Hybrid Biogeography-Based Optimization for Integer Programming

Algorithm 1

The original BBO algorithm.

(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)  for   𝑑=1   to   𝐷   do

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

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

(9)      𝐻_𝑖,𝑑←𝐻_𝑗,𝑑;

(10)  for   𝑖=1   to   𝑛   do

(11)     for   𝑑=1   to   𝐷   do

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

(13)      𝐻_𝑖,𝑑←𝑙_𝑑+rand()×(𝑢_𝑑−𝑙_𝑑);

(14)  Evaluate the fitness values of the habitats;

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

(16)  return the best known solution.