Tournament Selection Based Artificial Bee Colony Algorithm with Elitist Strategy - Technologies and Applications of Artificial Intelligence - page 390

, TSABC can adjust selection pressure flexibly under
different optimization problems. On the other hand, RWS strategy has to be converted
when solving minimum optimization problems. According to Eq. (3), the fitness value
fit i should be changed to its reciprocal or be switched within other functions which
can make the solution with smaller value has more chances to be chosen. On the
contrary, TS strategy is convenient and flexible for both minimum and maximum
problems.

With the parameter ʻ

4 Experimental Studies

In order to evaluate the performance of TSABC algorithm, thirteen benchmark
functions are used herein. These functions are described in Table 1. Each of them is
30-dimension function. to are unimodal functions while to
are multimodal functions.

Table 1. Benchmark functions

Accepted
value

Benchmark functions Dimension Domain Min

n

∑

()

2

fx = x

30 [-100.100] 0 1.00E-06

1 i

i = 1

n n

()

∑ ∏

fx = x + x 30 [-10,10] 0 1.00E-06

2 i i

i = 1 i = 1

∑∑

2

⊛ ⊞

n i

()

fx = x

30 [-100,100] 0 500

⊜ ⊝ ⊠

3 j

i = 1 j = 1

()

{ }

fx = max x ,1 ≤ in ≤

30 [-100,100] 0 0.01

4 i

i

n − 1

⊡

( )

2

⊤

()

∑

( )

2

2

fx = 100 x − x + x − 1 30 [-30,30] 0 0.01

⊢ ⊥

5

⊣

i + 1 i i

⊦

i = 1

2

n

∑ ( )

()

fx = x + 0.5

30 [-100,100] 0 0

⊢ ⊥

⊣ ⊦ 6 i

i = 1

n

[-
1.28,1.28]

()

∑

[ )

f x = ix

4

+ random 0,1 30 0 0.01

7 i

i = 1

n

( )

()

∑

fx

=−

x sin x

30 [-500,500] -12569.5 -12569

8 i i

i 1

n

[-
5.12,5.12]

()

∑

( )

fx = ⊡ x

2

− 10 cos 2 ˀ x + 10 ⊤ 30 0 1.00E-06

⊣ ⊦

9 i i

i = 1

⊛ ⊞ ⊛

n n

1 1 ⊞

∑ ∑

()

f x =− 20 exp − 0.2 x

2

− exp cos 2 ˀ x + 20 + e

⊜ ⊟ ⊜

30 [-32,32] 0 1.00E-06

⊟

⊜ ⊟

10 i i

n n

⊝ ⊠

⊝ ⊠

i = 1 i = 1

1

n n

⊛⊞ x

()

∑ ∏

2

f x = x − cos +

⊜ ⊝⊠

i

1

30 [-600,600] 0 1.00E-06

11 i

4000

i i = 1 i = 1

ˀ

⊧

n − 1

⊫

n

() ( )

∑

( )

2

( ) ( )

2

∑

( )

2

⊡

2

⊤

x = 10sin ˀ y + y − 1 1 + 10 sin ˀ y + y − 1 + u x ,10,100, 4

f

⊨ ⊬

⊣ ⊦

12 i i i + 1 n i

⊩ ⊭

i = 1 i = 1

⊧

( )

m

kx a − , x > a ,

30 [-50,50] 0 1.00E-06

i i

⊪ ⊪

1

( ) ( )

y =+ 1 x + 1 , u x , a k m , , = 0, a x a

kxa x

−≤ ≤ ,

⊨
⊪

i i i i

4

( )

m

−− , <− a .

⊪ ⊩ i i

n − 1 n

⊧ ⊫

( )

∑

( )

2

( ) ( )

2

( )

∑

( )

2

⊡

2

⊤ ⊡

2

⊤

f = 0.1 sin 3 ˀ x + x − 1 1 sin 3 + ˀ x + x − 1 1 sin + 2 ˀ x + u x ,5,100,4

30 [-50,50] 0 1.00E-06

⊨ ⊬

⊣ ⊦ ⊣ ⊦

13 i i i + 1 n n i

⊩ ⊭

i = 1 i = 1