R中的遗传算法

Question

我有这样的问题： 我需要找到不超过最大重量的物品的最佳组合。 对于这个问题，我使用了遗传算法。

这是我的数据

dataset <- data.frame(name = paste0("x",1:11),
                  Weight = c(2.14083022,7.32592911,0.50945094,4.94405846,12.02631340,14.59102403,0.07583312,0.36318323,10.64413370,3.54882187,1.79507759),
                  stringsAsFactors = F)

这是我的成本函数：

max_weight = 10
fitness_function <- function(x){
   current_weight <- x %*% dataset$Weight
          if ( current_weight > max_weight){
      return(0)
   } else {
      return( -1* current_weight)
   }
}

然后我从两个包中尝试了 ga：genalg 和 GA

genalg

    ga_genalg <- rbga.bin(size = 11,
                          popSize = 100, 
                          mutationChance = .1,
                          evalFunc = fitness_function)

好的，结果如下：

cat(summary(ga_genalg))
GA Settings
  Type                  = binary chromosome
  Population size       = 100
  Number of Generations = 100
  Elitism               = 20
  Mutation Chance       = 0.1

Search Domain
  Var 1 = [,]
  Var 0 = [,]

GA Results
  Best Solution : 0 1 1 0 0 0 0 1 0 0 1 

我检查了最佳解决方案，看起来不错：

genalg_best_solution = c(0,1,1,0,0,0,0,1,0,0,1)
dataset$Weight %*% genalg_best_solution 
         [,1]
[1,] 9.993641

附言。有人知道如何在不输入和正则表达式的情况下获得这个最佳解向量吗？

GA

ga_GA <- ga(type = "binary", fitness = fitness_function, popSize = 100, pmutation = .1, nBits = 11)
ga_best_solution = ga_GA@solution 
dim(ga_best_solution)
[1] 73 11

解决方案是 73 行的矩阵。同样ga_GA@bestSol 返回list()

这个包中我最好的解决方案在哪里？或者我需要检查所有 73 行并找到最好的（我已经尝试并得到了 73 个零）？

PPS。第二题解法：GA 最大化函数和 genalg 最小化函数 =/. 有人知道如何从 genalg 包中提取最佳解决方案吗？

Answer 1

这里有很多问题。我的观点是 GA 为您想要的输出提供了更简单的输出：最佳解决方案和适应度得分。

你说得对，GA 最大化适应度得分，而 genalg 最小化 - 我创建了第二个适应度函数，它不返回适应度值乘以 -1。这导致两者的解决方案相同。

另外，我没有得到您为 ga() 的输出提供的维度。就我而言，这只是包含 11 个二进制值的单行：

library(GA)
library(genalg)

dataset <- data.frame(name = paste0("x",1:11),
  Weight = c(
    2.14083022,7.32592911,0.50945094,4.94405846,
    12.02631340,14.59102403,0.07583312,0.36318323,
    10.64413370,3.54882187,1.79507759
  ),
  stringsAsFactors = F
)

max_weight = 10


# genalg ------------------------------------------------------------------

# fitness function for genalg 
fitness_function <- function(x){
   current_weight <- x %*% dataset$Weight
   if ( current_weight > max_weight){
      return(0)
   } else {
      return(-current_weight)
   }
}


ga_genalg <- rbga.bin(size = 11,
  popSize = 100, 
  mutationChance = .1,
  evalFunc = fitness_function
)
tail(ga_genalg$best, 1) # best fitness
summary(ga_genalg, echo=TRUE)

plot(ga_genalg) # plot

# helper function from ?rbga.bin
monitor <- function(obj) {
    minEval = min(obj$evaluations);
    filter = obj$evaluations == minEval;
    bestObjectCount = sum(rep(1, obj$popSize)[filter]);
    # ok, deal with the situation that more than one object is best
    if (bestObjectCount > 1) {
        bestSolution = obj$population[filter,][1,];
    } else {
        bestSolution = obj$population[filter,];
    }
    outputBest = paste(obj$iter, " #selected=", sum(bestSolution),
                       " Best (Error=", minEval, "): ", sep="");
    for (var in 1:length(bestSolution)) {
        outputBest = paste(outputBest,
            bestSolution[var], " ",
            sep="");
    }
    outputBest = paste(outputBest, "\n", sep="");

    cat(outputBest);
}

monitor(ga_genalg)
# 100 #selected=4 Best (Error=-9.99364087): 0 1 1 0 0 0 0 1 0 0 1 



# GA ----------------------------------------------------------------------

# fitness function for GA (maximizes fitness)
fitness_function2 <- function(x){
   current_weight <- x %*% dataset$Weight
   if ( current_weight > max_weight){
      return(0)
   } else {
      return(current_weight)
   }
}

ga_GA <- ga(type = "binary", fitness = fitness_function2, popSize = 100, pmutation = .1, nBits = 11)
ga_GA@solution 
#     x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11
# [1,]  0  1  1  0  0  0  0  1  0   0   1
dim(ga_best_solution)
# [1]  1 11

ga_GA@fitnessValue
# [1] 9.993641