Chapter 6 MI500: Exploitation rate results
Here we present the results for best performances found by each selection scheme replicate on the exploitation rate diagnostic with our base configurations. For our base configuration, we assume that there are migrations every 500 generations, 4 islands, and a ring topology. When migrations occur, we swap two individuals (same position on each island) and guarantee that no solution can return to the same island. Best performance found refers to the largest average trait score found in a given population. Note that performance values fall between 0.0 and 100.0.
6.2 Truncation selection
Here we analyze how the different population structures affect truncation selection (size 8) on the exploitation rate diagnostic.
6.2.1 Performance over time
lines = filter(base_over_time, Diagnostic == 'EXPLOITATION_RATE' & `Selection\nScheme` == 'TRUNCATION') %>%
group_by(Structure, Generations) %>%
dplyr::summarise(
min = min(pop_fit_max) / DIMENSIONALITY,
mean = mean(pop_fit_max) / DIMENSIONALITY,
max = max(pop_fit_max) / DIMENSIONALITY
)
ggplot(lines, aes(x=Generations, y=mean, group = Structure, fill = Structure, color = Structure, shape = Structure)) +
geom_ribbon(aes(ymin = min, ymax = max), alpha = 0.1) +
geom_line(size = 0.5) +
geom_point(data = filter(lines, Generations %% 2000 == 0), size = 2.5, stroke = 2.0, alpha = 1.0) +
scale_y_continuous(
name="Average trait score",
limits=c(-1, 101),
breaks=seq(0,100, 20),
labels=c("0", "20", "40", "60", "80", "100")
) +
scale_x_continuous(
name="Generations",
limits=c(0, 50000),
breaks=c(0, 10000, 20000, 30000, 40000, 50000),
labels=c("0e+4", "1e+4", "2e+4", "3e+4", "4e+4", "5e+4")
) +
scale_shape_manual(values=SHAPE)+
scale_colour_manual(values = cb_palette) +
scale_fill_manual(values = cb_palette) +
ggtitle("Best performance over time") +
p_theme
6.2.2 Generation satisfactory solution found
First generation a satisfactory solution is found throughout the 50,000 generations.
filter(base_ssf, Diagnostic == 'EXPLOITATION_RATE' & `Selection\nScheme` == 'TRUNCATION') %>%
ggplot(., aes(x = Structure, y = Generations , color = Structure, fill = Structure, shape = Structure)) +
geom_flat_violin(position = position_nudge(x = .2, y = 0), scale = 'width', alpha = 0.2) +
geom_point(position = position_jitter(width = .1), size = 1.5, alpha = 1.0) +
geom_boxplot(color = 'black', width = .2, outlier.shape = NA, alpha = 0.0) +
scale_y_continuous(
name="Generation"
) +
scale_x_discrete(
name="Structure"
)+
scale_shape_manual(values=SHAPE)+
scale_colour_manual(values = cb_palette, ) +
scale_fill_manual(values = cb_palette) +
ggtitle('Generation satisfactory solution found')+
p_theme + coord_flip()
6.2.3 Stats
Summary statistics for the first generation a satisfactory solution is found.
ssf = filter(base_ssf, Diagnostic == 'EXPLOITATION_RATE' & `Selection\nScheme` == 'TRUNCATION' & Generations < 60000)
ssf %>%
group_by(Structure) %>%
dplyr::summarise(
count = n(),
na_cnt = sum(is.na(Generations)),
min = min(Generations, na.rm = TRUE),
median = median(Generations, na.rm = TRUE),
mean = mean(Generations, na.rm = TRUE),
max = max(Generations, na.rm = TRUE),
IQR = IQR(Generations, na.rm = TRUE)
)## # A tibble: 3 x 8
## Structure count na_cnt min median mean max IQR
## <fct> <int> <int> <int> <dbl> <dbl> <int> <dbl>
## 1 EA 100 0 3377 3424. 3423. 3472 26.2
## 2 IS 100 0 4680 4752. 4754. 4839 25
## 3 NMIS 100 0 4733 4790. 4791. 4846 32.5Kruskal–Wallis test provides evidence of difference among selection schemes.
##
## Kruskal-Wallis rank sum test
##
## data: Generations by Structure
## Kruskal-Wallis chi-squared = 237.99, df = 2, p-value < 2.2e-16Results for post-hoc Wilcoxon rank-sum test with a Bonferroni correction.
pairwise.wilcox.test(x = ssf$Generations, g = ssf$Structure, p.adjust.method = "bonferroni",
paired = FALSE, conf.int = FALSE, alternative = 'g')##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: ssf$Generations and ssf$Structure
##
## EA IS
## IS <2e-16 -
## NMIS <2e-16 <2e-16
##
## P value adjustment method: bonferroni6.3 Tournament selection
Here we analyze how the different population structures affect tournament selection (size 8) on the exploitation rate diagnostic.
6.3.1 Performance over time
lines = filter(base_over_time, Diagnostic == 'EXPLOITATION_RATE' & `Selection\nScheme` == 'TOURNAMENT') %>%
group_by(Structure, Generations) %>%
dplyr::summarise(
min = min(pop_fit_max) / DIMENSIONALITY,
mean = mean(pop_fit_max) / DIMENSIONALITY,
max = max(pop_fit_max) / DIMENSIONALITY
)
ggplot(lines, aes(x=Generations, y=mean, group = Structure, fill = Structure, color = Structure, shape = Structure)) +
geom_ribbon(aes(ymin = min, ymax = max), alpha = 0.1) +
geom_line(size = 0.5) +
geom_point(data = filter(lines, Generations %% 2000 == 0), size = 2.5, stroke = 2.0, alpha = 1.0) +
scale_y_continuous(
name="Average trait score",
limits=c(-1, 101),
breaks=seq(0,100, 20),
labels=c("0", "20", "40", "60", "80", "100")
) +
scale_x_continuous(
name="Generations",
limits=c(0, 50000),
breaks=c(0, 10000, 20000, 30000, 40000, 50000),
labels=c("0e+4", "1e+4", "2e+4", "3e+4", "4e+4", "5e+4")
) +
scale_shape_manual(values=SHAPE)+
scale_colour_manual(values = cb_palette) +
scale_fill_manual(values = cb_palette) +
ggtitle("Best performance over time") +
p_theme
6.3.2 Generation satisfactory solution found
First generation a satisfactory solution is found throughout the 50,000 generations.
filter(base_ssf, Diagnostic == 'EXPLOITATION_RATE' & `Selection\nScheme` == 'TOURNAMENT') %>%
ggplot(., aes(x = Structure, y = Generations , color = Structure, fill = Structure, shape = Structure)) +
geom_flat_violin(position = position_nudge(x = .2, y = 0), scale = 'width', alpha = 0.2) +
geom_point(position = position_jitter(width = .1), size = 1.5, alpha = 1.0) +
geom_boxplot(color = 'black', width = .2, outlier.shape = NA, alpha = 0.0) +
scale_y_continuous(
name="Generation"
) +
scale_x_discrete(
name="Structure"
)+
scale_shape_manual(values=SHAPE)+
scale_colour_manual(values = cb_palette, ) +
scale_fill_manual(values = cb_palette) +
ggtitle('Generation satisfactory solution found')+
p_theme + coord_flip()
6.3.3 Stats
Summary statistics for the first generation a satisfactory solution is found.
ssf = filter(base_ssf, Diagnostic == 'EXPLOITATION_RATE' & `Selection\nScheme` == 'TOURNAMENT' & Generations < 60000)
ssf %>%
group_by(Structure) %>%
dplyr::summarise(
count = n(),
na_cnt = sum(is.na(Generations)),
min = min(Generations, na.rm = TRUE),
median = median(Generations, na.rm = TRUE),
mean = mean(Generations, na.rm = TRUE),
max = max(Generations, na.rm = TRUE),
IQR = IQR(Generations, na.rm = TRUE)
)## # A tibble: 3 x 8
## Structure count na_cnt min median mean max IQR
## <fct> <int> <int> <int> <dbl> <dbl> <int> <dbl>
## 1 EA 100 0 5392 5446 5449. 5550 41.2
## 2 IS 100 0 5741 5862 5862. 5979 51.2
## 3 NMIS 100 0 5818 5908. 5909. 6002 39.2Kruskal–Wallis test provides evidence of difference among selection schemes.
##
## Kruskal-Wallis rank sum test
##
## data: Generations by Structure
## Kruskal-Wallis chi-squared = 226.27, df = 2, p-value < 2.2e-16Results for post-hoc Wilcoxon rank-sum test with a Bonferroni correction.
pairwise.wilcox.test(x = ssf$Generations, g = ssf$Structure, p.adjust.method = "bonferroni",
paired = FALSE, conf.int = FALSE, alternative = 'g')##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: ssf$Generations and ssf$Structure
##
## EA IS
## IS < 2e-16 -
## NMIS < 2e-16 1.1e-14
##
## P value adjustment method: bonferroni6.4 Lexicase selection
Here we analyze how the different population structures affect standard lexicase selection on the exploitation rate diagnostic.
6.4.1 Performance over time
lines = filter(base_over_time, Diagnostic == 'EXPLOITATION_RATE' & `Selection\nScheme` == 'LEXICASE') %>%
group_by(Structure, Generations) %>%
dplyr::summarise(
min = min(pop_fit_max) / DIMENSIONALITY,
mean = mean(pop_fit_max) / DIMENSIONALITY,
max = max(pop_fit_max) / DIMENSIONALITY
)
ggplot(lines, aes(x=Generations, y=mean, group = Structure, fill = Structure, color = Structure, shape = Structure)) +
geom_ribbon(aes(ymin = min, ymax = max), alpha = 0.1) +
geom_line(size = 0.5) +
geom_point(data = filter(lines, Generations %% 2000 == 0), size = 2.5, stroke = 2.0, alpha = 1.0) +
scale_y_continuous(
name="Average trait score",
limits=c(-1, 101),
breaks=seq(0,100, 20),
labels=c("0", "20", "40", "60", "80", "100")
) +
scale_x_continuous(
name="Generations",
limits=c(0, 50000),
breaks=c(0, 10000, 20000, 30000, 40000, 50000),
labels=c("0e+4", "1e+4", "2e+4", "3e+4", "4e+4", "5e+4")
) +
scale_shape_manual(values=SHAPE)+
scale_colour_manual(values = cb_palette) +
scale_fill_manual(values = cb_palette) +
ggtitle("Best performance over time") +
p_theme
6.4.2 Generation satisfactory solution found
First generation a satisfactory solution is found throughout the 50,000 generations.
filter(base_ssf, Diagnostic == 'EXPLOITATION_RATE' & `Selection\nScheme` == 'LEXICASE') %>%
ggplot(., aes(x = Structure, y = Generations , color = Structure, fill = Structure, shape = Structure)) +
geom_flat_violin(position = position_nudge(x = .2, y = 0), scale = 'width', alpha = 0.2) +
geom_point(position = position_jitter(width = .1), size = 1.5, alpha = 1.0) +
geom_boxplot(color = 'black', width = .2, outlier.shape = NA, alpha = 0.0) +
scale_y_continuous(
name="Generation"
) +
scale_x_discrete(
name="Structure"
)+
scale_shape_manual(values=SHAPE)+
scale_colour_manual(values = cb_palette, ) +
scale_fill_manual(values = cb_palette) +
ggtitle('Generation satisfactory solution found')+
p_theme + coord_flip()
6.4.3 Stats
Summary statistics for the first generation a satisfactory solution is found.
ssf = filter(base_ssf, Diagnostic == 'EXPLOITATION_RATE' & `Selection\nScheme` == 'LEXICASE' & Generations < 60000)
ssf %>%
group_by(Structure) %>%
dplyr::summarise(
count = n(),
na_cnt = sum(is.na(Generations)),
min = min(Generations, na.rm = TRUE),
median = median(Generations, na.rm = TRUE),
mean = mean(Generations, na.rm = TRUE),
max = max(Generations, na.rm = TRUE),
IQR = IQR(Generations, na.rm = TRUE)
)## # A tibble: 3 x 8
## Structure count na_cnt min median mean max IQR
## <fct> <int> <int> <int> <dbl> <dbl> <int> <dbl>
## 1 EA 100 0 22764 25666. 26026. 32687 2344
## 2 IS 100 0 23649 27080. 27635. 38266 2628.
## 3 NMIS 100 0 24412 27358. 27906. 34604 2396.Kruskal–Wallis test provides evidence of difference among selection schemes.
##
## Kruskal-Wallis rank sum test
##
## data: Generations by Structure
## Kruskal-Wallis chi-squared = 52.814, df = 2, p-value = 3.401e-12Results for post-hoc Wilcoxon rank-sum test with a Bonferroni correction.
pairwise.wilcox.test(x = ssf$Generations, g = ssf$Structure, p.adjust.method = "bonferroni",
paired = FALSE, conf.int = FALSE, alternative = 'g')##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: ssf$Generations and ssf$Structure
##
## EA IS
## IS 3.0e-08 -
## NMIS 2.2e-11 0.24
##
## P value adjustment method: bonferroni