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How can I implement a Generalized Assignment Problem: https://en.wikipedia.org/wiki/Generalized_assignment_problem to be solved with Genetic Algorithms https://cran.r-project.org/web/packages/GA/GA.pdf in R.

I have a working example of the code but its not working:

require(GA)
p <- matrix(c(5, 1, 5, 1, 5, 5, 5, 5, 1), nrow = 3)
t <- c(2, 2, 2) 
w <- c(2, 2, 2)

assigment <- function(x) {
  f <- sum(x * p)
  penalty1 <- sum(w)*(sum(t)-sum(w*x))
  penalty2 <- sum(w)*(1-sum(x))
  f - penalty1 - penalty2  
}  

GA <- ga(type = "binary", fitness = assigment, nBits = length(p),
       maxiter = 1000, run = 200, popSize = 20)
summary(GA)
Ushuaia81
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  • Have you seen these publications: [A Genetic Algorithm for the Generalised Assignment Problem](https://www.jstor.org/stable/pdf/3010707.pdf) and [A genetic algorithm for the generalised assignment problem](https://www.sciencedirect.com/science/article/pii/S0305054896000329)? A google search reveals many more optimised/specialised GA implementations. – Maurits Evers Sep 19 '18 at 04:53

1 Answers1

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It seems there are problems in your definition of the fitness function, i.e. the assigment() function.

  • x is a binary vector, and not a matrix as in the theory, so sum(x * p) is not doing what you likely expect (note that x has length 9 and p is a 3x3 matrix in your example);
  • the constrain on the sum of x_{ij} is not correctly taken into account by the penalty2 term;
  • the penalisations should act differently for penalty1 and penalty2, the first is an inequality (i.e. <=) while the second is a strict equality (i.e. =).
  • w is defined as a vector, but it should be a matrix of the same size as x
Luca Scrucca
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