A Comparative Study of Improved Artificial Bee Colony Algorithms Applied to Multilevel Image Thresholding

Algorithm 1

(IABC/best/1 algorithm).

01 Initialize the population: 𝑛 is the number of the threshold. SN is the population size.

    𝑥_𝑖,𝑗=𝑥_min,𝑗+rand(0,1)(𝑥_max,𝑗−𝑥_min,𝑗), 𝑖=1,2,…,𝑆𝑁, 𝑗=1,2,…,𝑛.

02 Evaluate the population: 𝑦 = Evaluate(𝑥) by Otsu’s function, (4)

03 generation = 1, trial_𝑖=0, limit = 50, NFC = SN,

04 Repeat

05 /* Employed Bees Phase */

06  For 𝑖 = 1 to SN

07     Randomly choose 𝑥_𝑟1≠𝑥_𝑖, 𝑥_𝑟2≠𝑥_𝑖, 𝑥_𝑟1≠𝑥_𝑟2 from current population

08     Randomly choose 𝑗 from {1,2,…,𝑛}

09     𝑣_𝑖,𝑗=𝑥_best,𝑗+𝜙_𝑖,𝑗(𝑥_𝑖,𝑗−𝑥_𝑟1,𝑗), (15)

10      𝑦_new = Evaluate(𝑣_𝑖) by Otsu’s function, (4), NFC = NFC + 1,

11      If 𝑦_new>𝑦_𝑖

12       𝑥_𝑖=𝑣_𝑖, 𝑦_𝑖=𝑦_new, trial_𝑖=0

13      Else

14       trial_𝑖=trial_𝑖+1

15      End If

16   End For

17   Calculate the probability values 𝑝_𝑖 by (12)

18  /* Onlooker Bees Phase */

19  𝑖=1

20  For 𝑡=1 to SN

21   If rand(0,1)<𝑝_𝑖 then

22    Randomly choose 𝑥_𝑟1≠𝑥_𝑖, 𝑥_𝑟2≠𝑥_𝑖, 𝑥_𝑟1≠𝑥_𝑟2 from current population

23    Randomly choose 𝑗 from {1,2,…,𝑛}

24    𝑣_𝑖,𝑗=𝑥_best,𝑗+𝜙_𝑖,𝑗(𝑥_𝑖,𝑗−𝑥_𝑟1,𝑗), (15)

25     𝑦_new = Evaluate(𝑣_𝑖) by (4), NFC = NFC + 1,

26    If 𝑦_new>𝑦_𝑖

27      𝑥_𝑖=𝑣_𝑖,𝑦_𝑖=𝑦_new, trial_𝑖=0

28    Else

29        trial_𝑖=trial_𝑖+1

30    End If

31  End If

32   𝑖=𝑖+1

33   If 𝑖>𝑆𝑁

34   𝑖=1

35   End If

36 End For

37   /* Scout Bees Phase */

38 For 𝑖 = 1 to SN

39  If trial_𝑖>limit

40    𝑥_𝑖,𝑗=𝑥_min,𝑗+rand(0,1)(𝑥_max,𝑗−𝑥_min,𝑗), 𝑗=1,2,…,𝑛, trial_𝑖=0

41    𝑦_𝑖 = Evaluate(𝑥_𝑖) by (4), NFC = NFC + 1,

42  End If

43 End For

44 Memorize the best solution achieved so far

45 generation = generation + 1

46 Until (generation = Maximum Generation)