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

Algorithm 3

Framework of our memetic algorithm.

create an initial population of a fixed size 𝑃;

do

 for  𝑖←1  to  𝑃/2

  choose parent1 𝑖 and parent2 𝑖 from population;

  𝑜𝑓𝑓𝑠𝑝𝑟𝑖𝑛𝑔_𝑖 ← crossover(parent1 𝑖, parent2 𝑖);

  mutation(𝑜𝑓𝑓𝑠𝑝𝑟𝑖𝑛𝑔_𝑖);

  apply a local improvement heuristic to 𝑜𝑓𝑓𝑠𝑝𝑟𝑖𝑛𝑔_𝑖;

 replace(population, {𝑜𝑓𝑓𝑠𝑝𝑟𝑖𝑛𝑔_𝑖});

until (stopping condition)

return the best individual;