正确指定“逻辑条件”（在 R 中）

我正在使用 R 编程语言 - 我正在尝试遵循此 stackoverflow 帖子中的答案（将 R 中的参数传递给多个实数变量的函数 https://stackoverflow.com/questions/56359838/argument-passing-in-r-to-functions-of-several-real-variables），展示如何执行“多目标约束优化”。

我为此示例创建了一些数据：

#load libraries
library(dplyr)


# create some data for this example
a1 = rnorm(1000,100,10)
b1 = rnorm(1000,100,5)
c1 = sample.int(1000, 1000, replace = TRUE)
train_data = data.frame(a1,b1,c1)

然后我定义了一个具有“4 个目标”的函数（“funct_set”）（f[1], f[2], f[3], f[4]）对于一组“七个输入”（[x1], [x2], [x3], x[4], x[5], x[6], x[7]):

#load libraries
    library(dplyr)
    library(mco)
    
#define function

funct_set <- function (x) {
    x1 <- x[1]; x2 <- x[2]; x3 <- x[3] ; x4 <- x[4]; x5 <- x[5]; x6 <- x[6]; x[7] <- x[7]
    f <- numeric(4)
    
    
    #bin data according to random criteria
    train_data <- train_data %>%
        mutate(cat = ifelse(a1 <= x1 & b1 <= x3, "a",
                            ifelse(a1 <= x2 & b1 <= x4, "b", "c")))
    
    train_data$cat = as.factor(train_data$cat)
    
    #new splits
    a_table = train_data %>%
        filter(cat == "a") %>%
        select(a1, b1, c1, cat)
    
    b_table = train_data %>%
        filter(cat == "b") %>%
        select(a1, b1, c1, cat)
    
    c_table = train_data %>%
        filter(cat == "c") %>%
        select(a1, b1, c1, cat)
    
    
    
    #calculate  quantile ("quant") for each bin
    
    table_a = data.frame(a_table%>% group_by(cat) %>%
                             mutate(quant = ifelse(c1 > x[5],1,0 )))
    
    table_b = data.frame(b_table%>% group_by(cat) %>%
                             mutate(quant = ifelse(c1 > x[6],1,0 )))
    
    table_c = data.frame(c_table%>% group_by(cat) %>%
                             mutate(quant = ifelse(c1 > x[7],1,0 )))
    
    f[1] = -mean(table_a$quant)
    f[2] = -mean(table_b$quant)
    f[3] = -mean(table_c$quant)
    
    
    #group all tables
    
    final_table = rbind(table_a, table_b, table_c)
    # calculate the total mean : this is what needs to be optimized
    
    f[4] = -mean(final_table$quant)
    
    
    return (f);
}

接下来，我定义了优化中使用的一系列 4 个“限制”（即逻辑条件/约束）：

#define restrictions

restrictions <- function (x) {
    x1 <- x[1]; x2 <- x[2]; x3 <- x[3]; x4 <- x[4]; x5<- x[5] ; x6 <- x[6]; x7 <- x[7]
    restrictions <- logical(4)
    restrictions[1] <- (x3 - x1 >= 0)
    restrictions[2] <- (x4 - x2 >= 0)
    restrictions[3] <- (x7 - x6 >= 0)
 restrictions[4] <- (x6 - x5 >= 0)
    return (restrictions);
}

最后，我运行优化算法，尝试同时最小化所有 4 个目标的限制：

#run optimization


optimization <- nsga2(funct_set, idim = 7, odim = 4 ,   constraints = restrictions, cdim = 4,
                      
                      generations=150,
                      popsize=100,
                      cprob=0.7,
                      cdist=20,
                      mprob=0.2,
                      mdist=20,
                      lower.bounds=rep(80,80,80,80, 100,200,300),
                      upper.bounds=rep(120,120,120,120,200,300,400)
)

上面的代码工作正常。

Problem：我注意到在这段代码的输出中，优化算法没有遵守限制。例如：

在上图中，我识别出了一些违反限制中指定的逻辑条件的行。

有谁知道为什么会发生这种情况？我是否错误地指定了限制？有人可以告诉我如何解决这个问题吗？

Thanks

UPDATE:

我想我能够解决这个问题 - 现在“逻辑条件”在最终输出中受到尊重：

#load libraries
library(dplyr)
library(mco)

#define function

funct_set <- function (x) {
    x1 <- x[1]; x2 <- x[2]; x3 <- x[3] ; x4 <- x[4]; x5 <- x[5]; x6 <- x[6]; x[7] <- x[7]
    f <- numeric(4)
    
    
    #bin data according to random criteria
    train_data <- train_data %>%
        mutate(cat = ifelse(a1 <= x1 & b1 <= x3, "a",
                            ifelse(a1 <= x2 & b1 <= x4, "b", "c")))
    
    train_data$cat = as.factor(train_data$cat)
    
    #new splits
    a_table = train_data %>%
        filter(cat == "a") %>%
        select(a1, b1, c1, cat)
    
    b_table = train_data %>%
        filter(cat == "b") %>%
        select(a1, b1, c1, cat)
    
    c_table = train_data %>%
        filter(cat == "c") %>%
        select(a1, b1, c1, cat)
    
    
    
    #calculate  quantile ("quant") for each bin
    
    table_a = data.frame(a_table%>% group_by(cat) %>%
                             mutate(quant = ifelse(c1 > x[5],1,0 )))
    
    table_b = data.frame(b_table%>% group_by(cat) %>%
                             mutate(quant = ifelse(c1 > x[6],1,0 )))
    
    table_c = data.frame(c_table%>% group_by(cat) %>%
                             mutate(quant = ifelse(c1 > x[7],1,0 )))
    
    f[1] = mean(table_a$quant)
    f[2] = mean(table_b$quant)
    f[3] = mean(table_c$quant)
    
    
    #group all tables
    
    final_table = rbind(table_a, table_b, table_c)
    # calculate the total mean : this is what needs to be optimized
    
    f[4] = mean(final_table$quant)
    
    
    return (f);
}


gn <- function(x) {
    g1 <- x[3] - x[1] 
    g2<- x[4] - x[2] 
    g3 <- x[7] - x[6]
    g4 <- x[6] - x[5] 
    return(c(g1,g2,g3,g4))
}

optimization <- nsga2(funct_set, idim = 7, odim = 4 , constraints = gn, cdim = 4,
                      
                      generations=150,
                      popsize=100,
                      cprob=0.7,
                      cdist=20,
                      mprob=0.2,
                      mdist=20,
                      lower.bounds=rep(80,80,80,80, 100,200,300),
                      upper.bounds=rep(120,120,120,120,200,300,400)
)

现在，如果我们看一下输出：

#view output
optimization

所有逻辑条件（即“约束”）现在都得到尊重！

注意：如果可能的话，我仍然有兴趣了解解决此问题的替代方法

感谢大家！