I need help solving this problem.

The following table is provided by a laboratory, consisting of a serial of samples recorded during the

bio-chemical refining process

x f(x)

0 0

15 0.221456693

30 0.415231299

45 0.581323819

60 0.719734252

75 0.830462598

90 0.913508858

105 0.968873031

120 0.996555118

128 1

135 0.996555118

150 0.968873031

165 0.913508858

180 0.830462598

195 0.719734252

210 0.581323819

225 0.415231299

240 0.221456693

255 0

We will use this table to model a polynomial that interpolates f(x) at the given point

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This polynomial will be used to calculate the fitness of the individual that we will randomly determine.

Write a java program that:

1. Calculates the interpolation polynomial that we will denote P(x).

The values from the table above are provided by Polynomial.txt file that your Java program

will open and read through a dialog box.

2. Initializes the population by using a random number generator (maximum of 16 individuals).

This initialization should be done by using the binary string (Don’t use native binary, use

rather Gray representation) of maximum 8 digits

3. Transforms the gray representation of each individual into the decimal coding

4. Calculates the fitness of each individual

a. Calculate the frequency of each individual

b. Normalize the frequency of each individual

c. Calculate the cumulative frequency of each individual

d. Generate 16 random numbers to determine the destiny of each individual

5. Reproduces new population and pairs up the individuals based on their sequence of

apparition in 4.d (to be selected).

6. Applies crossover as follow:

a. For each pair, a random Boolean will determine if the pair is subject to crossover or

not (all the pairs should be affected).

b. If yes, two random numbers between 0 to 7 will be generated to each individual to

determine the range where crossover will be applied (First number = start, second

number = end).

7. Applies randomly one mutation on each individual (jth bit where j = number of bits to “1” in

this individual. E.g. for 10011000, bit 3 should be muted)

8. Produce the result of the first generation

9. Runs recursively until produce the result of the 5th generations

10. Provide your conclusion

Bonus : Modify your program and run it until you get all the individual with fitness greater than

0.95. How many generations were needed to get this output?

This is what I need actually

Can you help me with the opening Java statement. I do not want you to do my homework for me. But I just need a lead how to start cos I have no clue what the opening statement is. With that I can do the rest.