I have used Genetic Algorithms for solving Equations. This is done using python.

• no. of chromosome in pop. is 6
• c[1] = [a:b:c:d] = [12;05;23;08]
• upto c[6] = [a:b:c:d] = [20;5;17;1]

• f_ob[1] = abs((12 + 25 + 233 +4*8) - 30)
• and so on f_ob[6] = abs((20 + 52 + 173 + 4*1) -30)

• the fittest chromosome having higher prob. will be selected for next gen.
• fitness[1] = 1/(1+ f_ob[1]) = 1/94 = 0.0106 and so on upto fitness[6] after that add them
• total = fitness[1] + ... + fitness[6] = 0.0845

• p[1] = 0.0106/0.0845 = 0.1254 and so on p[6]
• p[4] has the highest fitness to get selected for the next gen.

• roulette wheel take scumulative prob. value for individual chromosomes

• c[0] = 0

• c[1] = 0.1254

• c[2] = p[1]+p[2]= 0.2710

• c[3] = 0.4118

• c[4] = 0.6639

• c[5] = 0.7882

• c[6] = p[1] + ...p[6] = 1.0

• R[1] = 0.201

• R[2] = 0.284

• R[3] = 0.099

• R[4] = 0.822

• R[5] = 0.398

• R[6] = 0.501

• if R[1] lies bet. c[1] and c[2] then select chromosome[2] as a chromosome in the new pop for the next gen. as it is a higher value.

• new_chromosome[1] = chromosome[2]

• new_chromosome[2] = chromosome[3]

• new_chromosome[3] = chromosome[1]

• new_chromosome[4] = chromosome[6]

• new_chromosome[5] = chromosome[3]

• new_chromosome[6] = chromosome[4]

• chromosomes in the pop. thus become

• chromosome[1] = [2;21;18;3]

• chromosome[2] = [10;4;13;14]

• chromosome[3] = [12;5;23;8]

• chromosome[4] = [20;5;17;1]

• chromosome[5] = [10;4;13;14]

• chromosome[6] = [20;1;10;6]

• chromosome is controlled using crossover rate(pc = 0.25)

• begin

• k = 0

• while(k<pop):

• R[k] = random(0-1)

• if(R[k] < pc):

• select chromosome[k] as parent

• end

• k +=1

• end

• end

• accordingly for R[1],R[4],R[5] parents are chromosome[1],chromosome[4] chromosome[5] selected.

• chromosome[1] = chromosome[1] >< chromosome[4]

• chromosome[4] = chromosome[4] >< chromosome[5]

• chromosome[5] = chromosome[5] >< chromosome[1]

• c[1] = 1
• c[2] = 1
• c[3] = 2

we selected the random values between 1 to 3

• chromosome[1] = chromosome[1] ><chromosome[4] = [2;21;18;3]><[20;5;17;1] = [2;5;17;1]

• chromosome[4] = chromosome[4] ><chromosome[5] = [20;5;17;1]><[10;4;13;14] = [20;4;13;14]

• chromosome[5] = chromosome[5] ><chromosome[1] = [10;4;13;14]><[2;21;18;3] = [10;4;18;3]

• hence the new chromosome are:

• chromosome[1] = [2;5;17;1]

• chromosome[2] = [10;4;13;14]

• chromosome[3] = [12;5;23;8]

• chromosome[4] = [20;4;13;14]

• chromosome[5] = [10;4;18;3]

• chromosome[6] = [20;1;10;6]

a new value. we must compute the total length of gen. total_gen = no_of_gene_in_chromosome * no. of pop. = 4*6 = 24

• mutation process is generating a random no. bet. 1 to 24 if generated random no. is smaller than mutation rate(pm) variable

• suppose we define pm(mutation_rate) 10% . it is expected that 10% (0.1) of total_genes in the pop. that will be mutated: no. of mutations = 0.1*24 = 2.4 = 2(apprx.)

• suppose generation of random number yield 12 and 18 then the chromosome which have mutation are chromosome number 3 gen number 4 and chromosome 5 gen. number 2. the value of mutated point is replaced by a random number between 0-30 .

• suppose generated random number are 2 and 5 then chromosome composition after mutation are :

• chromosome[1] = [2;5;17;1]

• chromosome[2] = [10;4;13;14]

• chromosome[3] = [12;5;18;3]

• chromosome[4] = [20;4;13;14]

• chromosome[5] = [10;5;18;3]

• chromosome[6] = [20;1;10;6]

• these new chromosomes will undergo chromosomes such as evaluation selction,crossover,mutation and at the end it produce new generation of chromosomes for the next iteration. this process will be repeated until a predetermined no. of gen. after running 50 generations best chromosome is obt. a = 7,b = 5,c = 3 and d = 1.

Thanks for reading.