如何使用 GA 包在 R 中优化具有两个变量和多个参数的函数

Question

我是使用遗传算法，尤其是遗传算法的初学者。 我想知道如何优化具有两个自变量和多个参数的函数。 我的第一个变量是连续变量，第二个变量是二进制变量。 这是我生成的代码，但它不起作用。

This is what i want to obtain

Var1_obs <- c(-1.942000, -1.338000, -2.065000, -2.080125, -3.247944, -5.365086,
              -1.608000, -3.970000, -1.423000, -8.180000, -4.620000, -1.657000, 
              -5.200000, -6.850000, -6.950000, -1.180000, -1.175000, -1.969000, 
              -1.115000, -2.620000, -1.870000, -0.433000, -1.102000, -2.093687, 
              -2.480000, -0.580000, -0.600000, -1.807383, -2.367000, -2.276017, 
              -2.125331)

Var2_obs <- c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 
              1, 1, 1, 1, 1, 1, 1, 1, 1)

TE_obs <- c(92.73958, 93.39356, 84.39019, 93.40717, 97.53228, 92.04734, 82.06016, 
            78.50015, 83.43671, 55.24498, 67.92513, 77.53455, 65.33344, 47.05005, 
            46.52794, 96.79697, 84.79326, 83.64457, 82.17259, 88.96605, 84.93663, 
            83.16691, 95.22838, 96.46441, 79.61302, 80.39901, 88.38439, 72.23954, 
            85.64084, 69.33542, 82.30360)

data<-data.frame(Var1_obs,Var2_obs,TE_obs)

plot(data$Var1_obs[data$Var2_obs==0],data$TE_obs[data$Var2_obs==0],
xlim=range(data$Var1_obs), ylim=range(data$TE_obs), col=2, pch=19,
xlab='Var1_obs', ylab='TE_obs')

points(data$Var1_obs[data$Var2_obs==1],data$TE_obs[data$Var2_obs==1],
xlim=range(data$Var1_obs), ylim=range(data$TE_obs), col=3, pch=19)

library(GA)
library(hydroGOF)

My_function <- function(Var1, Var2, P1, P2, P3, P4, P5, P6, P7) {
  A <- (-1 * (Var1 + P1 - P2) - sqrt((Var1 + P1 - P2)^2 + 4 * (Var1 * P2))) / (2 * P2)
  B <- 1 - P1 / Var1
  C <- c(A, B)
  Sel <- c(A > B, B > A)

  RS <- C[Sel]

  PC <- 100 / (1 + exp(P3 / 25 * (Var1 - P4)))

  RMC <- (1 - RS)
  symp <- RMC * (1 / (P5 / 1000) - 1) * 100 * (1 - P6)
  apo <- (1 - PC / 100) * (1 / (P5 / 1000) - 1) * 100 * (P6)

  TE_Pred <- (apo + symp) * (1 + P7 * Var2)

  NRMSE <- (nrmse(TE_Pred, TE_obs, na.rm = T, norm = "sd"))
  # if(is.na(NRMSE)|is.nan(NRMSE)|is.infinite(NRMSE)) NRMSE <- -1e6
  return(NRMSE)
}


# ----------------------- BOUNDARIES --------------------------- #

P1 <- c(-3.5, -2.3)
P2 <- c(5, 15)
P3 <- c(15, 60)
P4 <- c(-7.5, -6)
P5 <- c(500, 600)
P6 <- c(0.3, 0.6)
P7 <- c(-1, 0)

min_boundary <- c(P1[1], P2[1], P3[1], P4[1], P5[1], P6[1], P7[1])
max_boundary <- c(P1[2], P2[2], P3[2], P4[2], P5[2], P6[2], P7[2])

ga(
  type = "real-valued",
  fitness = function(x) -My_function(Var1 = Var1_obs, Var2 = Var2_obs, P1[1], 
                                     P2[2], P3[3], P4[4], P5[5], P6[6], P7[7]),
  lower = min_boundary, upper = max_boundary,
  popSize = 50, maxiter = 1000, run = 100
)

我在运行代码时得到了这个

#> GA | iter = 1 | Mean =  NaN | Best = -Inf
#> GA | iter = 2 | Mean =  NaN | Best = -Inf

#> Error in if (object@run >= run) break : 
#>   missing value where TRUE/FALSE needed

感谢您的帮助

Answer 1

ga 函数的设计方式需要一个适应度函数，该函数接受一个输入（可以说是变量）。

一般解决方案

如果您想使用两个变量 x1 和 x2 最小化函数 f（也就是说，您希望找到 x1 和 x2 的值，它们的最小值为 @987654327 @)，你必须像这样调用函数

# Taken from `?ga` 3) two-dimensional Rastrigin function
# slightly adopted to have three parameters (that are not optimized)
library(GA)

f <- function(x1, x2, p1 = 20, p2 = -10, p3 = 2) {
  p1 + x1^2 + x2^2 + p2*(cos(p3*pi*x1) + cos(p3*pi*x2))
}

# evaluate the function at (2, 4)
f(2, 4, p1 = 20, p2 = -10, p3 = 2)
#> [1] 20

# minimize the Rastrigin function
GA <- ga(type = "real-valued", fitness =  function(x) -f(x[1], x[2], 20, 10, 2),
         lower = c(-5.12, -5.12), upper = c(5.12, 5.12), 
         popSize = 50, maxiter = 100, seed = 1521)
summary(GA)
#> -- Genetic Algorithm ------------------- 
#> 
#> GA settings: 
#> Type                  =  real-valued 
#> Population size       =  50 
#> Number of generations =  100 
#> Elitism               =  2 
#> Crossover probability =  0.8 
#> Mutation probability  =  0.1 
#> Search domain = 
#>          x1    x2
#> lower -5.12 -5.12
#> upper  5.12  5.12
#> 
#> GA results: 
#> Iterations             = 100 
#> Fitness function value = -0.4974871 
#> Solution = 
#>              x1        x2
#> [1,] -0.4976645 0.4975342

适合您问题的解决方案

如果你想找到My_Function() 函数最小化的值P1 - P7（给定Val1 和Val2 的值，你可以这样做：

# ...
res <- ga(
  type = "real-valued",
  fitness = function(x) -My_function(Var1 = Var1_obs, Var2 = Var2_obs, 
                                     x[1], x[2], x[3], x[4], x[5], x[6], x[7]),
  lower = min_boundary, upper = max_boundary,
  popSize = 50, maxiter = 1000, run = 100
)
summary(res)
#> -- Genetic Algorithm ------------------- 
#> 
#> GA settings: 
#> Type                  =  real-valued 
#> Population size       =  50 
#> Number of generations =  1000 
#> Elitism               =  2 
#> Crossover probability =  0.8 
#> Mutation probability  =  0.1 
#> Search domain = 
#>         x1 x2 x3   x4  x5  x6 x7
#> lower -3.5  5 15 -7.5 500 0.3 -1
#> upper -2.3 15 60 -6.0 600 0.6  0
#> 
#> GA results: 
#> Iterations             = 341 
#> Fitness function value = -63.2 
#> Solution = 
#>             x1       x2       x3        x4       x5        x6         x7
#> [1,] -3.353621 9.373742 27.51849 -6.217355 511.5233 0.5698783 -0.0307688

请注意我们如何将 x 中的值替换为您问题中的参数 P1 - P7。

为什么是-my_function()？

咨询?ga，我们看到ga函数最大化目标函数，因为你想最小化函数，取负数有效地最小化函数。