帕累托优化-非支配点 [英] Pareto optimization - non-dominated points

问题描述

我编写了一种算法，该算法返回的列表类似于nsga2返回的列表. (软件包"mco"的nsga2( pdf ))

该算法本身无法识别某个点是否为非支配点.它返回的某些点占主导地位，并且仅包含点及其值，而不包含nsga2返回的逻辑向量.

我正在尝试获取非支配点(不是它们的值).

使用nsga2的结果，您可以使用paretoSet()来获取值，但这取决于在nsga2期间是否已预先计算逻辑向量.

我还查看了"mco"的paretoFront()/paretoFilter()和"emoa"包的nondominated_points()(解决方案

我自己找到了答案. (没有人回答超过2天似乎有点动机)

为直观起见，此示例显示了实现非支配计算时如何保留点的颜色，显然，您也可以将其搜索空间坐标存储在多列中. (请注意:此示例专门针对2个目标，但可以概括)

x = runif(20)
y = runif(20)
from = 1:20
d = data.frame(x, y, from)
d
D = d[order(d$x, d$y), ]
nondom = D[which(!duplicated(cummin(D$y))), ]
nondom
plot(d[,1:2], col=d$from, xlim=c(0,1), ylim=c(0,1))
plot(nondom[,1:2], col=nondom$from, xlim=c(0,1), ylim=c(0,1))

I wrote an algorithm that returns a list similar to that which nsga2 returns. (nsga2 of package "mco" (pdf))

The algorithm can not itself recognize if a point is non-dominated. Some of the points it returns are dominated and it only contains the points and their values, not the logic-vector that nsga2 returns.

I am trying to get the non-dominated points (not their values).

With nsga2's result you can use paretoSet() to get the values, however that depends on that the logic-vector has been precomputed during nsga2.

I also looked at paretoFront()/paretoFilter() of "mco" and nondominated_points() of package "emoa" (pdf), however they only work with the values, there is no way to get the points.

One way to solve this would be to accept the values, and then for every value go through the points, look if it has that value and if so add it to a list. But I think there has to exist a function that returns the points.

To reproduce this you could use:

res = nsga2(func, 3, 2, lower.bounds=rep(0, 5), upper.bounds=rep(1, 5))
res$pareto.optimal = NULL
points = paretoSet(res) # points will be empty because res does 
                        # not have the logic vector

解决方案

Found the answer myself. (No one answering for more than 2 days seems somewhat of a motivation)

For visualization this example shows how you would retain the color of points when you implement non-dominated-calculation, obviously you can also store their search-space coordinates in multiple columns instead. (note: this example is specialized on 2 objectives but that can be generalized)

x = runif(20)
y = runif(20)
from = 1:20
d = data.frame(x, y, from)
d
D = d[order(d$x, d$y), ]
nondom = D[which(!duplicated(cummin(D$y))), ]
nondom
plot(d[,1:2], col=d$from, xlim=c(0,1), ylim=c(0,1))
plot(nondom[,1:2], col=nondom$from, xlim=c(0,1), ylim=c(0,1))

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