Write own evolutionary algorithm to solve an optimization problem.
1.) Data Generator:
- Write a piece of code which produces our ground truth data as y=f(x) where f (x)=−0.1 + 0.3x – 0.7x^2 + 0.1x^3 and x should be in the range [- 1,1]. Produce a plot of f(x).
2.) Fit Function:
- The function we’d like to fit is f(x ; α, β, γ, δ) = α + βx + γx^2 + δx^3. Write a piece of code which produces y_hat = f(x ; α, β, γ, δ). Produce a plot for all parameters equal to one.
3.) Mutation of Genes:
- A Gene in our algorithm is the set of parameters α, β, γ, δ, for f(x). Write a piece of code which randomly adds Gaussian noise to a set of parameters. Produce a histogram of α and one of β with 100 successive mutations each. Use as starting point α = 0.0 and β = 1.0. The Gaussian noise should have zero mean and a standard deviation of 0.1.
4.) Produce a Population:
- A population is a set of genes. Write a piece of code which randomly produces a population of size 100. The parameters should be Gauss distributed with mean zero and standard deviation one. Plot a histogram for β and γ.
5.) Evolving a Population:
- Evolution is performed by producing a new generation of genes -a.) Evaluate Genes: For each gene compute y_hat and compute the loss using RMSE with respect to y. -b.) Keep best: Sort the genes by loss and keep the best 10 -c.) Mutate: Mutate the 10 best genes until you have a total of 100 again.
6.) Fit the Function:
- Keep evolving your population for some time and monitor the loss of the best 10 genes as function of generations.
Run the Source/run_this.py file. The parameter passed can be changed in this file.
The output graphs for all tasks and the console output are stored in the Graphs_and_output/ folder
