Hybrid Biogeography-Based Optimization for Integer Programming

Algorithm 2

The BBO with the blended mutation for integer programming.

(1) Randomly initialize a population of 𝑛 solutions (habitats);

(2) while stop criterion is not satisfied do

(3)  for   𝑖=1   to   𝑛   do

(4)  Calculate 𝜆_𝑖, 𝜇_𝑖, and 𝜋_𝑖 according to 𝑓_𝑖;

(5)  for   𝑖=1   to   𝑛   do

(6)  Let 𝐻^′_𝑖=𝐻_𝑖;

(7)  for   𝑑=1   to   𝐷   do

(8)      if   rand()<𝜆_𝑖   then //migration

(9)     Select a habitat 𝐻_𝑗 with probability ∝𝜇_𝑗;

(10)      𝐻^′_𝑖,𝑑←𝐻_𝑗,𝑑;

(11)   if   𝑓(𝐻_𝑖)<𝑓(𝐻^′_𝑖)   then   𝐻_𝑖←𝐻^′_𝑖;

(12)  else

(13)    for   𝑑=1   to   𝐷   do

(14)     if   rand()<𝜋_𝑖   then //mutation

(15)      Let   𝛼=rand() and select a habitat 𝐻_𝑗 with probability ∝𝜇_𝑗;

(16)      𝐻_𝑖,𝑑←round(𝛼𝐻_𝑖,𝑑+(1−𝛼)𝐻_𝑗,𝑑);

(17)  Evaluate the fitness values of the habitats;

(18)  Update 𝑓_max,𝑃_max, and the best known solution;

(19)  return the best known solution.