I improved my answer, the outline of the boxplot would display different colors if color in the aes is assigned as a factor of the id from the melted data frame. i.e., geom_boxplot(aes(color=factor(ID1)))
The following code results in a plot as below,
plt <- ggplot(subset(df_mlt, value > 0), aes(x=ID1,y=value)) +
geom_boxplot(aes(color=factor(ID1))) +
scale_y_log10(breaks = trans_breaks("log10", function(x) 10^x), labels = trans_format("log10", math_format(10^.x))) +
theme_bw() +
theme(legend.text=element_text(size=14), legend.title=element_text(size=14))+
theme(axis.text=element_text(size=20)) +
theme(axis.title=element_text(size=20,face="bold")) +
labs(x = "x", y = "y",colour="legend" ) +
annotation_logticks(sides = "rl") +
theme(panel.grid.minor = element_blank()) +
guides(title.hjust=0.5) +
theme(plot.margin=unit(c(0,1,0,0),"mm"))
plt