case, CPSA found the lowest energy (—10.48). However, SMMP found the lower energy in the worst and average case for this small peptide.
Table 2: Met°® — enkephaline Results Table 2 shows the best, worst and average solution for that CPSA, SMMP and TSA. For the best solution case, CPSA found the lowest energy (—10.48). However, SMMP found the lower energy in the worst and average case for this small peptide.
Table 3: C-Peptide Results In Table 3, CPSA and TSA results for a little larger protein (C-peptide) of thirteen amino acids are shown. In this case CPSA9 obtains the best quality results (columns 2-6), that is a considerable reduction in computational time than the other two approaches. The other CPSA variants have better quality results than TSA; besides, the execution time of CPSAQ is significantly reduced, and all the results overcome the quality of the solution of TSA and SMMP.
Table 3: C-Peptide Results In Table 3, CPSA and TSA results for a little larger protein (C-peptide) of thirteen amino acids are shown. In this case CPSA9 obtains the best quality results (columns 2-6), that is a considerable reduction in computational time than the other two approaches. The other CPSA variants have better quality results than TSA; besides, the execution time of CPSAQ is significantly reduced, and all the results overcome the quality of the solution of TSA and SMMP.
Table 5: Final Results (All Proteins with the algorithms SMMP, TSA, and CP90) According to the results presented in Table 5. CPSA obtained the best results for Met°® — enkephaline, these results are to close with that obtained by those recently publised in the literature [Sudha et al., 2013].
Table 5: Final Results (All Proteins with the algorithms SMMP, TSA, and CP90) According to the results presented in Table 5. CPSA obtained the best results for Met°® — enkephaline, these results are to close with that obtained by those recently publised in the literature [Sudha et al., 2013].
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