An Effective Heuristic-Based Approach for Partitioning

Algorithm 2

Genetic algorithm.

(1) Initialize the parameters of the genetic algorithm;

(2) Randomly generate the 𝑜𝑙𝑑_𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛;

(3) 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛∶=1;

(4) while (𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛≤𝑚𝑎𝑥_𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛) do

(5)  clear the 𝑛𝑒𝑤_𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛;

(6)  compute fitness of individuals in the 𝑜𝑙𝑑_𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛;

(7)  copy the individual with the highest fitness;

(8)  while (𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙_𝑛𝑢𝑚𝑏𝑒𝑟<𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛_𝑠𝑖𝑧𝑒) do

(9)   Select two parents from the 𝑜𝑙𝑑_𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛;

(10)   Perform the crossover to produce two offsprings;

(11)   Mutate each offspring based on 𝑚𝑢𝑡𝑎𝑡𝑖𝑜𝑛_𝑟𝑎𝑡𝑒;

(12)   Place the offspring to 𝑛𝑒𝑤_𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛;

(13)  end while

(14) Replace the 𝑜𝑙𝑑_𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 by the 𝑛𝑒𝑤_𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛;

(15) end while

(16) return  𝑛𝑒𝑤_𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 with the best fitness;