Application of Artificial Bee Colony Algorithm to Portfolio Adjustment Problem with Transaction Costs

Algorithm 1

Standard ABC algorithm.

(1) Initialize the population of solutions 𝑥_𝑖,𝑗, 𝑖=1,…,SN, 𝑗=1,…,𝐷

(2) Evaluate the population

(3) cycle = 1

(4) Repeat

(5) Produce new solutions 𝑣_𝑖,𝑗 for the employed bees by using (24) and evaluate them

(6)  Apply the greedy selection process for the employed bees

(7)  Calculate the probability values 𝑃_𝑖,𝑗 for the solutions 𝑥_𝑖,𝑗 by (25)

(8)  Produce the new solutions 𝑣_𝑖,𝑗 for the onlookers from the solutions 𝑥_𝑖,𝑗 selected depending on 𝑃_𝑖,𝑗 and evaluate them

(9)  Apply the greedy selection process for the onlooker bees

(10)  Determine the abandoned solution for the scout, if exists, and replace it with a new

  randomly produced solution 𝑥_𝑖,𝑗 by (26)

(11)   Memorize the best solution achieved so far

(12)  cycle = cycle + 1

(13) Until cycle = MCN