C.- CONVENCION INTERAMERICANA SOBRE RESTITUCION INTERNACIONAL DE MENORES.
VI.- LA PERSPECTIVA EN EL MERCOSUR.
The performance of the optimisers regarding their convergence is studied comparatively through plots presented in Figure 4.10, with respect to the objective functions:
Bubble size represents CO2 emission;
Colour represents costs
Bubble size represents costs;
Colour represents CO2
Chapter Four
70
a. Convergence w.r.t CO2 emission b. Convergence w.r.t costs
Figure 4.10 Comparative convergence plots of the GA-based optimisers
It is evident from plot ‘a’ and plot ‘b’ of Figure 4.10 that the NSGA-II algorithm is converging in a comparatively better way than that of MOGA-II. History plots, Box Whiskers and Density plots (Appendix B.3) are considered for statistical analysis of the results.
4.7.1.2. ANOVA
One-way ANOVA is performed for both the total CO2 emission and total costs of trans- portation to compare the means of multiple groups of the optimised data. ANOVA computes the p-value for the null hypothesis to detect if data from several groups have a common mean. Tables 4.14 and 4.15 present the ANOVA results for the two GA-based optimisers with respect to CO2 emission and costs respectively. The ANOVA statistics are used to test the null-hypothesis (Walpole et al. 2006). For the two optimisers ANO- VA computes the source of the variability, sum of squares (SS) due to each source, de- grees of freedom (Df) associated with each source, mean squares (MS) for each source (SS/Df ratio), F-statistic (ratio of two MS) and p-value given by the cdf of F. It is noted that as the F-ratio increases, the p-value decreases. The ANOvA test presented in Tables 4.14 and 4.15 are calculated for refined realistic results. The insignificance in p-value could be a result of this selection of results. It is necessary to mention again that not all results are realistic and they have to be refined in order to find the realistic results. Table 4.14 ANOVA for CO2 emission on the refined realistic results
Optimiser
Source of Variation
SS Df MS F-ratio p-value
MOGA-II
Between groups 6.0825E6 8.1000E1 7.5093E4 3.1338E0 2.5970E-8
Within groups 2.5160E6 1.0500E2 2.3962E4 –– ––
Total 8.5985E6 1.8600E2
NSGA-II
Between groups 1.7674E6 4.0000E0 4.4185E5 1.6424E1 1.0559E-12
Within groups 1.4419E7 5.3600E2 2.6902E4 –– ––
Total 1.6187E7 5.4000E2
Chapter Four
70
a. Convergence w.r.t CO2 emission b. Convergence w.r.t costs
Figure 4.10 Comparative convergence plots of the GA-based optimisers
It is evident from plot ‘a’ and plot ‘b’ of Figure 4.10 that the NSGA-II algorithm is converging in a comparatively better way than that of MOGA-II. History plots, Box Whiskers and Density plots (Appendix B.3) are considered for statistical analysis of the results.
4.7.1.2. ANOVA
One-way ANOVA is performed for both the total CO2 emission and total costs of trans- portation to compare the means of multiple groups of the optimised data. ANOVA computes the p-value for the null hypothesis to detect if data from several groups have a common mean. Tables 4.14 and 4.15 present the ANOVA results for the two GA-based optimisers with respect to CO2 emission and costs respectively. The ANOVA statistics are used to test the null-hypothesis (Walpole et al. 2006). For the two optimisers ANO- VA computes the source of the variability, sum of squares (SS) due to each source, de- grees of freedom (Df) associated with each source, mean squares (MS) for each source (SS/Df ratio), F-statistic (ratio of two MS) and p-value given by the cdf of F. It is noted that as the F-ratio increases, the p-value decreases. The ANOvA test presented in Tables 4.14 and 4.15 are calculated for refined realistic results. The insignificance in p-value could be a result of this selection of results. It is necessary to mention again that not all results are realistic and they have to be refined in order to find the realistic results. Table 4.14 ANOVA for CO2 emission on the refined realistic results
Optimiser
Source of Variation
SS Df MS F-ratio p-value
MOGA-II
Between groups 6.0825E6 8.1000E1 7.5093E4 3.1338E0 2.5970E-8
Within groups 2.5160E6 1.0500E2 2.3962E4 –– ––
Total 8.5985E6 1.8600E2
NSGA-II
Between groups 1.7674E6 4.0000E0 4.4185E5 1.6424E1 1.0559E-12
Within groups 1.4419E7 5.3600E2 2.6902E4 –– ––
Total 1.6187E7 5.4000E2
Chapter Four
70
a. Convergence w.r.t CO2 emission b. Convergence w.r.t costs
Figure 4.10 Comparative convergence plots of the GA-based optimisers
It is evident from plot ‘a’ and plot ‘b’ of Figure 4.10 that the NSGA-II algorithm is converging in a comparatively better way than that of MOGA-II. History plots, Box Whiskers and Density plots (Appendix B.3) are considered for statistical analysis of the results.
4.7.1.2. ANOVA
One-way ANOVA is performed for both the total CO2 emission and total costs of trans- portation to compare the means of multiple groups of the optimised data. ANOVA computes the p-value for the null hypothesis to detect if data from several groups have a common mean. Tables 4.14 and 4.15 present the ANOVA results for the two GA-based optimisers with respect to CO2 emission and costs respectively. The ANOVA statistics are used to test the null-hypothesis (Walpole et al. 2006). For the two optimisers ANO- VA computes the source of the variability, sum of squares (SS) due to each source, de- grees of freedom (Df) associated with each source, mean squares (MS) for each source (SS/Df ratio), F-statistic (ratio of two MS) and p-value given by the cdf of F. It is noted that as the F-ratio increases, the p-value decreases. The ANOvA test presented in Tables 4.14 and 4.15 are calculated for refined realistic results. The insignificance in p-value could be a result of this selection of results. It is necessary to mention again that not all results are realistic and they have to be refined in order to find the realistic results. Table 4.14 ANOVA for CO2 emission on the refined realistic results
Optimiser
Source of Variation
SS Df MS F-ratio p-value
MOGA-II
Between groups 6.0825E6 8.1000E1 7.5093E4 3.1338E0 2.5970E-8
Within groups 2.5160E6 1.0500E2 2.3962E4 –– ––
Total 8.5985E6 1.8600E2
NSGA-II
Between groups 1.7674E6 4.0000E0 4.4185E5 1.6424E1 1.0559E-12
Within groups 1.4419E7 5.3600E2 2.6902E4 –– ––
Total 1.6187E7 5.4000E2
Chapter Four
70
a. Convergence w.r.t CO2 emission b. Convergence w.r.t costs
Figure 4.10 Comparative convergence plots of the GA-based optimisers
It is evident from plot ‘a’ and plot ‘b’ of Figure 4.10 that the NSGA-II algorithm is converging in a comparatively better way than that of MOGA-II. History plots, Box Whiskers and Density plots (Appendix B.3) are considered for statistical analysis of the results.
4.7.1.2. ANOVA
One-way ANOVA is performed for both the total CO2 emission and total costs of trans- portation to compare the means of multiple groups of the optimised data. ANOVA computes the p-value for the null hypothesis to detect if data from several groups have a common mean. Tables 4.14 and 4.15 present the ANOVA results for the two GA-based optimisers with respect to CO2 emission and costs respectively. The ANOVA statistics are used to test the null-hypothesis (Walpole et al. 2006). For the two optimisers ANO- VA computes the source of the variability, sum of squares (SS) due to each source, de- grees of freedom (Df) associated with each source, mean squares (MS) for each source (SS/Df ratio), F-statistic (ratio of two MS) and p-value given by the cdf of F. It is noted that as the F-ratio increases, the p-value decreases. The ANOvA test presented in Tables 4.14 and 4.15 are calculated for refined realistic results. The insignificance in p-value could be a result of this selection of results. It is necessary to mention again that not all results are realistic and they have to be refined in order to find the realistic results. Table 4.14 ANOVA for CO2 emission on the refined realistic results
Optimiser
Source of Variation
SS Df MS F-ratio p-value
MOGA-II
Between groups 6.0825E6 8.1000E1 7.5093E4 3.1338E0 2.5970E-8
Within groups 2.5160E6 1.0500E2 2.3962E4 –– ––
Total 8.5985E6 1.8600E2
NSGA-II
Between groups 1.7674E6 4.0000E0 4.4185E5 1.6424E1 1.0559E-12
Within groups 1.4419E7 5.3600E2 2.6902E4 –– ––
Total 1.6187E7 5.4000E2
Chapter Four
70
a. Convergence w.r.t CO2 emission b. Convergence w.r.t costs
Figure 4.10 Comparative convergence plots of the GA-based optimisers
It is evident from plot ‘a’ and plot ‘b’ of Figure 4.10 that the NSGA-II algorithm is converging in a comparatively better way than that of MOGA-II. History plots, Box Whiskers and Density plots (Appendix B.3) are considered for statistical analysis of the results.
4.7.1.2. ANOVA
One-way ANOVA is performed for both the total CO2 emission and total costs of trans- portation to compare the means of multiple groups of the optimised data. ANOVA computes the p-value for the null hypothesis to detect if data from several groups have a common mean. Tables 4.14 and 4.15 present the ANOVA results for the two GA-based optimisers with respect to CO2 emission and costs respectively. The ANOVA statistics are used to test the null-hypothesis (Walpole et al. 2006). For the two optimisers ANO- VA computes the source of the variability, sum of squares (SS) due to each source, de- grees of freedom (Df) associated with each source, mean squares (MS) for each source (SS/Df ratio), F-statistic (ratio of two MS) and p-value given by the cdf of F. It is noted that as the F-ratio increases, the p-value decreases. The ANOvA test presented in Tables 4.14 and 4.15 are calculated for refined realistic results. The insignificance in p-value could be a result of this selection of results. It is necessary to mention again that not all results are realistic and they have to be refined in order to find the realistic results. Table 4.14 ANOVA for CO2 emission on the refined realistic results
Optimiser
Source of Variation
SS Df MS F-ratio p-value
MOGA-II
Between groups 6.0825E6 8.1000E1 7.5093E4 3.1338E0 2.5970E-8
Within groups 2.5160E6 1.0500E2 2.3962E4 –– ––
Total 8.5985E6 1.8600E2
NSGA-II
Between groups 1.7674E6 4.0000E0 4.4185E5 1.6424E1 1.0559E-12
Within groups 1.4419E7 5.3600E2 2.6902E4 –– ––
Total 1.6187E7 5.4000E2
Chapter Four
70
a. Convergence w.r.t CO2 emission b. Convergence w.r.t costs
Figure 4.10 Comparative convergence plots of the GA-based optimisers
It is evident from plot ‘a’ and plot ‘b’ of Figure 4.10 that the NSGA-II algorithm is converging in a comparatively better way than that of MOGA-II. History plots, Box Whiskers and Density plots (Appendix B.3) are considered for statistical analysis of the results.
4.7.1.2. ANOVA
One-way ANOVA is performed for both the total CO2 emission and total costs of trans- portation to compare the means of multiple groups of the optimised data. ANOVA computes the p-value for the null hypothesis to detect if data from several groups have a common mean. Tables 4.14 and 4.15 present the ANOVA results for the two GA-based optimisers with respect to CO2 emission and costs respectively. The ANOVA statistics are used to test the null-hypothesis (Walpole et al. 2006). For the two optimisers ANO- VA computes the source of the variability, sum of squares (SS) due to each source, de- grees of freedom (Df) associated with each source, mean squares (MS) for each source (SS/Df ratio), F-statistic (ratio of two MS) and p-value given by the cdf of F. It is noted that as the F-ratio increases, the p-value decreases. The ANOvA test presented in Tables 4.14 and 4.15 are calculated for refined realistic results. The insignificance in p-value could be a result of this selection of results. It is necessary to mention again that not all results are realistic and they have to be refined in order to find the realistic results. Table 4.14 ANOVA for CO2 emission on the refined realistic results
Optimiser
Source of Variation
SS Df MS F-ratio p-value
MOGA-II
Between groups 6.0825E6 8.1000E1 7.5093E4 3.1338E0 2.5970E-8
Within groups 2.5160E6 1.0500E2 2.3962E4 –– ––
Total 8.5985E6 1.8600E2
NSGA-II
Between groups 1.7674E6 4.0000E0 4.4185E5 1.6424E1 1.0559E-12
Within groups 1.4419E7 5.3600E2 2.6902E4 –– ––
Total 1.6187E7 5.4000E2
Chapter Four
70
a. Convergence w.r.t CO2 emission b. Convergence w.r.t costs
Figure 4.10 Comparative convergence plots of the GA-based optimisers
It is evident from plot ‘a’ and plot ‘b’ of Figure 4.10 that the NSGA-II algorithm is converging in a comparatively better way than that of MOGA-II. History plots, Box Whiskers and Density plots (Appendix B.3) are considered for statistical analysis of the results.
4.7.1.2. ANOVA
One-way ANOVA is performed for both the total CO2 emission and total costs of trans- portation to compare the means of multiple groups of the optimised data. ANOVA computes the p-value for the null hypothesis to detect if data from several groups have a common mean. Tables 4.14 and 4.15 present the ANOVA results for the two GA-based optimisers with respect to CO2 emission and costs respectively. The ANOVA statistics are used to test the null-hypothesis (Walpole et al. 2006). For the two optimisers ANO- VA computes the source of the variability, sum of squares (SS) due to each source, de- grees of freedom (Df) associated with each source, mean squares (MS) for each source (SS/Df ratio), F-statistic (ratio of two MS) and p-value given by the cdf of F. It is noted that as the F-ratio increases, the p-value decreases. The ANOvA test presented in Tables 4.14 and 4.15 are calculated for refined realistic results. The insignificance in p-value could be a result of this selection of results. It is necessary to mention again that not all results are realistic and they have to be refined in order to find the realistic results. Table 4.14 ANOVA for CO2 emission on the refined realistic results
Optimiser
Source of Variation
SS Df MS F-ratio p-value
MOGA-II
Between groups 6.0825E6 8.1000E1 7.5093E4 3.1338E0 2.5970E-8
Within groups 2.5160E6 1.0500E2 2.3962E4 –– ––
Total 8.5985E6 1.8600E2
NSGA-II
Between groups 1.7674E6 4.0000E0 4.4185E5 1.6424E1 1.0559E-12
Within groups 1.4419E7 5.3600E2 2.6902E4 –– ––
Total 1.6187E7 5.4000E2
Chapter Four
70
a. Convergence w.r.t CO2 emission b. Convergence w.r.t costs
Figure 4.10 Comparative convergence plots of the GA-based optimisers
It is evident from plot ‘a’ and plot ‘b’ of Figure 4.10 that the NSGA-II algorithm is converging in a comparatively better way than that of MOGA-II. History plots, Box Whiskers and Density plots (Appendix B.3) are considered for statistical analysis of the results.
4.7.1.2. ANOVA
One-way ANOVA is performed for both the total CO2 emission and total costs of trans- portation to compare the means of multiple groups of the optimised data. ANOVA computes the p-value for the null hypothesis to detect if data from several groups have a common mean. Tables 4.14 and 4.15 present the ANOVA results for the two GA-based optimisers with respect to CO2 emission and costs respectively. The ANOVA statistics are used to test the null-hypothesis (Walpole et al. 2006). For the two optimisers ANO- VA computes the source of the variability, sum of squares (SS) due to each source, de- grees of freedom (Df) associated with each source, mean squares (MS) for each source (SS/Df ratio), F-statistic (ratio of two MS) and p-value given by the cdf of F. It is noted that as the F-ratio increases, the p-value decreases. The ANOvA test presented in Tables 4.14 and 4.15 are calculated for refined realistic results. The insignificance in p-value could be a result of this selection of results. It is necessary to mention again that not all results are realistic and they have to be refined in order to find the realistic results. Table 4.14 ANOVA for CO2 emission on the refined realistic results
Optimiser
Source of Variation
SS Df MS F-ratio p-value
MOGA-II
Between groups 6.0825E6 8.1000E1 7.5093E4 3.1338E0 2.5970E-8
Within groups 2.5160E6 1.0500E2 2.3962E4 –– ––
Total 8.5985E6 1.8600E2
NSGA-II
Between groups 1.7674E6 4.0000E0 4.4185E5 1.6424E1 1.0559E-12
Within groups 1.4419E7 5.3600E2 2.6902E4 –– ––
Total 1.6187E7 5.4000E2
Chapter Four
70
a. Convergence w.r.t CO2 emission b. Convergence w.r.t costs
Figure 4.10 Comparative convergence plots of the GA-based optimisers
It is evident from plot ‘a’ and plot ‘b’ of Figure 4.10 that the NSGA-II algorithm is converging in a comparatively better way than that of MOGA-II. History plots, Box Whiskers and Density plots (Appendix B.3) are considered for statistical analysis of the results.
4.7.1.2. ANOVA
One-way ANOVA is performed for both the total CO2 emission and total costs of trans- portation to compare the means of multiple groups of the optimised data. ANOVA computes the p-value for the null hypothesis to detect if data from several groups have a common mean. Tables 4.14 and 4.15 present the ANOVA results for the two GA-based optimisers with respect to CO2 emission and costs respectively. The ANOVA statistics are used to test the null-hypothesis (Walpole et al. 2006). For the two optimisers ANO- VA computes the source of the variability, sum of squares (SS) due to each source, de- grees of freedom (Df) associated with each source, mean squares (MS) for each source (SS/Df ratio), F-statistic (ratio of two MS) and p-value given by the cdf of F. It is noted that as the F-ratio increases, the p-value decreases. The ANOvA test presented in Tables 4.14 and 4.15 are calculated for refined realistic results. The insignificance in p-value could be a result of this selection of results. It is necessary to mention again that not all results are realistic and they have to be refined in order to find the realistic results. Table 4.14 ANOVA for CO2 emission on the refined realistic results
Optimiser
Source of Variation
SS Df MS F-ratio p-value
MOGA-II
Between groups 6.0825E6 8.1000E1 7.5093E4 3.1338E0 2.5970E-8
Within groups 2.5160E6 1.0500E2 2.3962E4 –– ––
Total 8.5985E6 1.8600E2
NSGA-II
Between groups 1.7674E6 4.0000E0 4.4185E5 1.6424E1 1.0559E-12
Within groups 1.4419E7 5.3600E2 2.6902E4 –– ––
Total 1.6187E7 5.4000E2
Chapter Four
70
a. Convergence w.r.t CO2 emission b. Convergence w.r.t costs
Figure 4.10 Comparative convergence plots of the GA-based optimisers
It is evident from plot ‘a’ and plot ‘b’ of Figure 4.10 that the NSGA-II algorithm is converging in a comparatively better way than that of MOGA-II. History plots, Box Whiskers and Density plots (Appendix B.3) are considered for statistical analysis of the results.
4.7.1.2. ANOVA
One-way ANOVA is performed for both the total CO2 emission and total costs of trans- portation to compare the means of multiple groups of the optimised data. ANOVA computes the p-value for the null hypothesis to detect if data from several groups have a common mean. Tables 4.14 and 4.15 present the ANOVA results for the two GA-based optimisers with respect to CO2 emission and costs respectively. The ANOVA statistics are used to test the null-hypothesis (Walpole et al. 2006). For the two optimisers ANO- VA computes the source of the variability, sum of squares (SS) due to each source, de- grees of freedom (Df) associated with each source, mean squares (MS) for each source (SS/Df ratio), F-statistic (ratio of two MS) and p-value given by the cdf of F. It is noted that as the F-ratio increases, the p-value decreases. The ANOvA test presented in Tables 4.14 and 4.15 are calculated for refined realistic results. The insignificance in p-value could be a result of this selection of results. It is necessary to mention again that not all results are realistic and they have to be refined in order to find the realistic results.