In general, if a parameter that takes values in [xmin xma is represented by an m-bit binary string, then the conversion is given below b.2 10 x X=x mIn max mn 无法显示该图片。 2021/1/30 EIE426-AICV
2021/1/30 EIE426-AICV 16 ( ) ( ) min max min 1 0 1 0 1 1 0 2 min max 2 1 ' , , 2 ' by an - bit binary string, then the conversion is given below : In general, if a parameter that takes values in , is represente d x x x x x b b b b x m x x m m i i m i − − = + = = − = −
Generation of initial population A set of N 22-bit binary strings can be randomly generated as the initial population 2021/1/30 EIE426-AICV
2021/1/30 EIE426-AICV 17 ◼ Generation of initial population A set of N 22-bit binary strings can be randomly generated as the initial population
Fitness calculation Since f(x)>0 in the interval, We can directly use f(x) as a fitness function f(s)=f( e.g-, S1=<1000101110110101000111>,(s1)=2586345 2=<000000111000000100003,fS2)=1.078878 3=<1110000011110017,(s3)=3250650 2021/1/30 EIE426-AICV 18
2021/1/30 EIE426-AICV 18 ◼ Fitness calculation Since f(x) > 0 in the interval, we can directly use f(x) as a fitness function: f(s) = f(x) e.g., s1 = <1000101110110101000111>, f(s1 )=2.586345 s2 = <0000001110000000010000>, f(s2 )=1.078878 s3 = <1110000000111111000101>, f(s3 )= 3.250650
Genetic operation (1) Selection: based on the fitness of individuals e.g., roulette wheel selection(fitness proportionate selection) (2) Crossover(with a probability p e. g S2=<00000011100000010000,(S2)=1.078878 S3=<111000000011100101,f(S3)=3250650 After the crossover operation 2=<000000000011111000101>,f(S2)=1940865 s3=<11100011100000000>,f(S3)=3459245 2021/1/30 EIE426-AICV
2021/1/30 EIE426-AICV 19 ◼ Genetic operation (1) Selection: based on the fitness of individuals e.g., roulette wheel selection (fitness proportionate selection) (2) Crossover (with a probability pc ) e.g., s2 = <00000 | 01110000000010000>, f(s2 )=1.078878 s3 = <11100 | 00000111111000101>, f(s3 )= 3.250650 After the crossover operation: s’2 = <00000 | 00000111111000101>, f(s’2 )=1.940865 s’3 = <11100 | 01110000000010000 >, f(s’3 )= 3.459245
(3)Mutation(with a probability pm) e. g i3=<111000001100101 f(S3)=3250650 After the mutation operation 3=<1110100000111100101> f(s3=0917743 or i3=<111000001111001017 S”2=<1110000001111111000101> 3 f(S3)=3343555 2021/1/30 EIE426-AICV
2021/1/30 EIE426-AICV 20 (3) Mutation (with a probability pm) e.g., s3 = <1110000000111111000101> f(s3 )= 3.250650 After the mutation operation: s’3 = <1110100000111111000101 > f(s’3 )= 0.917743 or s3 = <1110000000111111000101> s”3 = <1110000001111111000101 > f(s”3 )= 3.343555