Chapter 14 MI5000: Exploitation rate results
Here we present the results for best performances found by each selection scheme replicate on the exploitation rate diagnostic with configurations presented below. For our the configuration of these experiments, we execute migrations every 50 generations and there are 4 islands in 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.
14.2 Truncation selection
Here we analyze how the different population structures affect truncation selection (size 8) on the exploitation rate diagnostic.
14.2.1 Performance over time
lines = filter(mi5000_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
14.2.2 Generation satisfactory solution found
First generation a satisfactory solution is found throughout the 50,000 generations.
filter(mi5000_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()
14.2.3 Stats
Summary statistics for the first generation a satisfactory solution is found.
ssf = filter(mi5000_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 3382 3422 3421. 3473 26
## 2 IS 100 0 4718 4788. 4786. 4834 40
## 3 NMIS 100 0 4736 4783 4782. 4830 25.2Kruskal–Wallis test provides evidence of difference among selection schemes.
##
## Kruskal-Wallis rank sum test
##
## data: Generations by Structure
## Kruskal-Wallis chi-squared = 200.03, 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
##
## P value adjustment method: bonferroni14.3 Tournament selection
Here we analyze how the different population structures affect tournament selection (size 8) on the exploitation rate diagnostic.
14.3.1 Performance over time
lines = filter(mi5000_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
14.3.2 Generation satisfactory solution found
First generation a satisfactory solution is found throughout the 50,000 generations.
filter(mi5000_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()
14.3.3 Stats
Summary statistics for the first generation a satisfactory solution is found.
ssf = filter(mi5000_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 5358 5456. 5453. 5526 41.8
## 2 IS 100 0 5819 5900 5903. 5973 40.8
## 3 NMIS 100 0 5821 5914 5912. 5977 41.8Kruskal–Wallis test provides evidence of difference among selection schemes.
##
## Kruskal-Wallis rank sum test
##
## data: Generations by Structure
## Kruskal-Wallis chi-squared = 201.55, 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 0.04
##
## P value adjustment method: bonferroni14.4 Lexicase selection
Here we analyze how the different population structures affect standard lexicase selection on the exploitation rate diagnostic.
14.4.1 Performance over time
lines = filter(mi5000_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
14.4.2 Generation satisfactory solution found
First generation a satisfactory solution is found throughout the 50,000 generations.
filter(mi5000_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()
14.4.3 Stats
Summary statistics for the first generation a satisfactory solution is found.
ssf = filter(mi5000_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 23129 25376 25814. 32119 1658.
## 2 IS 100 0 24579 27304. 27591. 34039 1903.
## 3 NMIS 100 0 24476 27170. 27601. 34985 1759.Kruskal–Wallis test provides evidence of difference among selection schemes.
##
## Kruskal-Wallis rank sum test
##
## data: Generations by Structure
## Kruskal-Wallis chi-squared = 72.912, 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 1.1e-13 -
## NMIS 5.6e-13 1
##
## P value adjustment method: bonferroni