A Memetic Lagrangian Heuristic for the 0-1 Multidimensional Knapsack Problem

Algorithm 1

Randomized constructive heuristic [13, 19].

R-CONS(0-1MKP instance)

{

 𝝀←𝟎;

 𝐼←{1,2,…,𝑛};

 do

  𝑘← random integer in [1,𝑚];

  for  𝑖∈𝐼

   𝛼_𝑖←(𝑣_𝑖−∑^𝑚_𝑗=1𝜆_𝑗𝑤_𝑗𝑖)/𝑤_𝑘𝑖;

  𝜆_𝑘←𝜆_𝑘+min_𝑖∈𝐼𝛼_𝑖;

  𝐼←𝐼⧵{argmin_𝑖∈𝐼𝛼_𝑖};

  (𝐱^∗,𝐛^∗)=LMMKP(𝝀);

 until  𝐱^∗ satisfies all the constraints;

 return  𝝀;

}