使用R对分组变量进行非线性优化 [英] Nonlinear optimization with R for grouped variables

问题描述

我正在尝试为以下目标函数找到最大值:

I am trying to find maximum values for below objective function:

objective <-function(bid,revenue,click,cost) {

    revenue_2 <- sum((revenue / cost)*                                                      
                    (bid*click*bid*(cost/click) / cost)^(-0.2*revenue/cost)*              
                    (bid*click)*bid*(cost/click))

  return(-revenue_2)
}

以

roas_2 <- function(bid, revenue,click,cost) {

  revenue_2 <- ((revenue / cost)*                                                      
               (bid*click*bid*(cost/click) / cost)^(-0.2*revenue/cost))*              
               (bid*click)*bid*(cost/click)

  cost_2 <- (bid*click)*bid*(cost/click)

  roas_2 <- (sum(revenue_2)/sum(cost_2)) -1.2

  return(-roas_2)
}

我的值如下:

click <- c(123565, 94434, 79345, 152944, 83657, 67872, 80534, 48726, 107977, 138871, 116918, 41024, 63143)
revenue <- c(117251, 91806, 75356, 105787, 84419, 44139 , 57942 ,36283, 110902 ,130689, 116093, 36541, 37718)
cost <- c(93031,74764,73168,87510,66791,37637,50043,29209,90300,103276,93972,27228,32556)
cluster <- c(1,1,1,1,1,1,1,1,1,2,2,2,2)
bid <- c(1.2,1,1.6,1,1,1.2,1.2,1,1,1,1,1,1)

我正在使用R的nloptr库

I am using nloptr library of R

图书馆(nloptr)

library(nloptr)

res <- nloptr(x0=bid,
              eval_f=objective, 
              lb=c(0,0,0,0,0,0,0,0,0,0,0,0,0),
              ub=c(2,2,2,2,2,2,2,2,2,2,2,2,2),
              eval_g_ineq  = roas_2,
              # opts = list(algorithm="NLOPT_LN_COBYLA",maxeval=1000000),
              opts = list(algorithm="NLOPT_GN_ISRES",maxeval=105000),
              revenue=revenue,
              click=click,
              cost=cost)

通过上述代码，我可以找到使目标函数最大化的出价值，但是我想根据集群"对我的值进行分组，并为每个具有相同约束条件的最大化目标函数的集群寻找出价"值.

With above code I can find bid values which maximizes my objective function but I would like to group my values according to "cluster" and find "bid" values for each cluster which maximizes above objective function with same constraints.

您能帮我解决这个问题吗?

Could you please help me to overcome that problem?

推荐答案

我找到了一个不是最好的解决方案，但却挽救了我的一天.简要地说，我为目标函数和约束编写了循环

I found a solution which is not best but saved my day. Briefly, I wrote loop for objective function and constraint

目标函数的新形式变得像.

And new form of objective function became like.

   objective <-function(bid,revenue,click,cost, cluster) {

      revenue_2 <- 0

      for (i in 1:13) {

        t <- cluster[i]

          revenue_2[i] <- (revenue[i]/cost[i])*
                          ((bid[t]*click[i]*bid[t]*(cost[i]/click[i]) / cost[i])^(-0.2*revenue[i]/cost[i]))*
                          (bid[t]*click[i])*bid[t]*(cost[i]/click[i])

      } 

      revenue_2 <- sum(revenue_2)

      return(-revenue_2)
    }

约束变成了:

roas_2 <- function(bid, revenue,click,cost,cluster) {

  revenue_2 <- 0
  cost_2 <- 0

  for(i in 1:13) {

    t <- cluster[i]

    revenue_2[i] <- ((revenue[i] / cost[i])*                                                     
                            (bid[t]*click[i]*bid[t]*(cost[i]/click[i]) / cost[i])^(-0.2*revenue[i]/cost[i]))*              #new cost / old cost
                            (bid[t]*click[i])*bid[t]*(cost[i]/click[i])

    cost_2[i] <- (bid[t]*click[i])*bid[t]*(cost[i]/click[i])

    roas_2 <- (sum(revenue_2)/sum(cost_2)) - 1.2 

  }

  return(-roas_2)
}

最后一步，我在优化算法中添加了"cluster"参数:

As last step I added "cluster" parameter to optimization algorithm:

res <- nloptr(x0=bid,
              eval_f=objective, 
              lb=rep_len(0, 13),
              ub=rep_len(2, 13),
              eval_g_ineq  = roas_2,
              # opts = list(algorithm="NLOPT_LN_COBYLA",maxeval=1000000),
              opts = list(algorithm="NLOPT_GN_ISRES",maxeval=100000),
              revenue=revenue,
              click=click,
              cost=cost,
              cluster=cluster)

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