please , help me to solve this problem mathmatically not using matlab 1.Show the

Question

please , help me to solve this problem mathmatically not using matlab

1.Show the first 3 cycles of genetic evolution for optimizing the function y = x3 –27 in the interval

0 x 12. Use set P = { 1100, 1010, 1011, 0011} as the initial population.

2.Unlike the standard GA, suppose you devise a new type of algorithm, where in each cycle you randomly pick up M chromosomes and select good chromosomes from these by a selection function, and keep copies of the good schemata from the last cycle, the selected population size taking into consideration of the two types = N. Further, assume there is no crossover or mutation in your algorithm. Can you analyze the performance of your algorithm? Can you compare the performance with that of a standard GA?

3.Take different synthetic functions and optimize them using GA. What is the effect of changing crossover and mutation rate? Repeat the experiment for Rastringen’s function.

Explanation / Answer

1)

Genetic Evolution is to maximize the given function (y=x3-27), int the interval [0,12]. where x=0,1,2,3,4,5...12.

There are three rules.

Selection rules select the individuals, called parents, that contribute to the population at the next generation.

Crossover rules combine two parents to form children for the next generation.

Mutation rules apply random changes to individual parents to form children.

Now we decode the population, and calculate the fitness level of each individual with the help of the function y=x3-27.

1 1 0 0 -> 12 -> 15

1 0 1 0 -> 10 -> 3

1 0 1 1 -> 11 -> 6

0 0 1 1 -> 3 -> -18.

Now we select parent for crossover from the above data, which comes out to be 12 and 11. We can also apply random change in either function or vales to come out with healthier parents.

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2) Yes, we can always analyze the performance of the algoritm, though the evolution algorithms are some what difficult to analyze theoretically. A typicall approach will be to plot a graph of average performance over time. We can plot on a sample of 30 - 70 runs and campare the performance of both of the algorithm.

3) I find it beyond the scope of discussion . You can use matlab and it's library to experiment the optimization using GA and Rastringen's function.

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