Theoretical Analysis of Jumping Gene Operations - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 71

Example4.3

Consider. L g = ;.based.on.

Definition.4.6,.we.can.obtain.the.following.distribution.matrices:

S =

{

*00 * **, * 01* **, * 10 * **, * 11* * *

}

.and. 2

ξ

0.78 0.24 0.24 0.1 0.1 0.64 0.04 0.18

0.64 0.14 0.14 0.04 0.16 0.66 0.06 0.16

( )

1

( )

2

A = , A = ,

0.64 0.14 0.14 0.04 0.16 0.66 0.06 0.16

0.54 0.08 0.08 0.02 0.18 0.64 0.04 0.1

..

0.1 0.04 0.64 0.18 0.02 0.08 0.08 0.54

0.16 0.06 0.66 0.16 0.04 0.14 0.14 0.64

( ) ( )

3 4

, .

A = A =

0.16 0.06 0.66 0.16 0.04 0.14 0.14 0.64

0.18 0.04 0.64 0.1 0.1 0.24 0.24 0.78

..

Let.the.state.at.time. t .be

P ( , ) t

ξ
ξ
ξ

0.1
0.2
0.3
0.4

1

P ( , ) t 2

Y t ( ) = = ,

P ( , ) t

3

P ( ξ , ) t 4

Using . Equation.(4.57) ,.one.can.then.obtain

( )

( )

1

P ξ , t + 1 = Y t A Y t ′ ( ) ( ) 0.1396, =

1

( )

( )

2

P ξ , t + 1 = Y t A Y t ′ ( ) ( ) 0.2164, =

2

( )

3

P ( ξ , t + 1) = Y t A Y t ′ ( ) ( ) 0.2764, =

3

( )

4

P ( ξ , t + 1) = Y t A Y t ′ ( ) ( ) 0.3676. =

4

Therefore,.the.state.at.time. t +.1.is

0.1396
0.2164
0.2764
0.3676

Y t + ( 1) = .